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Iterative Learning Based Trajectory Optimization Using Fourier Series Basis Functions
Abstract
This letter presents an iterative, online trajectory optimization algorithm for systems performing repetitive processes. While typical iterative learning techniques are formulated for tracking control applications, a precise definition of the tracking reference is required. In repetitive applications where the optimal tracking reference is not fully defined, there exists an opportunity to improve system performance by altering the
trajectory
of the system based on information rich signals from previous cycles. In this letter, we develop an algorithm to optimize the parameterized trajectory of a system in real time utilizing constrained optimization of a cost function generated from the performance values of the previous cycle. Simulation results are used to illustrate the implementation of this iterative trajectory optimization framework while also benchmarking the performance against a norm optimal iterative learning controller with perfect system knowledge.
This article presents a complete design of non‐causal finite impulse response (FIR) and infinite impulse response (IIR) compensators for repetitive control. The concept of repetitive controllers involves imitating the inverse frequency response of the feedback control system by minimizing the amplitude of error propagation from one period to the next in the frequency domain. The FIR compensator design has already been presented in our previous work. However, it was not complete since some parameters, such as the number of causal gains and total number of gains were still left open for the designers to select. This work provides a reasonable suggestion on how to choose parameters based on the steepest descent method. In addition, an IIR compensator is further developed based on the designed FIR design. The gains of the IIR compensator are adjusted by aiming to minimize the cost function using the steepest descent. As can be observed from the results, the IIR compensator developed from the FIR compensator cannot overcome the original FIR compensator since its learning performance is relatively slow and the extra gains added to the denominator increase memory usage when executing.
This paper presents the real-time optimization of the crankshaft motion in a hybridized opposed piston (OP) engine using an iterative learning-based trajectory optimization scheme. The powertrain is oriented in a series hybrid design with each crankshaft directly coupled to electric motors, eliminating the conventional geartrain linking the two crankshafts along with the associated friction and weight. In this way, the electric motors can directly extract the work generated by the engine and regulate the crankshaft dynamics, introducing the capability to dynamically vary compression ratio, combustion volume, and scavenging dynamics on an inter-cycle basis. This control freedom increases the system's maximum potential efficiency, yet requires highly optimized intra-cycle crankshaft motion profiles to realize the improved work extraction efficiency of the dual motor-controlled OP engine. Leveraging the repetitive nature of the internal combustion engine, an iterative trajectory optimization (ITO) algorithm is used to define the optimal crankshaft motion profile in real-time for steady state operation. We demonstrate experimentally the rapid convergence and near optimal crankshaft motion profiles for the ITO strategy as well as its proficiency under both motored and fired cycle operation.
Data-driven feedforward tuning enables high performance for control systems that perform varying tasks by using past measurement data. The aim of this paper is to develop an approach for data-driven feedforward tuning that achieves high accuracy and at the same time is computationally inexpensive. A linear parametrization is employed that enables parsimonious modeling of inverse systems for feedforward through the use of non-causal rational orthonormal basis functions in L2. The benefits of the proposed parametrization are experimentally demonstrated on an industrial printer, including pre-actuation and cyclic pole repetition.
Recently, the importance of sustainable manufacturing has been widely discussed. The optimization of energy consumption in product manufacture has been deeply analyzed, mainly focusing on the energy directly absorbed by the manufacturing process. On the contrary, this paper focuses on the analysis and optimization of the energy consumption related to auxiliary robotic assembly processes, contributing to the identification of sustainable manufacturing strategies for pick and place robots. It proposes a methodology for the automatic generation of robot trajectories and the sequencing of the robot task, while minimizing the energy consumption. A probabilistic roadmap is created to identify a collision-free and minimum energy consumption trajectory for each couple of feasible tasks. Trajectory power consumption is evaluated exploiting dynamic information coming from the real robot motion planner using a model that takes into account the energy behavior of motors and drives and their operative conditions. A set of generated trajectories is selected, defining the task sequence and minimizing the robot cycle time. The differences between the results deriving by employment of the energy consumption minimization criterion versus time minimization criterion are presented through a simplified case.
This paper presents a guidance law to operate intelligence, surveillance and reconnaissance missions using cooperative UAVs under known static threats. The guidance law is classified into three levels. In level 1 as the highest level, waypoints of UAVs are selected using different cost functions. In level 2, preliminary paths are generated using the A* algorithm for avoiding threats, and approaching waypoints with efficient operation. In level 3, practical guidance commands are generated using a Lyapunov vector field to enable the UAVs to follow the path designed. Simulation results show that the integrated algorithm offers desirable flexibility, and can be implemented easily without much modification in real situations.
In this paper, three control methods—iterative learning control (ILC), repetitive control (RC), and run-to-run control (R2R)—are studied and compared. Some mathematical transformations allow ILC, RC, and R2R to be described in a uniform framework that highlights their similarities. These methods, which play an important role in controlling repetitive processes and run-based processes, are collectively referred to as learning-type control in this paper. According to the classification adopted in this paper, learning-type control has two classes—direct form and indirect form. The main ideas and designing procedures for these two patterns are introduced, separately. Approximately 400 papers related to learning-type control are categorized. Statistical analysis of the resulting data reveals some promising fields for learning-type control. Finally, a flowchart based on the unique features of the different methods is presented as a guideline for choosing an appropriate learning-type control for different problems.
This article surveyed the major results in iterative learning control (ILC) analysis and design over the past two decades. Problems in stability, performance, learning transient behavior, and robustness were discussed along with four design techniques that have emerged as among the most popular. The content of this survey was selected to provide the reader with a broad perspective of the important ideas, potential, and limitations of ILC. Indeed, the maturing field of ILC includes many results and learning algorithms beyond the scope of this survey. Though beginning its third decade of active research, the field of ILC shows no sign of slowing down.
This paper presents an iterative learning approach for optimizing the course geometry in repetitive path following applications. In particular, we focus on airborne wind energy (AWE) systems. Our proposed algorithm consists of two key features. First, a recursive least squares (RLS) fit is used to construct an estimate of the behavior of the performance index. Second, an iteration-to-iteration path adaptation law is used to adjust the path shape in the direction of optimal performance. We propose two candidate update laws, both of which parallel the mathematical structure of common iterative learning control (ILC) update laws but replace the tracking-dependent terms with terms based on the performance index. We apply our formulation to the iterative crosswind path optimization of an AWE system, where the goal is to maximize the average power output over a figure-8 path. Using a physics-based AWE system model, we demonstrate that the proposed adaptation strategy successfully achieves convergence to near-optimal figure-8 paths for a variety of initial conditions under both constant and real wind profiles.
In pick and place operations a mechanism moves an object from an initial to a final pose and repeats, with frequencies of operation that can achieve 150 picks per minute. The paper presents the concept of natural motion for this kind of operations, where the basic idea is to add elastic elements to the mechanism and try to match the desired motion with the natural motion of the system. This concept was implemented in a multibody simulation of a five-bar linkage by using numerical optimization to find the required spring constants as well as the trajectory that minimize the torque on the motors. The required energy of the system using the concept of natural motion was compared with that of a typical trajectory, finding that the use of springs and natural motion reduces the energy consumption by 68 % per cycle.
In order to study design tradeoffs in the development of an AWE system, it is useful to develop a code to optimize a trajectory for arbitrary objective function and constraints. We present a procedure for using direct collocation to optimize such a trajectory where a model is specified as a set of differential-algebraic equations. The six degree of freedom single-kite, pumping-mode AWE model developed in Chap. 10 is summarized, and two typical periodic optimal control problems are formulated and solved: maximum power and number of cycles per retraction. Finally, a procedure for optimally transitioning between two fixed trajectories is presented.
Iterative Learning Control (ILC) is a technique for improving the performance of processes which repeatedly perform a task defined over a finite interval. Traditional ILC is used to improve trajectory tracking across an entire cycle period. However, there exist applications (pick n' place, surveillance) in which only specific locations are of particular interest. For these applications, point-to-point ILC results in improved tracking at the selected points and enhanced controller flexibility between locations. The additional control freedom can be used to maximize the performance of additional performance metrics. Pareto optimization is a multi-objective approach in which two or more conflicting objectives exist. In this paper, the point-to-point ILC framework is reformatted into a pareto optimization-based ILC approach in which two or more performance metrics are incorporated into the controller design. The modified framework enables the controller to leverage the additional control flexibility from a point-to-point approach to maximize multiple performance objectives. Convergence and performance analysis for the novel control framework is presented. Simulation results validate the control framework and demonstrate trade-offs in the performance metrics as a function of controller design.
Laser Metal Deposition (LMD) is a layer-based manufacturing process in which a laser and powdered metal are used to create a molten bead that is then traced along a path to create functional parts. The properties of the structure, including shape and material microstructure, are the result of complex interactions between the laser, the powder, the part substrate and other factors. Thus, a control algorithm is needed to accurately produce the designed part. However, feedback control of the process can create phase lag in the resulting control structure, which in turn can create dimensional instability. Additionally, the LMD process has been shown to change with part height or layer number. Taking these issues into account, a feed-forward, adaptive-type controller that changes with each fabricated layer, should be used. This paper first presents a dynamic model for the LMD process that incorporates the dependency of the process on part height. Then, an optimal Iterative Learning Process Control algorithm is presented to regulate the melt pool morphology of a deposited part using layer number as the iteration axis. A simulation study on the LMD process using the designed process controller shows that it is able to achieve good tracking performance.
Iterative learning control (ILC) is concerned with tracking a reference trajectory defined over a finite time duration, and is applied to systems which perform this action repeatedly. However, in many application domains the output is not critical at all points over the task duration. In this paper the facility to track an arbitrary subset of points is therefore introduced, and the additional flexibility this brings is used to address other control objectives in the framework of iterative learning. These comprise hard and soft constraints involving the system input, output and states. Experimental results using a robotic arm confirm that embedding constraints in the ILC framework leads to superior performance than can be obtained using standard ILC and an a priori specified reference.
We address the controller design and the trajectory generation for a quadrotor maneuvering in three dimensions in a tightly constrained setting typical of indoor environments. In such settings, it is necessary to allow for significant excursions of the attitude from the hover state and small angle approximations cannot be justified for the roll and pitch. We develop an algorithm that enables the real-time generation of optimal trajectories through a sequence of 3-D positions and yaw angles, while ensuring safe passage through specified corridors and satisfying constraints on velocities, accelerations and inputs. A nonlinear controller ensures the faithful tracking of these trajectories. Experimental results illustrate the application of the method to fast motion (5-10 body lengths/second) in three-dimensional slalom courses.
A Fourier series based learning controller for the tracking
control of nonlinear uncertain systems is proposed. The Fourier series
based learning controller consists of a PD part and a learning part. The
learning part generates a feedforward term based on the Fourier series
approximation of the PD output. By introducing a system input-output
(I/O) mapping matrix, the coupling effects of the PD output harmonics in
the Fourier space are considered in our algorithm instead of treating
them individually. Trajectory tracking experiments conducted on a belt
driven positioning table indicated that the proposed method was more
effective than the same type of controller without the I/O matrix
We proposed a new learning controller for decentralized tracking
control of nonlinear robot manipulators. When the desired trajectory of
each subsystem of the robot lasts for a finite duration, it can be
approximated by a Fourier series with constant harmonic magnitudes. For
each subsystem of the robot, a learning controller is designed to
individually control each harmonic component of the actual output,
although it is cross-related to other components in nonlinear systems.
The learning algorithm is designed such that each harmonic magnitude of
the actual output converges to that of the desired trajectory within the
system bandwidth. Since this decentralized learning controller is
designed in Fourier space instead of time domain, the system's
time-delay could be easily compensated. This learning controller is only
based on the local input and output information; no a priori structure
or parameters of the system model are required. The experimental results
on a 3-DOF direct-drive robot are presented
The article formulates an iterative learning control (ILC) design problem and modal analysis approach in the frequency domain that uses the Fourier transform. Following that, the controller design specifications are formulated in a frequency domain form. Next, the LQ/LTR controller design procedure is presented where the quadratic penalty weights are used to recover the design specifications. Finally, a simulated example of ILC in a highly nonlinear batch thermal process illustrates an application of the developed approach.
Multivariable norm optimal iterative learning control with auxiliary optimisation
- D H Owens
- C T Freeman
- B Chu
Iterative learning control
- bristow