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Mixed Integer Quadratic Program trajectory generation for a quadrotor with a cable-suspended payload

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Abstract

In this paper, we present a trajectory planning method to navigate a quadrotor with a cable-suspended payload through known obstacle-filled environments. We model the system as a hybrid dynamical system and formulate the trajectory generation problem as a Mixed Integer Quadratic Program (MIQP). Specifically, we address two novel challenges. First, we plan for a multi-body system, and obstacle avoidance must be guaranteed for the quadrotor, load, and the cable. Second, our method accommodates transitions between subsystems of the hybrid dynamical system, allowing for maneuvers that would otherwise be infeasible if the cable were constrained to remain taut. Numerical and experimental results validate the proposed approach for the full hybrid system.

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... Endowed with the above advantages, several studies have been carried out on the cable-suspended payload transportation to achieve safe and efficient transportation [15][16][17]. By regarding a quadrotor with a suspended load as a hybrid system, a trajectory planning algorithm was proposed [18]. But the exact orders for hybrid subsystem transitions were assumed to be known as a priori. ...
... time, and its detailed form is given aṡ 3 ). (23) Together with (18), (20), and (22), E k (t) can be written as ...
... Consequently, the storage function after shaping is obtained from (18) and (44) as follows: ...
Article
As an ideal method for heavy or large payload delivery, collaborative aerial transportation with multiple unmanned aerial vehicles (UAVs) increases the load capacity. However, during the transportation process, collaborative transportation systems are always subject to environmental disturbances and system uncertainties, which poses a great challenge to safe and efficient payload transportation. Existing works without payload angle information in control inputs cannot exhibit satisfactory antiswing performance. To handle the aforementioned issues, this paper proposes a novel control strategy for rapid UAV positioning and payload swing elimination. Specifically, the dynamic model of the collaborative transportation system is described based on a redundant dynamic expression. Then, an artificially constructed UAV-payload unified signal is introduced to enhance the state coupling between the UAV positions and payload swing angles. Based on the newly defined signal, the energy storage function is constructed and the adaptive control law is derived. Additionally, the detailed Lyapunov analysis is provided to prove the system stability and convergence. It is worth noting that the difficulty of the stability analysis is greatly reduced with the help of the established redundant dynamic description. To validate the performance of the proposed control strategy, experimental studies have been carried out in different scenarios. Hardware experimental results show that the proposed method can effectively suppress load swing while ensuring rapid UAV positioning, even with external disturbances.
... The aforementioned works motivate the challenge addressed in this paper, that is, to implement aggressive load position and swing maneuvers on a quadrotor-slung-load system, through optimal trajectory generation with fast computation speed, and accurate trajectory tracking. In summary of the literature, the existing works either require significant computation time (Tang & Kumar 2015;Foehn et al. 2017), or do not consider optimality for the system dynamics (Son et al. 2020;de Crousaz et al. 2014;Guo et al. 2019), or are not fitted for direct implementation (Zeng et al. 2019) due to their mechanical complexity. ...
... Existing works, e.g. Tang & Kumar (2015) and Chen et al. (2015), solve this minimization problem by decoupling p L d into three dimensions and applying the optimization separately to each of them. However, this sacrifices the possibility of building relationship among the three dimensions of p L d or their time derivatives. ...
... Our method shows advantages on the computation time over the existing works that study aggressive load trajectory generation while considering optimal system dynamics. In comparable scenarios, the method in Tang & Kumar (2015) takes more than 3000 s to generate a trajectory for a quadrotor-slungload system to go through a window, the method in Foehn et al. (2017) takes on average around 30 s for generating loadthrowing and simple waypoints navigation trajectories. ...
Article
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The ability for a quadrotor with a slung load to perform agile and accurate maneuvers expands the variety of scenarios where load transportation can be applied and enhances its efficiency. Due to the complexity of the system dynamics, slung-load transportation remains a challenging problem, which also causes trajectory generation a time-consuming task. We propose a framework to efficiently generate aggressive load-swing trajectories. Trajectory generation for the load aims to minimize the fifth order time derivative of the load position which, indirectly, minimizes the quadrotor angular velocity actuation. Aggressive load-swing trajectories are obtained by having the constraints for load cable direction embedded into the trajectory generation via constraints on the load acceleration. The trajectory generation, together with an accurate trajectory tracking controller, allows the aggressive maneuvers to be easily performed on the quadrotor with a slung-load. Simulation and experimental results of three dimensional aggressive maneuvers are presented to validate the proposed trajectory generation methodology, including the quadrotor slung-load traversing a window by tilting the cable, and also going through an environment with obstacles that must avoided.
... Studies in the first category are concerned with designing controllers for tracking desired payload trajectories [5], [7], [8], [9], and [17]. On the other hand, studies in the second category are trajectory planning studies to optimize a particular objective function [3], [6], [15], [18], and [19]. Our study belongs to the second category. ...
... Unlike [9], the full 3D dynamic model is preferred over the flat model since we imposed constraints on the quadrotor's location and attitude. Additionally, different from previous studies [5], [6], and [18], we do trajectory planning for both the load and the quadrotor to avoid obstacles. The state vector is; 18 where is the position vector of load and is the unit vector from the quadrotor to load in the inertial frame. ...
... Additionally, different from previous studies [5], [6], and [18], we do trajectory planning for both the load and the quadrotor to avoid obstacles. The state vector is; 18 where is the position vector of load and is the unit vector from the quadrotor to load in the inertial frame. The input vector is = [ ] where is the lifting force acting on the system and , , are roll, pitch, and yaw moments, respectively (see Figure 2). ...
Article
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In this article, multi-objective trajectory planning has been carried out for a quadrotor carrying a slung load. The goal is to obtain non-dominated solutions for path length, mission duration, and dissipated energy cost functions. These costs are optimized by imposing constraints on the slung-load quadrotor system’s endpoints, borders, obstacles, and dynamical equations. The dynamic model of a slung-load quadrotor system is used in the Euler-Lagrange formulation. Although the differential flatness feature is mostly used in this system’s trajectory planning, a fully dynamic model has been used in our study. A new multi-objective Genetic Algorithm has been developed to solve path planning, aiming to optimize trajectory length, mission time, and energy consumed during the mission. The solution process has a three-phase algorithm: Phase-1 is about randomly generating waypoints, Phase-2 is about constructing the initial non-dominated pool, and the final phase, Phase-3, is obtaining the solution. In addition to conventional genetic operators, simple genetic operators are proposed to improve the trajectories locally. Pareto Fronts have been obtained corresponding to exciting scenarios. The method has been tested, and results have been presented at the end. A comparison of the solutions obtained with MOGA operators and MOPSO over hypervolume values is also presented.
... Such advantages are crucial in various military and civil applications such as surveillance, fire fighting, environmental monitoring to name a few [4], [5]. Most recently, global research is more and more interested in smart transport systems, where quadrotors are used in package delivery, construction works, disaster relief operation as a mode of smart aerial transportation [6], [7]. ...
... Despite the fact that carrying payload via a suspended cable is one of the most common ways for a quadrotor [6]- [8], it may not be optimal/desirable in indoor scenarios, especially in disaster sites, where the quadrotor might need to manoeuvre through constrained altitudes. In such scenarios, rigidly attaching a payload would be a preferred mode, which also provides the flexibility to autonomously pickup and drop the payload. ...
... IV. STABILITY ANALYSIS OF THE PROPOSED CONTROLLER Theorem 1: Under Properties 1-3 and Assumptions 1-2, the trajectories of the closed-loop systems (6) and (15) using the control laws (9) and (18) along with the adaptive laws (10) and (19) are Uniformly Ultimately Bounded (UUB). ...
... In [13] and [14], a motion model of a quadrotor UAV with the suspended payload was derived as a differentially flat hybrid system, which includes the dynamic model of nonzero and zero cable tension. A large swing trajectory including minimal swing in [13] was designed on the basis of the flatness property. ...
... A large swing trajectory including minimal swing in [13] was designed on the basis of the flatness property. In addition, the trajectory can be utilized for multiple tasks, obstacle avoidance, and payload release, using a mixed-integer quadratic program (MIQP) [14]. In addition, cooperative transportation by multiagents was studied, and numerical simulation validated the stability of the proposed geometric control [15]- [17]. ...
... The minimum snap trajectory minimizes a cost defined by the quadratic form of the UAV snap [23]. In addition, the motion constraints in (3a) should be considered to define the cost, unlike in the proposals of [13], [14], and [23]. Thus, the cost function J x , for the x-directional trajectory generation, can be derived using the Lagrange multiplier λ as (10) The Euler-Lagrange equations are derived in (11a) and (11b) to minimize J x . ...
Article
This brief presents a new trajectory generation and an effective antisway tracking control (ATC) method for a mul-tirotor unmanned aerial vehicle (UAV) with a cable-suspended payload. The UAV transportation system has been developed due to its ability to easily deliver small packages. However, existing methods lack research on transient response accompanied by aggressive rotation of the UAV and inevitable payload swing. Unfortunately, these motions become intensified when the input is dynamically unfeasible, such as step-like changes. Trajectory generation to minimize the swing motion provides a dynamically feasible trajectory between waypoints. The proposed method provides fast settling time with remarkably little payload swing. In addition, the ATC is developed on the basis of linear-quadratic (LQ) control to deal with motion coupling issues. A payload state estimator is also designed that requires no sensor for the payload. Finally, the performance of the proposed method is verified by numerical simulation and experimental results that show the possibility of safe and fast transportation with a minimal swing. Index Terms-Antisway control, antisway trajectory generation , linear quadratic optimal tracking, suspended load. NOMENCLATURE E Inertial frame: {x E , y E , z E }. B Unmanned aerial vehicle (UAV) body-fixed frame: {x B , y B , z B }. P Pendulum pivot fixed frame: {x P , y P , z P }. T Tension of the pendulum cable with respect to P. R η Rotation matrix of UAV from B to E. I U Moment of inertia tensor of the UAV: diag([I xx I yy I zz ]). m, m L Mass of the UAV and mass of the payload. r Length of the pendulum cable. p U Position of the UAV with respect to E: [x, y, z] T. p L Position of the load with respect to P: [x L , y L , z L ] T .
... Algorithms to achieve this have included, amongst others, optimisation and Reinforcement Learning (RL) techniques. In the former, optimal trajectories are computed as a cost minimisation problem subject to the task objectives and the MAVP model which are then encoded as full state evolutions (Foehn et al. 2017;Palunko et al. 2012a) or a reduced dimension state using differential-flatness (Sreenath et al. 2013;Tang and Kumar 2015). In RL, as used in Palunko et al. (2013), Faust et al. (2013) and Faust et al. (2017), feasible action policies (the trajectory) are generated that enforce the MAVP model on state transitions. ...
... The iLQG's iterative algorithm is exploited to generate locally optimal linear feedback controls to achieve the realtime, closed-loop performance. In a similar fashion to Tang and Kumar (2015), De Crousaz et al. (2014) apply iLQG to demonstrate impressive manoeuvres which included the flight through a narrow opening. However, the study by De Crousaz et al. (2014) did not consider planning in a dynamic environment. ...
... Two complex agile manoeuvres are performed; (i) the MAVP must fly over a high bar at 0.95 m with a virtual ceiling of 1.8 m, and (ii) similar to De Crousaz et al. (2014) and Tang and Kumar (2015) , the MAVP must fly through a narrow 0.7 × 0.7 m opening. For both manoeuvres, three passes over/through the obstacle are performed in a rapid, successive and bidirectional manner. ...
Article
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Micro Aerial Vehicles (MAVs) can be used for aerial transportation in remote and urban spaces where portability can be exploited to reach previously inaccessible and inhospitable spaces. Current approaches for path planning of MAV swung payload system either compute conservative minimal-swing trajectories or pre-generate agile collision-free trajectories. However, these approaches have failed to address the prospect of online re-planning in uncertain and dynamic environments, which is a prerequisite for real-world deployability. This paper describes an online method for agile and closed-loop local trajectory planning and control that relies on Non-Linear Model Predictive Control and that addresses the mentioned limitations of contemporary approaches. We integrate the controller in a full system framework, and demonstrate the algorithm’s effectiveness in simulation and in experimental studies. Results show the scalability and adaptability of our method to various dynamic setups with repeatable performance over several complex tasks that include flying through a narrow opening and avoiding moving humans.
... At the same time, the swing angle of the system is not controlled, and the coupling degree is increased. The literature [11] presents a path planning algorithm for quadrotors that models the payload delivered by a hanging rope as a hybrid dynamical system. The experimental results show that this approach is effective in generating an aggressive hybrid and avoidance maneuver trajectory, including state transitions. ...
... By combing Equations (3), (11) and (16), the eight-degree-of-freedom mathematical model of a quadrotor carrying a load including attitude, position and swing angle can be yielded: ...
Article
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This paper assumes that considering the unknown and time-varying nature of different strong and weak wind field disturbances and considering the nonlinear, under-driven, strongly coupled quadrotor carrying, a load is disturbed by the complex and variable wind field and unmodeled parts when flying in the real external environment, which will reduce the control effect of the nonlinear controller and make the vehicle fail to affect the flight effect. In order to ensure that the quadrotor carrying a load can carry supplies in the harsh environment for stable trajectory tracking, a neural network adaptive control algorithm is introduced in the article. The neural network algorithm has the role of online dynamic approximation, the compensation of arbitrary external disturbance and the compensation of external disturbance. Its structure is simple and low computation. In the article, the Lyapunov method is used to design the adaptive weight and estimate the weight of the online neural network, and the stability of the system is proved. Finally, the comparison of three algorithms verified by simulation proves that the above interference problem can be solved effectively by the proposed algorithm.
... At last, the control inputs and attitudes can be determined with the use of the RUAV position and yaw angle , since ( , ) is a flat output for the corresponding RUAV [28]. ■ Let ( ) ∶ [0, ] → R 3 present the trajectory of the th RUAV from the initial formation to the new formation of , where is the duration of the maneuvering, ( ) can be obtained by solving the optimization problem [28][29][30] as: ...
... where 0 ∈ R 3 and 0 ∈ R 3 denote the initial position and desired position of the payload. With (29) and (30), we could get ...
Article
The collaborative aerial transportation (CAT) of multiple rotorcraft unmanned aerial vehicles (RUAVs) collaboratively carrying a cable-suspended payload provides a feasible way to ship a heavy load by multiple small-sized RUAVs. Usually, the formation of the RUAVs for CAT has to be pre-designed according to the tension assignment on each RUAV, and maintained via control during flight. However, in case the tension assignment needs to be adjusted during flight, the formation of the RUAVs needs to be re-allocated accordingly. This situation may occur due to the changing circumstances, such as fuel condition, maximum payload capability, payload re-assignment, etc. In this paper, we propose an optimizing scheme for the re-allocation of two-RUAV CAT (TR-CAT) system to meet the commanded tension adjustment. A novel optimization structure is formulated with respect to the adjustable tension requirement, while multiple constraints, including task, safety, as well as dynamic constraints, are provided for the optimization formulation. The differential flatness of the TR-CAT system is also analyzed and proved. Besides the simulation validations, indoor and outdoor experiments were conducted on a real CAT system to demonstrate the efficacy of the proposed scheme.
... As we introduce a leash for the robot to guide the human, the system becomes hybrid as the leash could be taut or slack. For hybrid modes on leash tension, previous works about aerial systems formulate the path planning either through a special mechanical design [18], mixed-integer programming [19] or collocation-based optimization with complementarity constraints [20], [21]. However, physical human-robot interaction is not considered in [14], [19]- [21], and hybrid path planning for pHRI for applications using mobile robots still remains an open problem. ...
... For hybrid modes on leash tension, previous works about aerial systems formulate the path planning either through a special mechanical design [18], mixed-integer programming [19] or collocation-based optimization with complementarity constraints [20], [21]. However, physical human-robot interaction is not considered in [14], [19]- [21], and hybrid path planning for pHRI for applications using mobile robots still remains an open problem. ...
... Landry et al. (2016) describe aggressive flight of micro quadcopters through obstacle-dense environments. Flying with a cablesuspended payload is presented by Tang and Kumar (2015), Foehn et al. (2017), and Guo and Leang (2020). In the work by Neunert et al. (2016), nonlinear model-predictive control (NMPC) was used for flying through gaps. ...
... In the work by Neunert et al. (2016), nonlinear model-predictive control (NMPC) was used for flying through gaps. In the work described by Mellinger et al. (2012), Tang and Kumar (2015), and Neunert et al. (2016), the pose of the gaps were assumed to be known. In Liu et al. (2018), a hierarchical graph-search-based algorithm was proposed to find a dynamically-feasible trajectory for a quadcopter, where they assumed that a depth sensor measures the pose of the gap. ...
Article
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This article focuses on enabling an aerial robot to fly through multiple openings at high speed using image-based estimation, planning, and control. State-of-the-art approaches assume that the robot’s global translational variables (e.g., position and velocity) can either be measured directly with external localization sensors or estimated onboard. Unfortunately, estimating the translational variables may be impractical because modeling errors and sensor noise can lead to poor performance. Furthermore, monocular-camera-based pose estimation techniques typically require a model of the gap (window) in order to handle the unknown scale. Herein, a new scheme for image-based estimation, aggressive-maneuvering trajectory generation, and motion control is developed for multi-rotor aerial robots. The approach described does not rely on measurement of the translational variables and does not require the model of the gap or window. First, the robot dynamics are expressed in terms of the image features that are invariant to rotation (invariant features). This step decouples the robot’s attitude and keeps the invariant features in the flat output space of the differentially flat system. Second, an optimal trajectory is efficiently generated in real time to obtain the dynamically-feasible trajectory for the invariant features. Finally, a controller is designed to enable real-time, image-based tracking of the trajectory. The performance of the estimation, planning, and control scheme is validated in simulations and through 80 successful experimental trials. Results show the ability to successfully fly through two narrow openings, where the estimation and planning computation and motion control from one opening to the next are performed in real time on the robot.
... Assumption 2 ([6], [25], [26]): The desired position p d x d y d z d T and yaw trajectories ψ d are designed such that they are smooth and bounded. Remark 2 (Desired roll and pitch): As standard in literature [25], the desired roll (φ d ) and pitch (θ d ) angle trajectories are computed using τ p and ψ d . ...
Conference Paper
Quadrotors are becoming more and more essential for applications such as payload delivery, inspection and search-and-rescue. Such operations pose considerable control challenges, especially when various (a priori unbounded) state-dependent unknown dynamics arises from payload variations, aerodynamic effects and from reaction forces while operating close to the ground or in a confined space. However, existing adaptive control strategies for quadrotors cannot handle unknown state-dependent uncertainties. We address such unsolved control challenge in this work via a novel adaptive method for artificial time delay control,where unknown dynamics is robustly compensated by using input and state measurements collected at immediate past time instant (i.e., artificially delayed). Closed-loop stability is established via Lyapunov theory. The effectiveness of this controller is validated using experimental results.
... Over the past few years, unmanned aerial vehicles (UAVs), in particular quadrotors, have proven useful for many tasks, including multiagent missions [1][2][3][4][5], mapping and exploration [6][7][8][9], aerobatic performances [10], and also object manipulation for construction and transportation [11]. ...
Article
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This paper presents a practical validation of a heterogeneous formation of mobile robots in performing a load lifting, transportation, and delivery task. Assuming that an unmanned ground vehicle (UGV) is unable to perform a mission by itself due to the presence of an obstacle in the navigation route, an unmanned aerial vehicle (UAV) is then assigned to lift the cargo over this UGV, transport the obstacle, and deliver over another UGV. The UAV uses an electromagnetic actuator supported by a cable to pick up the load, the mass of which is 32% of that of the UAV. Experimental results demonstrate that the developed system is capable of performing cargo transport missions and can be scalable for applications such as package delivery in urban or remote areas and supply delivery in conflict or disaster zones.
... Compared to many studies in the literature [10,35,36], a comprehensive nonlinear mathematical model of the quadrotor payload system was established by taking into account external disturbances and parameter uncertainties. ...
Article
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Due to the quadrotor’s underactuated nature, suspended payload dynamics, parametric uncertainties, and external disturbances, designing a controller for tracking the desired trajectories for a quadrotor that carries a suspended payload is a challenging task. Furthermore, one of the most significant disadvantages of designing a controller for nonlinear systems is the infinite-time convergence to the desired trajectory. In this paper, a finite-time neuro-sliding mode controller (FTNSMC) for a quadrotor with a suspended payload that is subject to parametric uncertainties and external disturbances is designed. By constructing a finite-time sliding mode controller, the quadrotor can follow the reference trajectories in finite time. Furthermore, despite time-varying nonlinear dynamics, parametric uncertainties, and external disturbances, a neural network structure is added to the controller to effectively reduce chattering phenomena caused by high switching gains, and significantly reduce the size of the control signals. Following the completion of the controller design, the system’s stability is demonstrated using the Lyapunov stability criterion. Extensive numerical simulations with various scenarios are run to demonstrate the effectiveness of the proposed controller.
... Each corridor is a bounded convex flight space; the union of all these corridors form a nonconvex pathway connecting the quadrotor's current position to its target position [3,4]; see Since the flight space defined by the union of the corridors is nonconvex, optimizing the trajectories for the quadrotor is computationally challenging. One standard solution approach is mixed integer programming [5][6][7], which first uses binary variables to describe the union of all corridors, then optimizes quadrotor trajectories together with these binary variables [8][9][10][11]. However, the worst-case computation time of this approach increases exponentially as the number of binary variables increases. ...
Preprint
One of the keys to flying quadrotors is to optimize their trajectories within the set of collision-free corridors. These corridors impose nonconvex constraints on the trajectories, making real-time trajectory optimization challenging. We introduce a novel numerical method that approximates the nonconvex corridor constraints with time-triggered convex corridor constraints. This method combines bisection search and repeated infeasibility detection. We further develop a customized C++ implementation of the proposed method, based on a first-order conic optimization method that detects infeasibility and exploits problem structure. We demonstrate the efficiency and effectiveness of the proposed method using numerical simulation on randomly generated problem instances as well as indoor flight experiments with hoop obstacles. Compared with mixed integer programming, the proposed method is about 50--200 times faster.
... The adaptive control problem for cable-based manipulation tasks with a single quadrupedal robot has also been discussed in [28]. In the path planning problem for hybrid manipulation, mixed-integer optimization [29] or general nonlinear programming with force-based complementarity constraints [30] can be applied but these approaches suffer from nonlinear hybrid dynamics and can only be solved offline. Recently, authors in [6] applied a mixed-integer programming in the local planner which is deployed in real-time with a single robot manipulation task via a cable. ...
Article
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This letter tackles the problem of robots collaboratively towing a load with cables to a specified goal location while avoiding collisions in real time. The introduction of cables (as opposed to rigid links) enables the robotic team to travel through narrow spaces by changing its intrinsic dimensions through slack/taut switches of the cable. However, this is a challenging problem because of the hybrid mode switches and the dynamical coupling among multiple robots and the load. Previous attempts at addressing such a problem were performed offline and do not consider avoiding obstacles online. In this letter, we introduce a cascaded planning scheme with a parallelized centralized trajectory optimization that deals with hybrid mode switches. We additionally develop a set of decentralized planners per robot, which enables our approach to solve the problem of collaborative load manipulation online. We develop and demonstrate one of the first collaborative autonomy framework that is able to move a cable-towed load, which is too heavy to move by a single robot, through narrow spaces with real-time feedback and reactive planning in experiments.
... system [8]. Furthermore, the control performance of the QCSL is adversely affected by uncertain external disturbance. ...
Article
This paper is concerned with the motion control for a quadrotor with a cable-suspended load (QCSL). A fixed-time control strategy is presented to improve the transient response and robustness of the QCSL with external disturbance. The overall control scheme is designed with a cascade structure to better cope with the underactuated property of the QCSL and the indirect effect of the control force on the load’s velocity through the tensile force on the cable. The simulation results are given to demonstrate the performance of the proposed scheme. Furthermore, actual flight tests were performed on a new experimental QCSL to validate the effectiveness of the proposed control strategy.
... If an optimization problem in UAVs assisted network with mixed-integer variables containing nonlinear objective function and constraints, is called MINLP problems [72] while RRM UAVs problems containing mixed-integer variables with both linear objective and constraints called as MILP [73,74]. While if in a UAVs-assisted environment, an optimization problem contains a mixed-integer variable with quadratic type objectives, then the optimization problem is called a MIQP problem [75,76]. Other programming techniques found in the literature are nonlinear programming(NLP), matching game, stochastic optimization, general convex and non-convex problems etc. [77,78]. ...
Article
Unmanned aerial vehicles (UAVs) have huge potential in empowering new applications in different areas ranging from military to medical applications and traffic control to the entertainment information industry. There has been overwhelming interest in improving UAVs and multi-UAVs frameworks to collaborate and complete all missions efficiently. UAVs can be connected to IoT devices at any time and fulfill their requirements. Because of the constrained onboard resources, there is a need for radio resource management (RRM) in UAV correspondent situations. Optimization plays a significant role in the efficient utilization of these resources and provides services to the network’s edge. This survey presents a comprehensive overview of RRM optimization techniques, including cloud, fog, mobile edge computing (MEC), and cloudlet for UAVs. Further, the mathematical modelling of objectives and constraints discussed in the literature is also presented here. A summary of the challenges while using these computing paradigms is explored. Future research directions on the UAV-assisted network are introduced. In short, this survey provides key guidelines of how various radio resources in different environments are analyzed and optimized using different algorithms and strategies.
... In these cases, the QSL must realize high-performance motion control in various complex environments (Wu, Lv et al., 2018). However, the QSL is a strongly coupled, nonlinear, and underactuated system (Tang & Kumar, 2015). Furthermore, the control performance of QSL is adversely affected by air resistance and external perturbations. ...
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In this paper, we propose a nonlinear finite-time control strategy to solve the motion control problem for a quadrotor with a slung load (QSL). This work aims to realize high-performance motion control for the QSL, even in perturbations. To improve the dynamic performance and the robustness of the QSL system, a novel nonlinear controller is designed with cascade structure. The finite-time stability of the resulting closed-loop system is theoretically analyzed in this work. Furthermore, the advantages of the proposed control strategy are demonstrated by comparison results with different strategies through simulations in MATLAB/SimMechanics. Finally, the effectiveness of the proposed controller is verified in actual experiments on a specially designed experimental QSL.
... Research about UAV logistics includes drone lift [11], drone obstacle The associate editor coordinating the review of this manuscript and approving it for publication was Bidyadhar Subudhi . avoidance [12], collaborative drone robotic arm [13], [14], and drone trajectory tracking [15]. Among them, robustness to environmental disturbances and an unknown payload is necessary for UAV transportation applications. ...
Article
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This paper focuses on the disturbance attenuation control of the quadrotor suspended payload system with unknown payload mass. Since the quadrotor transportation system is an eight-degree-of-freedom system with only four actuated degrees, it is difficult to achieve rapid stabilization of the quadrotor under varying payload and external disturbances. In this paper, a nonlinear controller based on rotation matrix is designed to rapid stabilization of attitude. By analyzing the effect of load mass on the trajectory tracking control, a parameter adaptive controller is proposed for position control. A mass estimation algorithm is established to estimate the payload mass in the air, which improves the robustness of the system. This approach can maximize load-bearing capacity within the thrust range of the quadrotor. The Lyapunov-based analysis proves the exponential convergence of the attitude error and the stability of the whole system. The contrast simulations demonstrate that the controller is superior to the sliding-mode controller incorporating input shaping on mass estimation, trajectory tracking, and disturbance resistance.
... Here a and t represents the operating limits, α is the fractional operator order and R is the real part of alpha. The fractional order derivative and integrator defined by Riemann Liouville definition is given as following: [21] aD α t f (t) = ...
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This article proposes a computationally efficient adaptive robust control scheme for a quad-rotor with cable-suspended payloads. Motion of payload introduces unknown disturbances that affect the performance of the quad-rotor controlled with conventional schemes, thus novel adaptive robust controllers with both integer- and fractional-order dynamics are proposed for the trajectory tracking of quad-rotor with cable-suspended payload. The disturbances acting on quad-rotor due to the payload motion are estimated by utilizing adaptive laws derived from integer- and fractional-order Lyapunov functions. The stability of the proposed control systems is guaranteed using integer- and fractional-order Lyapunov theorems. Overall, three variants of the control schemes, namely adaptive fractional-order sliding mode (AFSMC), adaptive sliding mode (ASMC), and classical Sliding mode controllers (SMC)s) are tested using processor in the loop experiments, and based on the two performance indicators, namely robustness and computational resource utilization, the best control scheme is evaluated. From the results presented, it is verified that ASMC scheme exhibits comparable robustness as of SMC and AFSMC, while it utilizes less sources as compared to AFSMC.
... In [184], a technique that lets a quadrotor pass through a narrow gap while carrying a cable-suspended payload was presented and was experimentally validated using a motion-capture system for state estimation. ...
... Taking into account that the dynamical model of the MAV is an under-actuated, highly coupled, and nonlinear system, a number of control techniques have been developed for such class of similar systems. 34,35 Among them, sliding mode control, which has drawn much attention for researchers, has been a useful and efficient control strategy for handling systems with significant non-linearities, uncertainties, time-varying properties, and bounded external disturbances. Most of the control strategies have been proposed to preserve an appropriate behavior in the stability of the MAV on finite-time. ...
Article
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In this work, we present a novel design for vertical surface contact using a two degree of freedom robotic arm attached to a Micro Air Vehicle. To achieve this, we propose a controller based on a Gain-Scheduled Proportional–Integral–Derivative approach. In previous works, the Gain-Scheduled Proportional–Integral–Derivative method was used to control the attitude of the Micro Air Vehicle, thus mitigating the perturbations induced by the movement of the arm. The novel approach of this work focuses on the achievement of an automatized full-contact with a rigid vertical surface using a Micro Air Vehicle with a robotic arm. We have improved the capabilities of the Gain-Scheduled Proportional–Integral–Derivative control to consider the inherent issues of approximating to a flat structure in order to carry out an aerial interaction task successfully. For the Micro Air Vehicle’s position feedback, a motion capture system is used in this work. A paintbrush attached to the end effector of the arm is used to draw over a whiteboard surface to show the full contact of the aerial manipulator. A distance sensor is added to the on-board sensors to measure the distance between the vertical surface and the system to ensure a correct distance and achieve a safe contact. Experimental testing results show that the controller can maintain a stable flight with sufficient accuracy to complete the aerial interaction tasks.
Chapter
Considering the low payload carrying capacity for a single quadcopter, one option to increase the payload carrying capacity is the use of more than one quadcopter. This work focuses on trajectory planning and control of two quadcopters with a cable-suspended point mass payload system using a leader–follower scheme. For safe and stable transportation of suspended payload, the quadcopters should be controlled to not lead to cable slackness. Accordingly, wrench closure analysis is carried out for the follower quadcopter with respect to the leader quadcopter, which helps design desired trajectory generation for the quadcopters. The performance of the proposed motion planning strategy is verified by conducting simulation in SIMSCAPE multibody package in MATLAB.
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This paper introduces a method to navigate the UAV flight and to suppress the payload swing by a nonlinear coupling control augmented with time-varying cable length. Special error signals are introduced that bring further coupling of dynamics among various states of the UAV and enable the flight control to effectively suppress the payload swing. The control is designed with the help of the dynamic model of the UAV in lift and transport operation. The stability of the control is proven in the Lyapunov sense. Extensive simulations and experiments have been carried out to demonstrate the effectiveness of the proposed nonlinear coupling control. Two popular control approaches in the literature are chosen to compare with the current work. It is found that the proposed control is quite effective in suppressing the payload swing while tracking the pre-determined path at the same time.
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We investigate the planar dynamics of aerial payload systems, in which we model the tow-cable as a geometrically exact (GE) beam and the payload as a rigid body. A GE beam incorporates large displacements, large rotations, and cross-sectional shear. Aerodynamic loads on the cable are computed on each element and then summed. Given its large mass, the towing aircraft is taken to be unaffected by the system’s motion. We derive the equations of the system and solve these using a nonlinear finite element method. We then study the effect on the system’s dynamics of cable length, payload size, downwash, and wind speed. Finally, we investigate practically relevant transient flight scenarios. We find that the flight path influences the system’s response, and minimizing motion derivatives limits payload’s motion. Our general formulation is easily extended to three-dimensions and useful for many aerial or underwater towed systems.
Article
Aerial delivery is becoming a reality due to the development of microelectronics and communication technology. Most existing methods for cable-suspended transportation systems utilize fixed-length cable to connect the unmanned aerial vehicle quadrotor and the payload. Such aerial transportation systems present underactuated property, which is caused by the indirectly controllable payload motion and the underactuation of the quadrotor itself. In practical applications, payload hoisting and lowering motion independent of the quadrotor altitude will further expand the application scope in such areas as limited space crossing and offshore sample collection. To realize the aforementioned objectives, a flexible connection between the quadrotor and the payload is realized by mounting an actuator beneath the fuselage. Suffering from strong nonlinearity and complex dynamic coupling, the control problem becomes extremely challenging and more cumbersome, as the system’s degree of freedom (DOF) increases. To deal with these problems, in this article, a nonlinear control approach is presented by energy-based analysis, which achieves simultaneous quadrotor positioning, payload swing elimination and hoisting / lowering. Lyapunov techniques and LaSalle’s Invariance theorem are utilized to prove the asymptotic convergence of the equilibrium point. Finally, a series of hardware experiments are conducted on a self-built aerial transportation platform. As far as we know, this article provides the first mechanism and control solution for payload hoisting/lowering independent of the quadrotor altitude.
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Quadrotors find a vast potential use in delivery and disaster relief operations. Control becomes critical in such scenarios, especially when quadrotors have to manoeuvre through constrained spaces or deliver payloads at precise locations in the presence of external disturbances and parametric uncertainties stemming from uncertain payloads. Therefore, the controller has to guarantee a predefined tracking accuracy not to violate the state constraints . On the other hand, conventional fixed-valued state constraints are not suitable in many scenarios such as (i) initial offset being well beyond the expected accuracy, (ii) system dynamics experiencing significant transients due to the dropping of the payload. However, to the best of the authors’ knowledge, state-of-the-art controllers do not provide any solution for an underactuated system like a quadrotor when the system needs to honour time-varying constraints under uncertainties. This work proposes a controller for quadrotors which is robust against external disturbances and parametric variations and guarantees a time-varying predefined position, velocity, attitude, and attitude-rate accuracy. The closed-loop system stability is established analytically, and the effectiveness of the proposed controller is validated experimentally compared to the state-of-the-art under a precision payload delivery scenario.
Conference Paper
In recent times, quadrotors have become immensely applicable in scenarios such as relief operations, infrastructure maintenance, search-and-rescue missions etc. A key control design challenge arises in these applications when the quadrotor has to manoeuvre through constrained spaces such as narrow windows, pipelines in the presence of external disturbances and parametric uncertainties: such conditions necessitate the controller to guarantee predefined tracking accuracy so as to not violate the constraints and simultaneously tackle uncertainties. However, state-of-the-art controllers dealing with constrained system motion are not applicable either for an underactuated system like quadrotor or for uncertain system dynamics. This work proposes a robust controller that enables the quadrotor to follow a trajectory with predefined tracking accuracy in constrained space as well as to tackle uncertainties stemming from imprecise system modelling and external disturbances. The closed-loop system stability is analysed via the Barrier Lyapunov approach and the effectiveness of the proposed controller is validated via simulation with state of the art.
Article
In this study, we propose a practical path planning method that combines the A* search algorithm and minimum snap trajectory generation. The A* search algorithm determines a set of waypoints to avoid collisions with surrounding obstacles from a starting to a destination point. Only essential waypoints (waypoints necessary to generate smooth trajectories) are extracted from the waypoints determined by the A* search algorithm, and an appropriate time between two adjacent waypoints is allocated. The waypoints so determined are connected by a smooth minimum snap trajectory, a dynamically executable trajectory for the quadrotor. If the generated trajectory is invalid, we methodically determine when intermediate waypoints are needed and how to insert the points to modify the trajectory. We verified the performance of the proposed method by various simulation experiments and a real-world experiment in a forested outdoor environment.
Article
Different from the quadrotor suspended payload system with fixed length cable, the system with variable length cable can load and unload cargoes more efficiently under many conditions. This paper presents a method of modeling, control, and trajectory planning for a quadrotor suspended payload system with variable length cable. In order to effectively reduce the swing of the slung payload under the quadrotor, a coupled dynamic model and an integral backstepping control scheme for the system are designed, and a basic trajectory planning is carried out. The presented coupled dynamic model is composed of two parts, one is the dynamic equation of the quadrotor with payload pull, and the other is the dynamic model of the payload pendulum angles with variable length cable related with quadrotor flight acceleration. Meanwhile, the interaction forces between them are calculated. Based on the coupled dynamic model of the system, a cascade control scheme with trajectory planning is designed. The attitude and position control loop of the system adopt the integral backstepping algorithm to solve the reliable flight of quadrotor with slung payload. At the same time, the flight trajectories are generated by trajectory planning as the reference input of the control system, which can further reduce the payload swing. Simulation results show that the proposed scheme can realize stable and reliable flight of the quadrotor and limit the pendulum angles within the desired range to reduce the payload swing.
Article
Deploying quadcopters for aerial transportation can be cost effective in impromptu material handling applications. However, such applications are limited mainly due to the requirement of onboard localization sensors and associated computation. The current work presents a human-controlled modality to successfully execute spontaneous outdoor flight of a quadcopter with a cable-suspended payload. Stable and smooth flights are achieved through an onboard integration of a custom-built sensor system and a controller to minimize payload oscillations. The feasibility of the proposed modality is demonstrated by conducting outdoor experiments and a case study in an unstructured environment.
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In recent years, multiple applications have emerged in the area of payload transport using unmanned aerial vehicles (UAVs). This has attracted considerable interest among the scientific community, especially the cases involving one or several rotary wing UAVs. In this context, this work proposes a novel measurement system which can estimate the payload position and the force exerted by it on the UAV. This measurement system is low cost, easy to implement, and can be used either in indoor or outdoor environ-ments (no sensorized laboratory is needed). The measurement system is validated statically and dynamically. In the first test, the estim-ations obtained by the system are compared with measurements produced by high-precision devices. In the second test, the system is used in real experiments to compare its performance with the ones obtained using known procedures. These experiments allowed to draw interesting conclusions on which future research can be based.
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The problem of balancing a quadrotor with a suspended load in hovering and level flights has been achieved by using different linear and nonlinear control approaches. However, to the best of our knowledge, this problem has not been solved by using tension-based attitude tracking control. In this paper, a novel solution to the tension-based controller design for the quadrotor–load system has been demonstrated. Even more, pendular characteristics of the quadrotor with suspended load have been fully analyzed for the first time. Based on the results of the above-mentioned analysis and applying it to the proposed model, the expected attitude trajectory not only ensures the flight safety, but also reduces the energy consumption of the controller. Compared with existing control methods, this method provides the desired tension by a windlass mechanism which is mounted on the quadrotor. By employing the terminal sliding surfaces in a hierarchical way and performing the Lyapunov stability analysis, it has been shown that the tracking error in finite time converges to zero. Finally, a numerical simulation has been performed to demonstrate the effectiveness of the proposed scheme.
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The paper presents the design of a trajectory planner and feedback control system to autonomously navigate a quadrotor UAV with a suspended payload through a confined environment consisting of horizontal and vertical tunnels. The trajectory planning task is formulated as an optimal control problem and solved by applying an A⁎ search algorithm. A novel sequence-constrained action space is implemented to encourage the use of input shaping actions, which is an open-loop control technique for reducing vibrations in a response. To execute the planned trajectory, a trajectory regulator is designed to work in conjunction with the trajectory planner. The trajectory regulator uses feedback control to provide disturbance rejection and robustness to parameter uncertainty. The planning and execution is verified in simulation, using a system that is constrained to two dimensions. The trajectory planner successfully plans a collision-free path for the quadrotor with suspended payload through an environment with obstacles, tunnels and vertical chimneys. The regulator successfully controls the quadrotor with suspended payload to follow the planned trajectory through the environment, in the presence of external wind disturbances.
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Full-text available
In recent years, multiple applications have emerged in the area of payload transport using unmanned aerial vehicles (UAVs). This has attracted considerable interest among the scientific community, especially the cases involving one or several rotary-wing UAVs. In this context, this work proposes a novel measurement system which can estimate the payload position and the force exerted by it on the UAV. This measurement system is low cost, easy to implement, and can be used either in indoor or outdoor environments (no sensorized laboratory is needed). The measurement system is validated statically and dynamically. In the first test, the estimations obtained by the system are compared with measurements produced by high-precision devices. In the second test, the system is used in real experiments to compare its performance with the ones obtained using known procedures. These experiments allowed to draw interesting conclusions on which future research can be based.
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Transporting suspended payloads is challenging for autonomous aerial vehicles because the payload can cause significant and unpredictable changes to the robot's dynamics. These changes can lead to suboptimal flight performance or even catastrophic failure. Although adaptive control and learning-based methods can in principle adapt to changes in these hybrid robot-payload systems, rapid mid-flight adaptation to payloads that have a priori unknown physical properties remains an open problem. We propose a meta-learning approach that “learns how to learn” models of altered dynamics within seconds of post-connection flight data. Our experiments demonstrate that our online adaptation approach outperforms non-adaptive methods on a series of challenging suspended payload transportation tasks. Videos and other supplemental material are available on our website: https://sites.google.com/view/meta-rl-for-flight</uri
Article
In this paper, the control problem for the underactuated dynamic system which consists of a quadrotor unmanned aerial vehicle (UAV) and a suspended payload is investigated under the effects of unknown exogenous disturbances. A novel nonlinear controller based on the robust integral of the sign of the error (RISE) is developed to deal with the position trajectory tracking control and the anti-swing control of the suspended payload with the presence of unknown air turbulence. The Lyapunov-based stability analysis is employed to prove the asymptotic stability of the closed-loop system. The Real-time experimental results are presented to verify the performance of the proposed control design.
Article
The aerial transportation system is a kind of nonlinear underactuated mechatronic system, which suspends the cargo beneath the rotorcraft’s fuselage and undertakes two basic missions of rotorcraft positioning and cargo swing suppression. Currently, most available methods need simplifications such as the near hovering hypothesis and dimension reduction operations, which may badly degrade the control performance when state variables get far away from the equilibrium point. In addition, integral terms, which can eliminate the steady errors, are not reflected in controller design and stability analysis processes. To tackle the aforementioned issues, this article provides a novel nonlinear control approach with an elaborately constructed integral term for aerial transportation systems, which not only achieves satisfactory antiswing and positioning performance but also reduces steady errors in practical flight. Meanwhile, the actuating constraint is taken into consideration so as to avoid saturation problems. Without linearization operations, we prove the closed-loop asymptotic stability of the equilibrium by the explicit Lyapunov-based analysis. As far as we know, this article is the first solution for controller design with the consideration of both steady errors elimination and actuating constraints. Finally, several groups of hardware experimental results are provided to validate the effectiveness of the presented control scheme. Note to Practitioners —This article is motivated by the requirement of effective control schemes for aerial transportation systems. The unexpected cargo swing motion may lead to safety accidents; thus, the dual objective of swing suppression and rotorcraft positioning is the focus of research. Nevertheless, with underactuated property, the cargo swing motion cannot be directly controlled. Up until now, at the cost of model accuracy, most existing methods utilize the simplified models in near hovering state or 2-D transverse plane to reduce the control difficulty. Accounting for the foregoing problems, this article presents a novel control scheme with improved antiswing and positioning performance. With an elaborately constructed integral term, the designed controller could improve the positioning accuracy of the rotorcraft with the guaranteed theoretical analysis. Moreover, to avoid the problem of actuator saturation, the control inputs are restricted in allowable ranges during the transportation process. All these aspects are verified by rigorous theoretical analysis and groups of hardware experiments in different conditions. In future studies, we will apply the suggested control scheme in practical applications.
Conference Paper
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Micro Unmanned Aerial Vehicles (MAVs) have been used in a wide range of applications [1, 2, 3]. However, there are few papers addressing high-speed grasping and transportation of pay-loads using MAVs. Drawing inspiration from aerial hunting by birds of prey, we design and equip a quadrotor MAV with an actuated appendage enabling grasping and object retrieval at high speeds. We develop a nonlinear dynamic model of the system, demonstrate that the system is differentially flat, plan dynamic trajectories using the flatness property, and present experimental results with pick-up velocities at 2 m/s (6 body lengths / second) and 3 m/s (9 body lengths / second). Finally, the experimental results are compared with observations derived from video footage of a bald eagle swooping down and snatching a fish out of water.
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This paper provides new results for control of complex flight maneuvers for a quadrotor unmanned aerial vehicle (UAV). The flight maneuvers are defined by a concatenation of flight modes or primitives, each of which is achieved by a nonlinear controller that solves an output tracking problem. A mathematical model of the quadrotor UAV rigid body dynamics, defined on the configuration space $\SE$, is introduced as a basis for the analysis. The quadrotor UAV has four input degrees of freedom, namely the magnitudes of the four rotor thrusts; each flight mode is defined by solving an asymptotic optimal tracking problem. Although many flight modes can be studied, we focus on three output tracking problems, namely (1) outputs given by the vehicle attitude, (2) outputs given by the three position variables for the vehicle center of mass, and (3) output given by the three velocity variables for the vehicle center of mass. A nonlinear tracking controller is developed on the special Euclidean group $\SE$ for each flight mode, and the closed loop is shown to have desirable closed loop properties that are almost global in each case. Several numerical examples, including one example in which the quadrotor recovers from being initially upside down and another example that includes switching and transitions between different flight modes, illustrate the versatility and generality of the proposed approach.
Conference Paper
This paper addresses the dynamics, control, planning, and visual servoing for micro aerial vehicles to perform high-speed aerial grasping tasks. We draw inspiration from agile, fast-moving birds, such as raptors, that detect, locate, and execute high-speed swoop maneuvers to capture prey. Since these grasping maneuvers are predominantly in the sagittal plane, we consider the planar system and present mathematical models and algorithms for motion planning and control, required to incorporate similar capabilities in quadrotors equipped with a monocular camera. In particular, we develop a dynamical model directly in the image space, show that this is a differentially-flat system with the image features serving as flat outputs, outline a method for generating trajectories directly in the image feature space, develop a geometric visual controller that considers the second order dynamics (in contrast to most visual servoing controllers that assume first order dynamics), and present validation of our methods through both simulations and experiments.
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We present a new method for planning footstep placements for a robot walking on uneven terrain with obstacles, using a mixed-integer quadratically-constrained quadratic program (MIQCQP). Our approach is unique in that it handles obstacle avoidance, kinematic reachability, and rotation of footstep placements, which typically have required non-convex constraints, in a single mixed-integer optimization that can be efficiently solved to its global optimum. Reachability is enforced through a convex inner approximation of the reachable space for the robot's feet. Rotation of the footsteps is handled by a piecewise linear approximation of sine and cosine, designed to ensure that the approximation never overestimates the robot's reachability. Obstacle avoidance is ensured by decomposing the environment into convex regions of obstacle-free configuration space and assigning each footstep to one such safe region. We demonstrate this technique in simple 2D and 3D environments and with real environments sensed by a humanoid robot. We also discuss computational performance of the algorithm, which is currently capable of planning short sequences of a few steps in under one second or longer sequences of 10-30 footsteps in tens of seconds to minutes on common laptop computer hardware. Our implementation is available within the Drake MATLAB toolbox [1].
Conference Paper
A quadrotor with a cable-suspended load with eight degrees of freedom and four degrees underactuation is considered and a coordinate-free dynamic model, defined on the configuration space SE(3)×S2, is obtained by taking variations on manifolds. The quadrotor-load system is established to be a differentially-flat hybrid system with the load position and the quadrotor yaw serving as the flat outputs. A nonlinear geometric control design is developed, that enables tracking of outputs defined by (a) quadrotor attitude, (b) load attitude, and (c) position of the load. In each case, the closed-loop system exhibits almost-global properties. Stability proofs for the controller design, as well as simulations of the proposed controller are presented.
Conference Paper
Attaining autonomous flight is an important task in aerial robotics. Often flight trajectories are not only subject to unknown system dynamics, but also to specific task constraints. This paper presents a motion planning method for generating trajectories with minimal residual oscillations (swing-free) for rotorcraft carrying a suspended loads. We rely on a finite-sampling, batch reinforcement learning algorithm to train the system for a particular load. We find criteria that allow the trained agent to be transferred to a variety of models, state and action spaces and produce a number of different trajectories. Through a combination of simulations and experiments, we demonstrate that the inferred policy is robust to noise and the unmodeled dynamics of the system. The contributions of this work are 1) applying reinforcement learning to solve the problem of finding swing-free trajectories for rotorcraft, 2) designing a problem-specific feature vector for value function approximation, 3) giving sufficient conditions for successful learning transfer to different models, state and action spaces, and 4) verification of the resulting trajectories in both simulation and autonomous control of quadrotors with suspended loads.
Conference Paper
A quadrotor with a cable-suspended load with eight degrees of freedom and four degrees underactuation is considered and the system is established to be a differentially-flat hybrid system. Using the flatness property, a trajectory generation method is presented that enables finding nominal trajectories with various constraints that not only result in minimal load swing if required, but can also cause a large swing in the load for dynamically agile motions. A control design is presented for the system specialized to the planar case, that enables tracking of either the quadrotor attitude, the load attitude or the position of the load. Stability proofs for the controller design and experimental validation of the proposed controller are presented.
Article
We present an algorithm for the generation of optimal trajectories for teams of heterogeneous quadrotors in three-dimensional environments with obstacles. We formulate the problem using mixed-integer quadratic programs (MIQPs) where the integer constraints are used to enforce collision avoidance. The method allows for different sizes, capabilities, and varying dynamic effects between different quadrotors. Experimental results illustrate the method applied to teams of up to four quadrotors ranging from 65 to 962 grams and 21 to 67 cm in width following trajectories in three-dimensional environments with obstacles with accelerations approaching 1g.
Conference Paper
In this paper we present an overview of techniques and approaches used for a load transportation system based on small size unmanned helicopters. The focus is on the control approach and on the movement of the rope connecting helicopters and load. The proposed approach is based on two control loops: an outer loop to control the translation of each helicopter in compound and an inner loop to control the orientation of helicopters. The challenge here is that in both loops the dynamics of the whole system - all helicopters and load - should be accounted for. It is shown, that for designing the outer loop controller a complex model of the helicopters and load can be replaced by a simplified model based on interconnected mass points. For designing the inner loop controller, the complete dynamics of the whole system are considered. The usage of force sensors in the ropes is proposed in order to simplify the inner loop controller and to make it robust against variations of system parameters. The presented inner loop controller is independent of the number of coupled helicopters. The outer loop controller depends on the number of helicopters. The problem of oscillations in the flexible ropes due to external disturbancies (e.g. wind gusts) is discussed and a solution based on load state observer is presented. The performance of the presented system was verified in simulations and in real flight experiments with one and three helicopters transporting the load. The worldwide first demonstration of a slung load transportation using three helicopters was performed in December 2007.
Article
This paper describes the application of differential flatness techniques from nonlinear control theory to mechanical (Lagrangian) systems. Systems which are differentially flat have several useful properties which can be exploited to generate effective control strategies for nonlinear systems. For the special case of mechanical control systems, much more geometric information is present and the purpose of this paper is to explore the implications and features of that class of systems. We concentrate on several worked examples which illustrate the general theory and present a detailed catalog of known examples of differentially flat mechanical systems. Keywords: nonlinear control, mechanical systems, trajectory generation, differential flatness. 1 Introduction An emerging paradigm in nonlinear control is the use of two degree of freedom design techniques to generate nonlinear controllers for mechanical systems performing motion control tasks. The basic approach of two degree of freedo...
Aggressive optimal control for agile flight with a slung load
  • C De Crousaz
  • F Farshidian
  • J Buchli
Polynomial trajectory planning for quadrotor flight
  • C Richter
  • A Bry
  • N Roy