Optimal Control of a Robot Manipulator During a Load-Unload Operating Cycle

To consider the energy saving during the robot motion, optimal posture control method for a robot manipulator is proposed. The Chebyshev-Gauss (CG) Pseudo-spectral method is used to discuss the problem with the energy optimal control. The Lagrange interpolation of barycentre is adopted to approximate the state and control variables. The continuous optimal control problem can be converted to a discrete nonlinear programming (NLP) problem. And then it can be solved by Sequential Quadratic Programming (SQP) algorithm. The simulation results of optimal energy control make the robot manipulator from the initial state to the desired terminal posture successfully. The terminal angular velocity of each link is also meet the predetermined value. The control law does not exceed the preset boundary of control.

This paper proposes a novel reward based Single Network Adaptive Critic (SNAC) architecture for optimal kinematic control of a redundant robot manipulator. At first, the closed-loop positioning task is formulated as a discrete-time input affine system. The optimal controller is then derived for the reward based cost function with the adaptive critic. The notion of goal-directed optimal behavior is captured by defining a performance measure or cost function in terms of discounted reward function. The reward function is chosen to deliberately speed up convergence of the closed loop positioning error. The performance of the proposed reward based SNAC architecture is compared with standard quadratic cost based SNAC for kinematic control of the redundant robot manipulator. The results show faster convergence of the overall trajectory cost. The proposed kinematic solution has been validated in simulations and experimentally executed using 6 degrees of freedom (DOF) Universal Robot (UR) 10 robot manipulator for both regulation and tracking.

Optimal control strategies are very useful in manipulation problems of robots. However, most optimal controls are highly sensitive to plant-parameter variations and disturbances because optimal controls try to pick up exact information from the mathematical models in order to realize the best performance. We recognize that difficulties are involved in exact modeling of plants and prevention of disturbances. Therefore, we need a optimal control method with low sensitivity. The ideas of closed-loop control system design using LQG/TR techniques (linear quadratic Gaussian control with transfer recovery) are discussed in this paper. We combine optimal controls and LQG/TR control into two-degrees-of-freedom control systems to reduce the sensitivities of optimal control strategies. In digital simulations, we obtained excellent results of a two-link manipulator in an optimal time control problem using our method. Some modeling errors and considerable disturbances are allowed in the method. Thus, we can realize good performances in practical manipulation problems using our method.

This paper presents a diffusion-based learning approach to generalize optimal control of a robot manipulator over a bounded work space. Generally, optimal control requires to solve a two point boundary value problem with respect to increase and decrease of time and is very difficult to be solved analytically. In our approach, we first assume that, for some sets of initial and desired terminal conditions of the robots positions we already have the numerical optimal solutions (for example, using some complex numerical computation techniques). Then by using radial basis function network we parameterize these control inputs by a set of weight matrixes. Finally, we apply our diffusion-based algorithm to generalize these weight matrixes for different terminal position conditions. This approach greatly reduced computation cost for the robot to find its optimal control. In addition, since diffusion-based algorithm is a parallel distributed learning approach which only requires local interaction between the nodes of a learning network (a lattice), it can be realized by resent IC hardware technology easily. Computer simulations of a 2-DOF robot arm show the effectiveness of our approach.

This paper presents an event-triggered model predictive control (MPC) strategy with learning terminal cost for robotic manipulators containing model uncertainty and input constraints. In the proposed MPC structure, an adaptive predictive model for the robotic system is established by radial basis function neural networks (RBFNNs) firstly. Then, a terminal cost adjusted by the global learning mechanism is constructed. Both global steady-state optimization and transient fast convergence are achieved by adding the learning terminal cost to the MPC scheme. After that, a triggering condition of the MPC solving is developed based on the predictive model’s weights and the predictive tracking error. Besides, the condition to avoid Zeno behavior is obtained. The recursive feasibility of the proposed MPC strategy is verified, and the ultimately uniformly boundedness (UUB) of all variables is proved according to the Lyapunov theorem. Finally, experiments based on an xMate7 Pro robot are conducted to demonstrate the effectiveness of the presented method. Note to Practitioners—The tracking control of robotic manipulators is a common and important problem in industrial applications, such as grasping, loading, unloading, et al. There exist some limitations in existing control methods. For example, general control strategies such as adaptive control, sliding mode control neglect the balance between control costs and expected performance; existing optimal control approaches rarely consider global steady-state optimization and transient fast convergence under the influence of model uncertainty. This paper is motivated by these limitations of robotic control design and inspired by model predictive control and optimal control theory. It develops a novel strategy for tracking control of robotic manipulators, which includes three following items: (1) adopt an approximation model constructed by neural networks as the predictive model for estimating the robotic system; (2) introduce a critic network into the terminal cost of the objective function of MPC for learning global optimal solution; (3) establish an event-triggered mechanism for solving of the optimization problem. The proposed method is verified by experimental results. In our future work, the proposed control strategy will be applied to more industrial processes.

1 A Survey on Computational Optimal Control.- Issues in the Direct Transcription of Optimal Control Problems to Sparse Nonlinear Programs.- Optimization in Control of Robots.- Large-scale SQP Methods and their Application in Trajectory Optimization.- Solving Optimal Control and Pursuit-Evasion Game Problems of High Complexity.- 2 Theoretical Aspects of Optimal Control and Nonlinear Programming.- Continuation Methods In Boundary Value Problems.- Second Order Optimality Conditions for Singular Extremals.- Synthesis of Adaptive Optimal Controls for Linear Dynamic Systems.- Control Applications of Reduced SQP Methods.- Time Optimal Control of Mechanical Systems.- 3 Algorithms for Optimal Control Calculations.- Second Order Algorithm for Time Optimal Control of a Linear System.- An SQP-type Solution Method for Constrained Discrete-Time Optimal Control Problems.- Numerical Methods for Solving Differential Games, Prospective Applications to Technical Problems.- Construction of the Optimal Feedback Controller for Constrained Optimal Control Problems with Unknown Disturbances.- Repetitive Optimization for Predictive Control of Dynamic Systems under Uncertainty.- Optimal Control of Multistage Systems Described by High-Index Differential-Algebraic Equations.- A New Class of a High Order Interior Point Method for the Solution of Convex Semiinfinite Optimization Problems.- A Structured Interior Point SQP Method for Nonlinear Optimal Control Problems.- 4 Software for Optimal Control Calculations.- Automated Approach for Optimizing Dynamic Systems.- ANDECS: A Computation Environment for Control Applications of Optimization.- Application of Automatic Differentiation to Optimal Control Problems.- OCCAL: A mixed symbolic-numeric Optimal Control CALculator.- 5 Applications of Optimal Control.- A Robotic Satellite with Simplified Design.- Nonlinear Control under Constraints of a Biological System.- An Object-Oriented Approach to Optimally Describe and Specify a SCADA System Applied to a Power Network.- Near-Optimal Flight Trajectories Generated by Neural Networks.- Performance of a Feedback Method with Respect to Changes in the Air-Density during the Ascent of a Two-Stage-To-Orbit Vehicle.- Linear Optimal Control for Reentry Flight.- Steady-State Modelling of Turbine Engine with Controllers.- Shortest Paths for Satellite Mounted Robot Manipulators.- Optimal Control of the Industrial Robot Manutec r3.

Optimal Protection from Impact, Shock, and Vibration

A new nonlinear optimal control method is proposed for solving the problem of control and stabilization of a two-link robotic manipulator where the first link is rigid and the second link is flexible. The dynamic model of this robot describes both the rotational motion of the two links and the vibration modes which are excited at the flexible link. The control and stabilization problem of this 2-DOF rigid-flexible robot is nontrivial due to complex nonlinear dynamics and underactuation. To apply the proposed nonlinear optimal control method, the dynamic model of the two-link rigid-flexible robotic manipulator undergoes first approximate linearization around a temporary operating point that is updated at each iteration of the control algorithm. The linearization takes place through first-order Taylor series expansion and through the computation of the Jacobian matrices of the flexible manipulator’s state-space description. For the approximately linearized model of the two-link rigid-flexible robot, an H-infinity feedback controller is designed. Actually, the H-infinity controller stands for the solution of the optimal control problem for the rigid-flexible robot under uncertainty and external perturbations. For the computation of the feedback gains of the H-infinity controller, an algebraic Riccati equation is solved at each time-step of the control method. The stability properties of the control algorithm are proven through Lyapunov analysis. First, it is shown that the control scheme achieves H-infinity tracking performance which signifies robustness for the control loop of the two-link rigid-flexible robot under uncertainties and external perturbations. Next, it is also shown that the control loop of the 2-DOF rigid-flexible robot is globally asymptotically stable. The proposed control method achieves fast and accurate tracking of setpoints under moderate variations of the control inputs. The concept of the proposed nonlinear optimal control method has been to approximate locally and at each sampling interval the nonlinear dynamics of the rigid-flexible robotic manipulator by an equivalent linear state-space description and to solve the H-infinity control problem for the linearized model. Finally, the control inputs are applied to the initial nonlinear dynamics and stability proof is given for the initial nonlinear state-space model.

Robotics is a relatively new and evolving technology being applied to manufacturing automation and is fast replacing the special-purpose machines or hard automation as it is often called. Demands for higher productivity, better and uniform quality products, and better working environments are primary reasons for its development. An industrial robot is a multifunctional and computer-controlled mechanical manipulator exhibiting a complex and highly nonlinear behavior. Even though most current robots have anthropomorphic configurations, they have far inferior manipulating abilities compared to humans. A great deal of research effort is presently being directed toward improving their overall performance by using optimal mechanical structures and control strategies. The optimal design of robot manipulators can include kinematic performance characteristics such as workspace, accuracy, repeatability, and redundancy. The static load capacity as well as dynamic criteria such as generalized inertia ellipsoid, dynamic manipulability, and vibratory response have also been considered in the design stages. The optimal control problems typically involve trajectory planning, time-optimal control, energy-optimal control, and mixed-optimal control. The constraints in a robot manipulator design problem usually involve link stresses, actuator torques, elastic deformation of links, and collision avoidance. This paper presents a review of the literature on the issues of optimum design and control of robotic manipulators and also the various optimization techniques currently available for application to robotics.

We present a new optimal control approach to robust control of robot manipulators in the framework of state dependent Riccati equation (SDRE) technique. To treat this highly nonlinear control system, we formulate it as a nonlinear optimal regulator problem. SDRE technique was used to synthesize an optimal controller to this class of robot control problem. We also synthesize a neural network based extra controller to achieve the robustness in the presence of the parameter uncertainties. A typical two-link robot position control problem was studied to show the effectiveness of SDRE approach and robust extra control design to robotic application.

In recent years the advanced micro-electronics techniques are contributing to the progress of industrial robotic manipulators. Direct digital control of manipulators is one of the most promising applications of a new generation of computers. Improved control techniques are required for the digital control to attain a fine performance of manipulators. This paper proposes a software servo control system for linear quadratic optimal control with I-action (LQI control) for a good performance over a wide range of motions and payloads. The effectiveness of this control system is demonstrated in several simulations and experimental results.

This paper presents an optimal feedback controller capable of driving a non‐linear control system from an arbitrary initial state to a fixed final state in minimum time. The controller is based on a feedforward multilayer neural network trained repeatedly using open‐loop optimal control data which densely span the field of extremals of the non‐linear system. The effectiveness of the controller is clearly demonstrated by a simulation on a two‐link robot manipulator. The effect of sensor/actuator noise and parameter variation is also included to confirm the robustness of the controller.

Nowadays active vibration suppression of flexible manipulators is important in many engineering applications, such as robot manipulators and high-speed flexible mechanisms. The demand for short settling time and low energy consumption of the vibration suppression has necessitated the consideration to optimal control. For a wide range of operating conditions, the fixed optimal parameters determined for a control algorithm might not produce the highest performance. Hence, a self-tuning optimal control method for a flexible manipulator should be used to enhance the performance. This method can tune itself to the optimal parameters on the basis of the initial maximum responses of the controlled system. In this study, the multi-objective genetic algorithm is used to search for optimal parameters with regard to positive position feedback, thereby minimizing the settling time and energy consumption multi-objective functions. The experimental results reveal that the energy consumption can be reduced significantly while the settling time is still slightly increased.

This paper presents a survey of the most recent literature developments in the field of computational guidance and control for space applications. In recent years, the space sector has changed significantly, shifting towards solutions requiring increased performance and autonomy. This change has also been accelerated by the technical and economic needs of the new space approach. However, traditional guidance and control techniques cannot always meet the increasing requirements of autonomy and performance. For this reason, computational guidance and control has become of increasing interest to the aerospace sector. In contrast to traditional guidance and control, computational guidance and control generates commands in real time by using on-board numerical computation. It represents, therefore, a fundamental step on the way to system autonomy and autonomous operations, with the potential to increase system capabilities and reduce operational costs. On-board computation introduces, however, a series of challenges, including the need to develop algorithms which are computationally efficient, reliable and robust. The literature has classified computational guidance and control techniques into two major categories, namely model-based and data-based. The model-based category encompasses all techniques in which the guidance and control laws are explicitly related to the system dynamic and kinematic models. On the contrary, data-based techniques infer guidance and control laws from a set of data, derived from the models, but do not explicitly use such models in the algorithm itself. Model-based guidance and control includes optimal control, model predictive control and convex optimisation. For the specific case of space attitude re-orientation manoeuvres, additional techniques are path planning and artificial potential functions. The general concept behind the Model Predictive Control (MPC) framework is to solve an optimal control problem repeatedly, for example whenever new measurements are available. The MPC implements only the first element of the returned solution, and the process is then repeated. By doing so, the system is better able to cope autonomously with model uncertainties, failures, or errors. For spacecraft with limited on-board capability, having to repeatedly solve an optimisation problem on-board could represent a challenge. In this case, explicit implementations of the MPC have been proposed, in which the guidance and control laws are precomputed offline and implemented on-board using look-up tables or simple functions. If the optimal control problem of the MPC is convex, or if it can be convexified, convex optimisation can be used directly. If the problem cannot be convexified, the solution can be found by sequentially solving a convex approximation of the original non-convex problem. Convex optimisation can be used either repeatedly in the context of an MPC framework, or as a single function call to generate guidance and control laws, e.g. at the beginning of an attitude re-orientation manoeuvre. Convex optimisation has received increased attention in recent years, also due to its suitability to on-board implementation. In fact, if the optimal control problem is convex, it can be solved reliably and efficiently on-board. Convex optimisation has been successfully applied to the space sector with the notable examples of the SpaceX rocket booster landing and of the Mars pinpoint landing demonstration aboard the Masten Xombie sounding rocket. Model-based guidance techniques, not based on optimisation, have been increasingly explored in recent years, as guidance strategies employed in other engineering fields, such as robotics, are being applied to spacecraft. Among these strategies, of particular importance are path planning and artificial potential field methods, due to their applicability to spacecraft autonomous attitude manoeuvres. Path planning algorithms have been applied for decades to ground vehicles and robotic manipulators. These algorithms consist of techniques to find the best route between two points of a graph representing the search space of a problem. For spacecraft re-orientation applications, the literature has proposed different attitude representation conventions and various cost functions associated to the graph search algorithm. Each approach comes with advantages and disadvantages, which will be analysed in the paper. Along with path planning, Artificial Potential Function (APF) techniques have been developed in the field of robotics, and are now also considered for space applications, to track or maintain a specific reference under a set of constraints. The main idea behind these methods is to synthetise the controller using a potential function. This function is specifically built to grant asymptotic stability to the system, according to Lyapunov’s second stability theorem. This formulation grants flexibility to accommodate system constraints, in a computationally light-weight and efficient manner. Data-based guidance and control laws are mainly based on Artificial Intelligence (AI) technologies, and generate guidance commands after training an algorithm with a large set of data. The interest of the space sector towards AI has accelerated in the last years due to the greater maturity of the technology. Some of the most powerful examples lie in the area of machine learning, like reinforcement learning, supervised learning and deep learning. These algorithms are used to extract patterns from large amounts of data derived from complex nonlinear dynamical and kinematical models. Examples of such data can be numerical solutions of an optimal control problem. The patterns extracted from the data allow the system to identify, in a short computational time, the critical parameters needed to relate the state and control variables. Creating a sufficiently large dataset for training the algorithm requires a considerable computational effort, though, and for certain methods optimality cannot be guaranteed due to the lack of theoretical support derived from the optimality conditions. Advancements made in the last years span several research directions and open a wide variety of opportunities and challenges, which need to be examined to guide further exploration. In this paper, both model-based and data-based techniques and applications are presented. The considered techniques include model predictive control, convex optimisation and machine learning. In addition, for the implementation of autonomous attitude manoeuvres, path planning methods and artificial potential function methods are analysed. These techniques have been applied, in the literature, to a range of different applications. The applications discussed in this paper include, in addition to attitude manoeuvres, powered descent landing guidance, low-thrust orbital transfers, proximity operations and station keeping.

Optimal trajectory tracking control of robotic manipulator system added by discrete-time fast terminal sliding mode predictive approach.