Computed Torque Control Research Articles

Human‐centered active torque‐based AAN impedance control for lower limb patient‐exoskeleton coupling system in the rehabilitation

AbstractThis article presents a human‐centered active torque‐based assist‐as‐needed (ATAAN) impedance control for lower limb patient‐exoskeleton coupling system (LLPECS), which considers the coupling effects (e.g., elastic connections, human soft tissues). The proposed double loop structure controller is composed of the establishment of the ATAAN impedance model in the outer‐loop and an adaptive interaction torque‐based controller in the inner‐loop. In the outer‐loop, the patient's muscle torque is estimated by a nonlinear disturbance observer, and the estimated result is used to approximate the patient's active torque. The parameters of ATAAN impedance model are modulated according to the approximation of active torque and the patient's position error to achieve the assist‐as‐needed property. In the inner‐loop, the desired interaction torque, which is required to realize the target ATAAN impedance model, is designed by a robust computed torque controller. The desired trajectory of the exoskeleton is planned online according to the desired interaction torque with the dynamics model of coupling effects. The prescribed performance controller is utilized to achieve accurate trajectory tracking of the exoskeleton, which further enables the interaction torque to track the desired value. The stability of the system and realization of the target ATAAN impedance model are rigorously proved by the Lyapunov method. Co‐simulation experiments are conducted to demonstrate the superiority of the proposed method compared with other existing controllers and its robustness against modeling uncertainties. The effectiveness of the proposed method has been verified through experiments in rehabilitation scenarios.

Online reinforcement learning control of robotic arm in presence of high variation in friction forces

The operation and accuracy of industrial robotic arms can be negatively affected by significant fluctuations in friction forces within their joints, potentially resulting in financial and operational losses. To mitigate these issues, an online model-free reinforcement learning controller specifically designed to handle high variations in joints’ friction forces. To the best of our knowledge this is the first time where reinforcement learning controller is used to handle high friction variations in a robotic arm. Initially, the dynamic equations of the robotic arm are derived, verified and validated to ensure an accurate representation of real-world behaviour. The stability of the closed-loop system is analyzed using the Lyapunov second method. The performance of the proposed controller in terms of position tracking is compared against four commonly used controllers found in literature for similar applications: (i) nonlinear model-based computed torque controller, (ii) proportional-derivative controller, (iii) adaptive iterative learning controller and (iv) radial basis function neural network adaptive controller. Simulation results demonstrate that the reinforcement learning controller outperforms the other controllers in terms of tracking performance, even in the presence of significant variations in joint friction forces.

Design and Gait Control of an Active Lower Limb Exoskeleton for Walking Assistance

In the development of assistive lower-limb exoskeletons, both exoskeleton design, and gait control are critical for their successful applications. This paper introduces an assistive lower-limb exoskeleton (ALEXO) for active walking assistance. The development of the ALEXO including mechanical design, sensors and gait control is described. The exoskeleton adopts a hierarchical control. A 2-link model is built for dynamic analysis and lower-level control purposes. A trajectory tracking control method based on the computed torque control is proposed, in which physical interaction between the exoskeleton and the user is included. Simulations were conducted for different levels of interaction forces to verify the feasibility of the gait control. Moreover, walking trials of a healthy subject were performed, with muscle activities measured through EMG systems. Both simulation and system test results demonstrated the effectiveness of the developed exoskeleton with the proposed control method for walking assistance.

A Tangent Release Manipulation Controlled by a Dual-Arm Space Robot

As people further develop space with advanced technology, space robots have played a significant role in on-orbit servicing missions. Space robots can carry out more risky and complicated missions with less cost than astronauts. Dual-arm space robots can perform complex on-orbit space missions more effectively than single-arm space robots. Since the coupled dynamics between the free-floating base and the arms exist in space robots, accurate coordinate control of the base and the arms is essential. Spacecraft release missions have been proposed to berth/deberth a spacecraft to a space station. Based on the existing release missions, a tangent release strategy is introduced in this paper, which can release a space object in the tangent direction of the final link of a space manipulator. This strategy can control a dual-arm space robot to deploy cargo/spacecraft in variable directions in 3D space without thrusters and the associated fuel consumption. For instance, this tangent release operation can transport cargo or modules of large-scale spacecraft needing on-orbit assembly. Considering model uncertainties, robust controllers again model uncertainties that are used to control the dual-arm space robot with high accuracy. Hence, a robust sliding mode controller (SMC) is utilized to accurately control the space robot to carry out the proposed tangent release strategy. For comparison, we select a conventional computed torque control (CTC) implemented by a PD-type controller. In the simulations, the SMC performs better in tracking accuracy and robustness against the model uncertainties than the PD controller. Numerical simulations indicate the feasibility and effectiveness of the tangent release manipulation of a space object by a dual-arm space robot.

Torque control of a wheeled humanoid robot with dual redundant arms

Most of conventional controllers are prone to consume more computational time for controlling a wheeled humanoid robot. A nonlinear trajectory control of a wheeled humanoid robot using a model-based controller with less computational load and energy consumption is presented in this article. The upper body of the humanoid robot consists of two 6 degrees of freedom redundant arms, a three degrees of freedom torso and a two degrees of freedom neck. The nonholonomic mobile platform consists of two actuated wheels and two caster wheels. Nonlinearity of the robot dynamic model and coupling between various branches of the upper body are taken into account. The dynamic model derived using Newton–Euler approach along with decoupled Natural Orthogonal Complement matrix approach is used to derive dynamic equations of the upper body and the wheeled platform. Zero moment point based stability approach is used for verifying stable motion of the wheeled humanoid robot with minimum energy and time consumption to complete a task. The proposed computed torque controller is compared with other similar controllers developed for the same robot model to prove advantages of the proposed torque controller. Simulation results are experimentally validated with the real robot.

Dynamic parameter identification and adaptive control with trajectory scaling for robot-environment interaction.

To improve the force/position control performance of robots in contact with the environment, this paper proposes a control scheme comprising dynamic parameter identification, trajectory scaling, and computed-torque control based on adaptive parameter estimation. Based on the Newton-Euler method, the dynamic equation and its regression matrix is obtained, which is helpful to reduce the order of the model. Subsequently, the least-square method is implemented to calculate the values of the basic parameters of the dynamics. The identified dynamic parameters are used as initial values in the adaptive parameter estimation to obtain the torque, and trajectory scaling is applied to control the contact force between the robot and the environment. Finally, the dynamic parameter identification method and control algorithm are verified by conducting a simulation. The results show that the comprehensive application can help improve the control performance of robots.

Optimized Computer Torque Control and Dynamic Model of a Spatial Single Section Continuum robot

In this paper, an Optimized Computer Torque Controller (OCTC) based on dynamic model for a variable continuum robot is elaborately developed. Basically, the OCTC is applied for the first time on continuum robots in this paper aiming at finding out the required robot’s cables tension as well as the robot’s orientation/bending angles during tracking any prescribed trajectory. Interestingly, particle swarm optimization (PSO) is used to optimize CTC’s parameters which enables the robot to perform tasks with high precision and stability, even in the presence of external perturbations or uncertainties. The proposed controller is evaluated by testing its ability to track multiple trajectories even in the presence of external perturbations. The results of these simulations show that the OCTC controller exhibits superior performance in terms of settling time, overshoot, and robustness against disturbances for the continuum robots. It is noteworthy to say that CTC is able to capture the behavior of the robot quite rapidly when the robot faces a disturbance which perfectly fits in with real-world applications of continuum robot.

Adaptive Neural Trajectory Tracking Control for n-DOF Robotic Manipulators With State Constraints

This paper proposes an adaptive neural trajectory tracking control scheme for n-DOF robotic manipulators subjected to parameter variations, unknown functions, and time-varying external disturbances. First, the computed torque control (CTC) method is designed to reduce the system's nonlinearity. Second, radial basis function neural networks (RBFNNs) are constructed to approximate the uncertainties due to parameter variations and unknown functions. It's also important to note that the RBFNN's centers and widths are defined by state constraints. As a result of the nonlinear disturbance observer (NDO), the RBFNNs' approximation errors and disturbances are estimated to further improve tracking performance. The barrier Lyapunov function (BLF) ensures the closed-loop system's stability, guaranteeing tracking performance while preventing state constraint violation. Furthermore, sensitivity analysis provides a ranking of the importance of design parameters in influencing dynamic responses. Finally, simulations on a 7-DOF robotic manipulator are performed to validate the effectiveness of the proposed method.

Computed torque control and force analysis for mechanical leg with variable rotation axis powered by servo pneumatic muscle

It is difficult for a humanoid leg driven by two groups of antagonistic pneumatic muscles (PMs) to achieve a flexible humanoid gait, and its inherent strong coupling nonlinear characteristics make it hard to achieve good tracking performance in a large range of motion. Therefore, a four-bar linkage bionic knee joint structure with a variable axis and a double closed-loop servo position control strategy based on computed torque control are designed to improve anthropomorphic characteristics and the dynamic performance of the bionic mechanical leg powered by servo pneumatic muscle (SPM). Firstly, the relationship between the joint torque, the initial jump angle and the bounce height of the mechanical leg is established, and then we design a double-joint PM bionic mechanical leg containing a four-bar linkage mechanism of the knee joint. Secondly, a cascade position control strategy is developed, which consists of the outer position loop and the inner contraction force loop, and the mapping relationship is designed between joint torque and antagonistic PM contraction force. Finally, we further project bounce action timing of mechanical leg to realize the periodic jumping movement of the mechanical leg, and simulation and physical experiments of the real-style machine platform have been provided to demonstrate the effectiveness of the designed SPM controller.

Nieliniowe sterowanie predykcyjne ramion manipulatorów

The subject of the article are predictive control algorithms (of MPC type – Model Predictive Control) for rigid manipulator arms. MPC with a state-space model and with the latest disturbance and modeling error suppression technique was applied, which avoids dynamic disturbance modeling or resorting to additional disturbance cancellation techniques, such as SMC. First of all, the most computationally efficient MPC-NPL (Nonlinear Prediction and Linearization) algorithms are considered, in two versions: the first with constrained QP (Quadratic Programming) optimization and the second with explicit (analytical) optimization without constraints and satisfying a posteriori inequality constraints. For all considered algorithms, a comprehensive simulation analysis was carried out for a direct drive manipulator, with two kinds of disturbances: external and parametric. The obtained results were compared with those for the well-known CTC-PID algorithm (CTC – Computer Torque Control), showing better control quality with MPC algorithms. In addition, the influence of the length of the sampling period and of the computational delay on control quality was investigated, which is important for model-based algorithms with fast sampling.

Design computed torque control for Stewart platform with uncertainty to the rehabilitation of patients with leg disabilities

Physiotherapy is a treatment that may be required permanently by many patients. As a result, a robot that can execute physiotherapy exercises for the legs like a professional therapist with adequate performance and acceptable safety may be efficient and widely used. In this study, a robust control system for a Stewart platform with six degrees of freedom is provided. First, the Newton-Euler approach is used in conjunction with a methodology and some simplification tools to achieve explicit dynamics formulation for the Stewart platform. For the primary application of this research, which is to follow the specified trajectory of ankle rehabilitation, computed torque control law (CTCL) and polynomial chaos expansion (PCE) were used to examine and consider any uncertainty in geometric and physical parameters. In fact, this strategy integrated the uncertainties with CTCL using PCE. The suggested PCE-based CTCL eliminates the system’s nonlinearity by applying feedback linearization to evaluate generalized driving forces; hence, the nondeterministic multi-body system follows the desired direction. Uncertainties in the patient’s foot as well as the main diameter parameters of the moment of inertia of the upper platform of the Stewart robot with various uniform, beta, and normal distributions, have been analyzed. The PCE technique’s results were compared to the Monte Carlo method’s outcomes, and the strengths and weaknesses of each method were investigated. In brief, the PCE method operated far better than the Monte Carlo (MC) method in speed, accuracy, and numerical volume.

Energy efficient robots based on structures with tensegrity features and cable-driven mechanisms

The paper presents concept of energy efficient motion control of robots and other machines based on structures with tensegrity features and/or cable-driven mechanisms. The essence of concept is generalization of so called eigenmotion idea for these multi-DOF complex mechanisms. The term eigenmotion here refers to a motion of a mechanism in which the constant sum of kinetic and potential energy is maximally preserved. The operation of the drives is ideally used only to eliminate passive resistances and to minimize deviations of motion from the required trajectory. The main advantage of mechanisms with tensegrity features and cable-driven ones is a relatively high number of elements such as springs, active cables or variable bodies, whose energy absorbing properties can be suitably adjusted during design and some also continuously during operation. The variability of attainable eigenmotion trajectories of these types of mechanisms can be further extended thanks to number of drives higher than number of end-effector degrees of freedom. The concept is demonstrated on two planar systems, one structure with tensegrity features and one serial–parallel cable-driven robot. The examples show the optimization of the parameters to achieve the eigenmotion properties on the given trajectories, as well as the change of the eigenmotion trajectory by changing the adjustable parameters. The final control of mechanical models along energy efficient trajectories is realized by computed torque control method.

Trajectory Tracking and Adaptive Fuzzy Vibration Control of Multilink Space Manipulators with Experimental Validation

This paper investigates the problem of modeling and controlling a space manipulator system with flexible joints and links. The dynamic model of the flexible manipulator system is derived by using the Lagrange equation and the floating frame of reference formulation, where the assumed mode method is adopted to discretize flexible links, while the flexible joints are regarded as linear torsion springs. The natural characteristics of a single flexible link manipulator, under three different boundary conditions, are compared to reveal the effect of the flexibility of joints on the manipulator system and to choose suitable assumed modes. Furthermore, singular perturbation theory is introduced to decompose the system into a slow subsystem that describes the rigid-body motion, and a fast subsystem that describes the elastic vibration. Since the system is underactuated, a compound control strategy, which consists of the underactuated computed torque controller and the adaptive fuzzy controller, is presented to improve the accuracy of the trajectory tracking of the flexible joints and to suppress the elastic vibration of the flexible links, in the meantime. Both numerical simulation and experimentation are performed to verify the effectiveness of the proposed compound controller, and a comparison with the proportional-derivative (PD) controller is provided to highlight its superiority in suppressing the residual vibration of the tip.

NARMA-L2–based online computed torque control for robotic manipulators

Computed torque is an effective method for control of robotic manipulators. In this paper, a novel approach is proposed for computed torque control method, and also, it is integrated with online least squares support vector regression algorithm. The motive is to improve control performance and to build an adaptive architecture where no prior information on system model is required; the model is obtained continuously using a machine learning technique. There are two main contributions of the proposed work: the first one is the formulation of the computed torque control law using the nonlinear autoregressive moving average-L2 control methodology and the second contribution is the implementation of online least squares support vector regression method in estimating the dynamical model of the system and calculating the control law. The performance of the proposed method has been evaluated by simulations on a two-link robotic arm. The robustness of the method has also been evaluated for cases with disturbance and model uncertainty. Comparison with an existing computed torque control approach in the literature demonstrates the superiority of the proposed approach. Thus, it can be concluded that the method can be effectively used for first-order and second-order nonlinear systems without inherent instability.

Dynamic Modeling and Model-Based Control with Neural Network-Based Compensation of a Five Degrees-of-Freedom Parallel Mechanism

In this paper, a spatial parallel mechanism with five degrees of freedom is studied in order to provide a promising dynamic model for the control design. According to the inverse kinematics of the mechanism, the dynamic model is derived by using the Lagrangian method, and the co-simulation using MSC ADAMS and MATLAB/Simulink is adopted to verify the established dynamic model. Then the pre-trained deep neural network (DNN) is introduced to predict the real-time state of the end-effector of the mechanism. Compared to the traditional Newton’s method, the DNN method reduces the cost of the forward kinematics calculation while ensuring prediction accuracy, which enables the dynamic compensation based on feedback signals. Furthermore, the computed torque control with DNN-based feedback compensation is implemented for the trajectory tracking of the mechanism. The simulations show that, in the most complicated case that involves friction and external disturbance, the proposed controller has better tracking performance. The results indicate the necessity of dynamic modeling in the design of control with high precision.

Intelligent Computed Torque Control With Recurrent Legendre Fuzzy Neural Network for Permanent-Magnet Assisted Synchronous Reluctance Motor

The goal of this research is to develop an intelligent controlled permanent-magnet assisted synchronous reluctance motor (PMASynRM) drive system by utilizing an intelligent computed torque control with recurrent Legendre fuzzy neural network (ICTCRLFNN), in order to adjust the nonlinear and time-varying control specifications of the motor. The team first proposes an ANSYS Maxwell-2D dynamic model that contains a maximum torque per ampere (MTPA) control PMASynRM drive. A lookup table (LUT) is composed of the finite element analysis (FEA) results, which bring about the current angle of command within the MTPA. Subsequently, the team designs a computed torque control (CTC) system to control the speed reference command. Creating a working CTC for practical applications is quite complex because the detailed system dynamics, which includes the unpredictability of the PMASynRM drive system, is not available beforehand. Thus, this study suggests that a recurrent Legendre fuzzy neural network (RLFNN) can act as a close substitute for the CTC to resolve its existing complications. Furthermore, the team modifies an adaptive compensator to proactively adjust for the potential calculated deviance of the RLFNN. Asymptotical stability is assured by using the Lyapunov stability method, which generates the RLFNN’s online learning algorithms. This study concludes that certain experimental results verify the effective and robust qualities of the suggested ICTCRLFNN controlled PMASynRM drive.

Comparison Between Some Nonlinear Controllers for the Position Control of Lagrangian-type Robotic Systems

This work addresses the set-point control problem of the position of fully-actuated Lagrangian-type robotic systems by means of some nonlinear control laws. We adopt four different nonlinear control laws: the PD plus gravity compensation controller, the PD plus desired gravity compensation controller, the computed-torque controller and the augmented PD plus gravity compensation controller. An in-depth comparison between these control laws and their application is achieved. Indeed, using some properties, we design some conditions on the feedback gains of the nonlinear controllers ensuring the stability in the closed loop of the zero-equilibrium point and its uniqueness. At the end of this work, we adopt a planar two-degree-of-freedom manipulator robot to illustrate via simulation the difference between and the efficiency of the adopted nonlinear controllers.

Control Improvement of Low-Cost Cast Aluminium Robotic Arm Using Arduino Based Computed Torque Control

Gravity causes non-linearity in position control of an articulated industrial robotic arm. Especially for a joint position control of a robot’s shoulder and elbow that works parallel with the gravity direction. To overcome the problem, Computed Torque Control algorithm was implemented. This algorithm linearized the feedback, so a regular linear Proportional Derivative controller can be implemented. The contribution of this research is to find an effective controller to control a heavy weight low-cost robotic arm link/body using low-cost controller such as Arduino. A Computed Torque Control was implemented to control the shoulder joint of an articulated robotic arm. This joint is the most affected joint by the gravity. It works along the vertical plane, and loaded by the rest of the arm and the robot’s load. The proposed controller was compared to a Proportional Integral Derivative (PID) Controller and a Cascade PID Controller. The experiment showed that the Computed Torque Controller can control the position of the arm properly both in the direction along or against the gravity. A linear PID controller could not bring the arm to the set point when it moves against the gravity, but it works well when the arm moves in the opposite direction. A Cascade PID controller has an overshot when the arm moves along the gravity. But it works properly when it moves up against the gravity. A Computed Torque Control works well in both directions even in the presence of gravity force because it includes the gravity on its algorithm.

Robust PID optimal tuning of a Delta parallel robot based on a hybrid optimization algorithm of particle swarm optimization and differential evolution

AbstractIn this paper, we propose an approach to tune optimal parameters of a robust PID controller by means of computed torque control (CTC) strategy for trajectory tracking of a Delta parallel robot, using a hybrid optimization algorithm of Particle Swarm Optimization (PSO) and differential evolution (DE). It differs from previous works that they propose robust PID controller parameters tuning based on conventional gradient-based optimization algorithms and apply them to process control. First, we reduce the tuning problem of a robust PID controller with CTC strategy satisfying requirements including robustness and disturbance attenuation to an optimization problem with nonlinear constraints by considering the nonlinear dynamic model of a Delta parallel robot. Second, we set up the design characteristics for the trajectory tracking of a Delta parallel robot. Then, we propose a robust PID controller in a way of obtaining the global optimization solution of the nonlinear optimization problem by running a PSO-DE hybrid optimization algorithm of finding the global optimal solution by maintaining the diversity of swarm during evolution based on the evolution of cognitive experience. Simulation and experimental results demonstrate that the proposed controller outperforms previous works with respect to robust performance and active disturbance attenuation when it is applied to tracking control of a Delta parallel robot.

The variable-inertia modified computed-torque control of robot manipulators

The variable-inertia modified computed-torque control of robot manipulators