Adaptive Passivity-Based Multi-Task Tracking Control for Robotic Manipulators

This paper presents the current state of the art in the adaptive control of single rigid robotic manipulators in the constrained motion tasks. A complete mathematical model of a single rigid robotic manipulator in contact with dynamic environment is presented. The basic approaches in deriving the environment model are given. The significance of the dynamic environment in the scope of the stability problem of the whole system robot-dynamic environment is emphasized. A classification of the adaptive contact control concepts in manipulation robotics is presented. The main characteristics of the most important adaptive strategies in constrained manipulation are given. The advantages and the drawbacks of the presented methods are emphasized. The paper covers results published a few years ago, as well as some recent trends in this field. One important result in the stability analysis of robotic manipulators in the constrained motion tasks is reported. Finally, some concluding remarks are given and possible future investigation trends in adaptive control of robotic manipulators are indicated.

SUMMARYIn most dynamic adaptive control simulation of robotic manipulators, the Langrange–Euler (L–E) dynamic equations are first piecewise linearized about the desired reference and then discretized and rewritten in a state space form. This makes things very complicated and it is easy to make errors. What is more is that with a different reference this work must be done again. A new simulation scheme – Backward Recursive Self-Tuning Adaptive (BRSTA) – as it will be called, is suggested in this paper for adaptive controller design of robot manipulators. A two degree of freedom robot manipulator is used to verify the scheme in the condition of highly nonlinear and highly coupled system. A one degree of freedom robot manipulator is used for comparing both the forward and backward methods. The main advantages of this scheme include that it can be used for evaluating the self-tuning adaptive control laws and provide the initial process parameters for real-time control. And it is concluded here that the Newton–Euler (N–E) dynamic equations are equally well qualified as the Langrange–Euler (L-E) equations for the simulation of self-tuning adaptive control of robot manipulators.

In this study, we consider the output feedback position tracking control of robot manipulator via a fuzzy logic adaptation compensation method which enables the use of adaptive controller techniques for the full order but not fully linearly parameterized (LP) robot dynamics. Specifically we propose an output feedback position tracking controller that achieves semi-globally ultimately bounded link position tracking despite the lack of link velocity measurements and the non-LP uncertainties associated with the robot dynamics. Simulation results are presented to illustrate the performance of the controller

This paper studies the multiple-model based adaptive control of a robot manipulator moving in varying environments. The research problem is divided into two parts: the modeling of the system consisting of the robot manipulator and the varying environment, and the multiple-model based adaptive control of the robot manipulator. This paper considers the added mass, added moment of inertia, drag, and buoyancy as the environmental factors. In these dynamic models, the environmental factors and the mass, moment of inertia, and gravity of the robot are unknown parameters. By the linearity in the parameters property, we can write these parameters independently of the robot joint variables and thus can be estimated using an adaptive control law. After obtaining the system model, we adopt a multiple-model based adaptive control scheme. When the model of the robot changes, the parameter estimates can rapidly convert to a relatively closer one for the new true values. With a multiple-model based adaptive controller, the asymptotic tracking of the robot and the parameter boundedness are achieved, and the tracking is not disturbed by the variance of the environment parameters in the multiple model control case, which has better performance than the single model case.

In this paper, the global adaptive neural control with finite-time (FT) convergence learning performance for a general class of nonlinear robot manipulators has been investigated. The scheme proposed in this paper offers a subtle blend of neural controller with robust controller, which palliates the limitation of neural approximation region to ensure globally uniformly ultimately bounded (GUUB) stability by integrating a switching mechanism. Morever, the proposed scheme guarantees the estimated neural weights converging to optimal values in finite time by embedding an adaptive learning algorithm driven by the estimated weights error. The optimal weights obtained through the learning process of the neural networks (NNs) will be reused next time for repeated tasks, and can thus reduce computational load, improve transient performance and enhance robustness. The simulation studies have been carried out to demonstrate the superior performance of the controller in comparison to the conventional methods.

A switched adaptive controller is designed for robot manipulators with friction and changing loads. The nonlinear friction is depicted by a nonlinear friction model, and a switched nonlinear system is used to model the parameter jump caused by load change. Hyperstability theory is used in the designing procedure, which provides more options for adaptive laws than Lyapunov theory. In the presence of friction and changing loads, asymptotic tracking is achieved under arbitrary switching, which is not able to accomplish by a non-switched adaptive controller. The proposed method is validated by a simulation of a 2 degree of freedom manipulator.

In this paper, a controller for robot manipulators is proposed to guarantee the tracking error of the systems bounded by predefined decreasing boundary. In this control scheme, a multi-layer neural network is used to approximate the unknown non-linear items, and the robustifying control term is used to compensate the approximation errors. The adaptive laws of weights of the neural network and robustifying control term are derived based on the Lyapunov stability analysis, so that, under appropriate assumptions, the transient and steady-state error bounds can be guaranteed. Compared with the existing work, the adaptable parameters in the proposed method do not need an off-line training procedure for better approximation. Simulations performed on a two-link robot manipulator illustrate the developed controller and demonstrate its performance.

A new adaptation algorithm is presented for adaptive control of robot manipulators. The passivity property of the proposed algorithm is first established, then the stability is proved based on the passivity properties of the plant and those of the proposed algorithm. Because of the use of the past information and averaging effect, this algorithm gives a smoother tracking and parameter error in the presence of disturbances, and a parameter convergence under a weaker excitation condition. Computer simulations are presented to illustrate this effect. >

This paper presents a robust adaptive fuzzy neural controller (AFNC) suitable for motion control of multilink robot manipulators. The proposed controller has the following salient features: (1) self-organizing fuzzy neural structure, i.e., fuzzy control rules can be generated or deleted automatically according to their significance to the control system and the complexity of the mapped system and no predefined fuzzy rules are required; (2) fast online learning ability, i.e., no prescribed training models are needed for online learning and weights of the fuzzy neural controller are modified without any iterations; (3) fast convergence of tracking errors, i.e., manipulator joints can track the desired trajectories very quickly; (4) adaptive control, i.e., structure and parameters of the AFNC can be self-adaptive in the presence of disturbances to maintain high control performance; and (5) robust control, where asymptotic stability of the control system is established using the Lyapunov theorem. Experimental evaluation conducted on an industrial selectively compliant assembly robot arm demonstrates that excellent tracking performance can be achieved under time-varying conditions.

Adaptive control of robot manipulator is reviewed in this paper. General structure of the adaptive algorithms is presented with reference to the research carried out in recent years. General approach to the stability analysis of algorithms is highlighted. Extensive simulation study confirms the potential of adaptive control theory in dealing with the highly nonlinear, uncertain and complex robot arm dynamics.

The trajectory tracking problem of a class of robot manipulators is investigated by a simpler design adaptive neural network(NN) in this paper. The Radial Basis Function(RBF) NN is utilized to handle the uncertainties of the dynamics. Compared with the traditional schemes, the dimension of the input vectors of RBFNN is decrease from $4n$ to $3n$ but it have equal tracking and approximation performances. The output feedback control is considered when the velocity information cannot be obtained. Moreover, the weights of RBFNN converge to its optimal value by using the auxiliary filter to estimate weights error. The robot manipulator system is semi-globally and uniformly bounded which is proved by Lyapunov's theory. Simulation results demonstrate that the simpler controller has the same capability compared with the non-simplified method.

A new adaptive controller for robot manipulators is proposed. The new approach uses only position measurements. The main conclusions derived from the closed-loop system analysis are in two main results. In the first one, the global convergence of the position and velocity tracking errors is stated by using a condition that relates the viscous friction damping and the desired joint speed. In the second one, such a condition is dropped out but the local exponential stability of the closed-loop system is shown. To confirm the theoretical conclusions, a detailed experimental study in a two degrees-of-freedom direct-drive manipulator is provided, where the performance of the new controller is compared with respect to a known output feedback adaptive controller.

This paper presents two kinds of adaptive control schemes for robot manipulator which has the parametric uncertainties. In order to compensate these uncertainties, we use the NN (neural network system) that has the capability to approximate any nonlinear function over the compact input space. In the proposed control schemes, we need not derive the linear formulation of robot dynamic equation and tune the parameters. We also suggest the robust adaptive control laws in all proposed schemes for decreasing the effect of approximation error. To reduce the number of neural of network, we consider the properties of robot dynamics and the decomposition of the uncertainty function. The proposed controllers are robust not only to the structured uncertainty such as payload parameter, but also to the unstructured one such as friction model and disturbance. The validity of the control scheme is shown by computer simulations and experiment of dual-arm robot manipulator.

A decentralized adaptive control scheme is proposed for the trajectory tracking of a general n‐degree‐of‐freedom robot manipulator. The robot is considered as a set of decoupled second‐order systems with disturbances. The controller consists of feedforward from the desired trajectory based on the “inverse system” of the model, PID feedback from the actual trajectory, and auxiliary input for the compensation of the neglected terms in modeling in each subsystem. The gain is derived in diagonal matrix form, and is adjusted by the model reference adaptive control theory based on the Lyapunov's direct method. The result is high accuracy in path tracking despite the high speed, load change, and sudden torque disturbances. Numerical simulations on.a planar two‐link robot manipulator are presented to show the performance under various practical considerations.

This work proposes a non-singular fast terminal sliding mode control (NFTSMC) strategy based on the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm and a nonlinear disturbance observer (NDO) to address the issues of modeling errors, motion disturbances, and transmission friction in robotic manipulators. Firstly, a novel modular serial 5-DOF robotic manipulator configuration is designed, and its kinematic and dynamic models are established. Secondly, a nonlinear disturbance observer is employed to estimate the total disturbance of the system and apply feedforward compensation. Based on boundary layer technology, an improved NFTSMC method is proposed to accelerate the convergence of tracking errors, reduce chattering, and avoid singularity issues inherent in traditional terminal sliding mode control. The stability of the designed control system is proved using Lyapunov stability theory. Subsequently, a deep reinforcement learning (DRL) agent based on the TD3 algorithm is trained to adaptively adjust the control gains of the non-singular fast terminal sliding mode controller. The dynamic information of the robotic manipulator is used as the input to the TD3 agent, which searches for optimal controller parameters within a continuous action space. A composite reward function is designed to ensure the stable and efficient learning of the TD3 agent. Finally, the motion characteristics of three joints for the designed 5-DOF robotic manipulator are analyzed. The results show that compared to the non-singular fast terminal sliding mode control algorithm based on a nonlinear disturbance observer (NDONFT), the non-singular fast terminal sliding mode control algorithm integrating a nonlinear disturbance observer and the Twin Delayed Deep Deterministic Policy Gradient algorithm (TD3NDONFT) reduces the mean absolute error of position tracking for the three joints by 7.14%, 19.94%, and 6.14%, respectively, and reduces the mean absolute error of velocity tracking by 1.78%, 9.10%, and 2.11%, respectively. These results verify the effectiveness of the proposed algorithm in enhancing the trajectory tracking accuracy of the robotic manipulator under unknown time-varying disturbances and demonstrate its strong robustness against sudden disturbances.