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Human beings are highly efficient in maintaining standing balance under the influence of different perturbations. However, biped humanoid robots are far from exhibiting similar skills. This is mainly due to the limitations in the current control and modeling techniques used in humanoid robots. Even though approaches using the Linear Inverted Pendul...
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... the biomechanical literature (Winter, 1995;Uyar et al., 2009), the standing human body is modeled as an inverted pendulum to represent the stance leg as shown in Figure 1. Similarly, the humanoid robot is modeled as a point mass located at the center of mass (CoM) of the robot with a mass equal to the total mass. ...
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... trajectory is provided as a reference input to the energy controller for the CoM motion to follow. Figure 10 shows the projection of the CoM motion on the ground along with the step locations. ...
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... resulting CoM trajectory is shown in Figure 11. By com- parison to the findings of the CoM motion characterized by biomechanical researchers shown in Figure 12, we can see large similarities between the two trajectories. ...
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... resulting CoM trajectory is shown in Figure 11. By com- parison to the findings of the CoM motion characterized by biomechanical researchers shown in Figure 12, we can see large similarities between the two trajectories. The shape and phase of the forward direction resembles two sinusoidal curves. ...
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... lowest CoM position occurs at the moment of switching support. Figure 13 shows a series of screenshots of the resulting walking motion. It should be noted here that the entire motion was generated using the SIP CoM trajectories and a fifth-order polynomial to give the swing foot trajectory. ...
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Humanoid robots are complex multibody systems, and modeling and locomotion control for them are challenging tasks. In this paper, a rigid multibody model is first built for a home-made humanoid robot with kinematic loop closures. The inverse kinematics solutions based on geometric relationships are then presented for the parallel mechanisms of the...
Citations
... In [14], a set of different machine learning algorithms such as support vector machines (SVMs) and random forests, were applied successfully to classify step viability with data from the robot's legs and feet. These solutions not only improve the robot's ability to anticipate and avoid falls, but also enables more efficient movement, as it reduces the need for conservative, energy-intensive gait adjustments that traditional reactive control systems often require [15,16]. ...
The prediction of the stability of future steps taken by a biped robot is a very important task, since it allows the robot controller to adopt the necessary measures in order to minimize damages if a fall is predicted. We present a classifier to predict the viability of a given planned step taken by a biped robot, i.e., if it will be stable or unstable. The features of the classifier are extracted from a feature engineering process exploiting the useful information contained in the time series generated in the trajectory planning of the step. In order to state the problem as a supervised classification one, we need the ground truth class for each planned step. This is obtained using the Predicted Step Viability (PSV) criterion. We also present a procedure to obtain a balanced and challenging training/testing dataset of planned steps that contains many steps in the border between stable and non stable regions. Following this trajectory planning strategy for the creation of the dataset we are able to improve the robustness of the classifier. Results show that the classifier is able to obtain a 95% of ROC AUC for this demanding dataset using only four time series among all the signals required by PSV to check viability. This allows to replace the PSV stability criterion, which is safe, robust but impossible to apply in real-time, by a simple, fast and embeddable classifier that can run in real time consuming much less resources than the PSV.
... The model used was the spherical inverted pendulum (SIP) in the polar coordinate system; i.e., the 2 DOFs of the pendulum are the rotation around the vertical axis and one of the horizontal axes [12,13]. The approach exploited the anelastic energy restitution after the collision of the swing foot with the ground. ...
This paper extends the three-dimensional inverted pendulum (spherical inverted pendulum or SIP) in a polar coordinate system to simulate human walking in free fall and the energy recovery when the foot collides with the ground. The purpose is to propose a general model to account for all characteristics of the biped and of the gait, while adding minimal dynamical complexity with respect to the SIP. This model allows for both walking omnidirectionally on a flat surface and going up and down staircases. The technique does not use torque control. However, for the gait, the only action is the change in angular velocity at the start of a new step with respect to those given after the collision (emulating the torque action in the brief double stance period) to recover from the losses, as well as the preparation of the position in the frontal and sagittal planes of the swing foot for the next collision for balance and maneuvering. Moreover, in climbing or descending staircases, during the step, the length of the supporting leg is modified for the height of the step of the staircase. Simulation examples are offered for a rectilinear walk, ascending and descending rectilinear or spiral staircases, showing stability of the walk, and the expenditure of energy.
... The model used was the spherical inverted pendulum (SIP) in polar coordinate system, i.e. the 2 DOFs of the pendulum are the rotation around the vertical axis, and one of the horizontal axes [11,12]. With the SIP model the problem of gait is intertwined with the estimation in 3-D of the swing foot placement at the collision with the ground (FPE) [13][14][15][16][17]. ...
... the generalized momentum is defined as the partial derivative of the kinetic energy K with respect to the r-th generalized speed p r (t) = ∂K/∂u r , r = 1, · · · , n, (A. 12) then, Kane proves that ...
Classically the walk in biped robotics was obtained controlling balance during the whole step, i.e. guaranteeing that the pressure point under the soles always stayed in the polygon of the supporting feet. However, this assumed that the feet were able to transfer torque to the ground during the whole gait cycle. In spite of the fact that the amount of transferrable torque in the feet-ground contact is limited, it is possible only during some phases of the step, and the overall process is energetically inefficient. On the other side, starting from the passive motion of the rimless wheel falling on an inclined surface, and ending to the inverted pendulum with a compass, balance in the whole was proven in spite of dynamical instability inside each step. Along this line results of Foot Placement Estimation (FPE) in 2-D and 3-D showed how energy efficient walk was possible, emulating the human walk with a free fall on the swing foot and energy restitution at the foot collision with the ground for the next step. This model assumes pointy feet, so without torque transfer to the ground. In the realm of FPE, in previous papers the present author adopted the 3-D inverted pendulum in polar coordinates (Spherical Inverted Pendulum - SIP) to introduce omnidirectional walks with arbitrarily changing characteristics. No torque control was used during the step, i.e the pendulum was always in free fall at each step, the only control actions were at the beginning of the next step. These actions are: the change of angular velocities at the start of a new step, with respect to those given after the collision (emulating the torque action in the brief double stance period), to recover for the losses, and the preparation of the position in the frontal and sagittal planes of the swing foot for the next collision. The present paper improves this paradigm, proposing a general model to account for all characteristics of the biped and of the gait, with adding a minimum of dynamical complexity with respect to the SIP. This model allows, not only to walk omnidirectionally on a flat surface, but also to go up and down staircases.
... The inverted pendulum -cart system is a classic control engineering problem that has been studied for many years. It has many real world applications, one of the primary examples is in robotics where an upright humanoid J o u r n a l P r e -p r o o f Journal Pre-proof robot could be modeled as an inverted pendulum [1]. The applications extend upto and beyond aerospace engineering [2] and manufacturing [3]. ...
Linear Quadratic Regulator is one of the most common ways to control a linear system. Despite Linear Quadratic Regulator's (LQR) strong performance and solid resilience, developing these controllers have been challenging, largely because there is no reliable way to choose the Q and R weighing matrices. In this regard a deterministic method is used for choosing them in this paper, providing the designers a precise control over performance variables. An Artificial Bee Colony (ABC) optimisation is also used to find the sub-optimal gain matrices along with an analytical approach based on neural networks. A comparative study of the three approaches is performed using MATLAB simulations. These three approaches are applied on an inverted pendulum-cart system due to its complexity and dexterity. The results show that all the three methods show comparable performances with the proposed analytical method being slightly better in terms of transient characteristics.
... In particular, the control of underactuated mechanical systems with pendulum-like behaviors remains an attractive control problem for researchers because this class of mechanical systems is widely used to model more complex systems and for the achievement of challenging tasks. For instance, they are used for the design of posture balance and to produce walking patterns in biped robots, balancing techniques coupled with vehicles, and some other exciting tasks (see e.g., [2][3][4][5][6][7][8][9][10][11][12][13][14]). Some examples of mechanical systems belonging to this class are the Pendubot, the Acrobot, the inverted cart pendulum, the Furuta pendulum, the rotary inverted pendulums, the inertial wheel pendulums, among others. ...
The development of control laws for underactuated mechanical systems with pendulum-like behaviors is of paramount importance due to their use in the modeling of more complex systems and other challenging tasks. The underactuated feature describes constraints in the maneuverability and capabilities of a mechanical system with the advantage of offering less energy consumption. In this work, a novel methodology for solving the automation of evolved nonlinear controllers for the swing-up phase of switching control laws for underactuated inverted pendulums is proposed. Automatic synthesis of linear controllers with optimal performance applied to linear systems modeled as transfer functions is a forward leap proposed by Koza in 2003. Our proposed approach introduces the nonlinear nature within the automated construction of a set of swing-up controllers integrating an evolutionary process based on Genetic Programming (GP). The presented framework is based on an analytic behaviorist setup that merges Control Theory (CT) with GP. CT is applied to formulate the mathematical description of the problem and the design of the fitness function that guides the automated synthesis; GP is implemented as an evolutionary engine for the construction of the solutions. The advantage is that the symbolic feature of GP is exploited to develop large sets of nonlinear controllers that can be further studied with analytic tools from the CT approach. The proposed framework is applied to an underactuated two-link inverted pendulum giving a set of 13,590 evolved nonlinear swing-up controllers with the same and better fitness value than a state-of-the-art human-made design.
... In particular, the control of underactuated mechanical systems with pendulum-like behaviors remains an attractive control problem for researchers because these are widely used to model more complex systems, and for the achievement of challenging tasks. For instance, they are used for the design of posture balance and to produce walking patterns in biped robots, balancing techniques coupled with vehicles, and some other interesting tasks (see e.g., [2][3][4][5][6][7][8][9][10][11][12][13][14]). Some examples of mechanical systems belonging to this class are the Pendubot, the Acrobot, the inverted cart pendulum, the Furuta pendulum, the rotary inverted pendulums, the inertial wheel pendulums, among others. ...
The development of control laws for underactuated mechanical systems with pendulum-like behaviors is of paramount importance due to their use in the modeling of more complex systems and other challenging tasks. The underactuated feature describes constraints in the maneuverability and capabilities of a mechanical system with the advantage of offering less energy consumption. In this work, a novel methodology for solving the automation of evolved nonlinear controllers for the swing-up phase of switching control laws for underactuated inverted pendulums is proposed. Automatic synthesis of linear controllers with optimal performance applied to linear systems modeled as transfer functions is a forward leap proposed by Koza in 2003. Our proposed approach introduces the nonlinear nature within the automated construction of a set of swing-up controllers integrating an evolutionary process based on GP. The presented framework is based on an analytic behaviorist setup that merges Control Theory with Genetic Programming. Control Theory is applied to formulate the mathematical description of the problem and the design of the fitness function that guides the automated synthesis; Genetic Programming is implemented as an evolutionary engine for the construction of the solutions. The advantage is that the symbolic feature of Genetic Programming is exploited to develop large sets of nonlinear controllers that can be further studied with analytic tools from the Control Theory approach. The proposed framework is applied to an underactuated two-link inverted pendulum giving a set of 13590 evolved nonlinear swing-up controllers with the same and better fitness value than a state-of-the-art human-made design.
... Since then, researchers have started to consider the influence of perturbations and proposed corresponding control methods according to different types of perturbations. Successful results have been obtained for tilt ground [5][6][7], uneven ground [8], external force impact [9][10][11] and other perturbations. ...
This paper continues the proposed idea of stability training for legged robots with any number of legs and any size on a motion platform and introduces the concept of a learning-based controller, the global self-stabilizer, to obtain a self-stabilization capability in robots. The overall structure of the global self-stabilizer is divided into three modules: action selection, adjustment calculation and joint motion mapping, with corresponding learning algorithms proposed for each module. Taking the human-sized biped robot, GoRoBoT-II, as an example, simulations and experiments in three kinds of motions were performed to validate the feasibility of the proposed idea. A well-designed training platform was used to perform composite random amplitude-limited disturbances, such as the sagittal and lateral tilt perturbations (±25°) and impact perturbations (0.47 times the robot gravity). The results show that the proposed global self-stabilizer converges after training and can dynamically combine actions according to the system state. Compared with the controllers used to generate the training data, the trained global self-stabilizer increases the success rate of stability verification simulations and experiments by more than 20% and 15%, respectively.
... Our synthetic load test (Fig. 12) indicates that the VM can support around 150 operations for applications that operate around 250Hz (such as humanoid balance bots [9], autonomous vehicle platforms [36]). Our music program falls in the range of 200-500 Hz, and SynchronVM could sustain that frequency without introducing any jitter. ...
Programming embedded systems applications involve writing concurrent, event-driven and timing-aware programs. Traditionally, such programs are written in low-level machine-oriented programming languages like C or Assembly. We present an alternative by introducing Synchron, an API that offers high-level abstractions to the programmer while supporting the low-level infrastructure in an associated runtime system and one-time-effort drivers.
Embedded systems applications exhibit the general characteristics of being (i) concurrent, (ii) I/O-bound and (iii) timing-aware. To address each of these concerns, the Synchron API consists of three components- (1) a Concurrent ML (CML) inspired message-passing concurrency model, (2) a message-passing-based I/O interface that translates between low-level interrupt based and memory-mapped peripherals, and (3) a timing operator, syncT, that marries CML's sync operator with timing windows inspired from the TinyTimber kernel.
We implement the Synchron API as the bytecode instructions of a virtual machine called SynchronVM. SynchronVM hosts a Caml-inspired functional language as its frontend language, and the backend of the VM supports the STM32F4 and NRF52 microcontrollers, with RAM in the order of hundreds of kilobytes. We illustrate the expressiveness of the Synchron API by showing examples of expressing state machines commonly found in embedded systems. The timing functionality is demonstrated through a music programming exercise. Finally, we provide benchmarks on the response time, jitter rates, memory, and power usage of the SynchronVM.
... After summing up the research, it is found that there are three main types of methods that each use fundamentally different approaches for assessing the safety of the exoskeleton: 1) Biomechanical principles-based methods, like Stabilizing and Destabilizing Forces (SDF) (Duclos et al., 2009), Angular Momentum based Stability Index (AMSI) (Nott et al., 2013), Centroidal Momentum based Stability Index (CMSI) (Jung and Veneman, 2019), Foot Rotation Indicator (FRI) (Ali AbulKareem, 2020), Inverted Pendulum Model Approach (IPMA) (Elhasairi and Pechev, 2015), Capturability Region (CR) (Hong, 2019), Foot Placement Indicator (FPI) (Zutven et al., 2012); 2) Dynamic system theory-based methods, like Nearest Neighbor Gait Index (NNGI) (Gallego et al., 2012), Gait Sensitivity Norm (GSN) (Hobbelen and Wisse, 2007); 3) Probabilistic methods, like Trunk Orientation based Stability Index (TOSI) (Radkhah et al., 2010), Control Error Anomaly (CEA) (Ahmed and Ashton-Miller, 2007) and so on. ...
The lower limb exoskeleton is playing an increasing role in enabling individuals with spinal cord injury (SCI) to stand upright, walk, turn, and so on. Hence, it is essential to maintain the balance of the human-exoskeleton system during movements. However, the balance of the human-exoskeleton system is challenging to maintain. There are no effective balance control strategies because most of them can only be used in a specific movement like walking or standing. Hence, the primary aim of the current study is to propose a balance control strategy to improve the balance of the human-exoskeleton system in dynamic movements. This study proposes a new safety index named Enhanced Stability Pyramid Index (ESPI), and a new balance control strategy is based on the ESPI and the Dynamic Movement Primitives (DMPs). To incorporate dynamic information of the system, the ESPI employs eXtrapolated Center of Mass (XCoM) instead of the center of mass (CoM). Meanwhile, Time-to-Contact (TTC), the urgency of safety, is used as an automatic weight assignment factor of ESPI instead of the traditional manual one. Then, the balance control strategy utilizing DMPs to generate the gait trajectory according to the scalar and vector values of the ESPI is proposed. Finally, the walking simulation in Gazebo and the experiments of the human-exoskeleton system verify the effectiveness of the index and balance control strategy.
... The robot model presented has two aspects of high relevance that will define the mathematical derivations. The first one is that it will be modeled as a triple pendulum for kinematics as in [5] and [10]. The second one is that the friction in the model will not be considered for a matter of simplicity. ...
... This control law is applied directly in the direct kinematics robot model, and its error is computed as: (10) where θ id represents the extremity desired angle, and θ iR is the real angle measured by the acquisition system. ...
... where e i is the deviation error defined in (10). The performed simulations provide deviation errors. ...
In this paper, a mathematical model of a bipedal robot with six degrees of freedom (6 DoF) is presented and tested for some control strategies. For simplicity, one of the extremities is modeled, and it is assumed that the second one is similar. Some widely used tools, like Denavit-Hattender parametrization and Euler-Lagrange approaches, are applied to obtain the movement equations. A set of control laws are designed, applied to the system model, and compared among them. The study is carried out to evaluate deviation errors in the extremities, the proposed bipedal model's performance, and control strategies. The controllers' performances are evaluated in terms of the deviation errors, which are computed as the root mean square (RMS) of differences between desired and actual extremity-joint positions.
