Computed Torque Control Research Articles

Robust Hybrid Control Using Recurrent Wavelet- Neural-Network Sliding-Mode Controller for Two- Axis Motion Control System

In this paper, a robust hybrid control system (RHCS) for achieving high precision motion tracking performance of a two-axis motion control system is proposed. The proposed AHCS incorporating a recurrent wavelet-neuralnetwork controller (RWNNC) and a sliding-mode controller (SMC) to construct a RRWNNSMC. The two-axis motion control system is an x-y table of a computer numerical control machine that is driven by two field-oriented controlled permanent-magnet synchronous motors (PMSMs) servo drives. The RWNNC is used as the main motion tracking controller to mimic a perfect computed torque control law and the SMC controller is designed with adaptive bound estimation algorithm to compensate for the approximation error between the RWNNC and the ideal controller. The on-line learning algorithms of the connective weights, translations and dilations of the RWNNC are derived using Lyapunov stability analysis. A computer simulation and an experimental are developed to validate the effectiveness of the proposed RHCS. All control algorithms are implemented in a TMS320C31 DSP-based control computer. The simulation and experimental results using star and four leaves contours are provided to show the effectiveness of the RHCS. The motion tracking performance is significantly improved using the proposed RHCS and robustness to parameter variations, external disturbances, cross-coupled interference and frictional torque can be obtained as well for the two-axis motion control system.

Adaptive interaction torque-based AAN control for lower limb rehabilitation exoskeleton

In this paper, an adaptive interaction torque-based assist-as-needed (AITAAN) control method for the lower limb rehabilitation exoskeleton is proposed. Firstly, a desired input torque for the wearer’s lower limb is designed based on computed torque control (CTC). A nonlinear disturbance observer (NDO) is used to assess the lower limb muscle torque. Subtract the estimated muscle torque from the desired input torque, the exoskeleton only provides the remaining torque through interaction torque. Then, the interaction torque tracking problem can be converted to the exoskeleton trajectory tracking problem by using the spring–damper like dynamics model of the interaction force. A flexible boundary prescribed performance controller (PPC) is designed for the exoskeleton to achieve fast and accurate trajectory tracking. The coupled wearer-exoskeleton system is established in SolidWorks and imported to MATLAB/Simulink with SimMechanics. The AITAAN controller’s effectiveness and superiority were then verified through co-simulations.

Obstacle Avoidance Using CTC and Virtual Structure for Leader-Follower Formation on Mobile Robot

This research examined the development of the combination of virtual structure and leader-follower as an obstacle avoidance method in the formation control of a mobile robot. The formation of the robots are designed with the Separation Bearing Control (SBC) approach between the leader robot (RL) and the virtual robot (RV). The virtual robot is used as a virtual follower and a reference trajectory for the follower robot (RF). When the follower robot detects an obstacle, the follower robot trajectory is adjusted using a trajectory planner for obstacle avoidance. After passing the obstacle, the follower robot will track its position back in formation using virtual robot position and heading as reference. Leader robot and follower are perturbed by disturbances. In order to ensure the achievement of small error tracking, a controller is designed using the integration of kinematic and dynamics controllers with disturbance observer. The kinematic and dynamics controllers are designed using input-output linearisation (IOL) method and computed torque control (CTC). The effectiveness of the proposed method is verified by the simulation result.Keywords: CTC, leader follower, obstacle avoidance, SBC, virtual structure.

A device to reduce positioning errors due to the machine tool compliance

One of the main problems that large machine tool designers must face is the onset of deflection and vibration due to the forces involved during the process: the own weight of the elements of the machine, the cutting forces and the inertial forces. The last ones are especially relevant in the case of large and heavy machine tools with cantilever elements as rams or columns. To counteract these forces, the present work proposes the use of an inertial device, based on the rotation of two eccentric mases around the same axis. Hence, a simplified dynamic model of a column is first developed, and tested during a standard face milling operation. Then, the dynamic model of the device is also developed, and a Computed Torque Control is proposed to govern the action of the device. The simulations show that the use of this device has the potential to reduce drastically the effect of the inertial forces and even the lower frequency components of the cutting forces.

Tracking control of an uncertain heavy load robot based on super twisting sliding mode control and fuzzy compensator

AbstractThis paper presents a new combined strategy to control an uncertain heavy load robot with position disturbance caused by flexible foot, and the control strategy is realized only by position feedback. Firstly, deformation during motion is analyzed, and the position transformation generated by this deformation is treated as periodic position disturbance and non‐periodic position disturbance. Then, a control method combined by computed torque controller (CTC), super twisting sliding mode (STSM) controller, and fuzzy compensator is designed for the robot dynamic system to track ideal trajectory. Meanwhile, a proportional–integral–derivative (PID) controller based on CTC is designed as a comparison to verify the trajectory tracking performance and robustness of the combined strategy under external disturbances. Finally, simulation results show that CTC‐STSM is clearly found to converge faster and to show stronger ability to suppress interference than CTC‐PID. The addition of fuzzy compensator (CTC‐STSM‐Fuzzy) can further reduce the sliding mode chattering effect and improve the performance.

Robust Computed Torque Control for Uncertain Robotic Manipulators

يدرس هذا البحث السيطرة على ذراع روبوت حيث تم إقتراح بناء منظومة سيطرة بالاعتماد على طرق السيطرة الذكية. إذ إن ذراع الروبوت تمثل نظام لا خطيا وخاصة مع عدم القدرة على تمثيل النظام بشكل مثالي بسبب ازعاجات الحمل والإخطاء التي تحصل عند نمذجة النظام وهو مايسمى uncertainty system وهذا من خلال تحسين تحكم عزم الدورانCTC,استخدمت نظرية Lyapunov للحصول على استقرارية النظام. و تم اختبار أداء المتحكم المقترح بواسطه matlab - simulink ومقارنتها مع متحكم عزم الدوران المحسوب التقليدي, حيث توضح نتيجة المحاكاة قوة الطريقة المقترحة ومتانتها والحصول على تتبع مسار جيد وفق الاداء الطلوب.

Optimal adaptive computed torque control for haptic-teleoperation system with uncertain dynamics

This study aimed to eliminate dynamic uncertainty, one of the main problems of haptic teleoperation robotic systems. The optimal adaptive computed torque control method was used to overcome this problem. As is known, excellent stability and transparency are required in teleoperation systems. However, dynamic uncertainty that causes stability problems in the control of these systems also causes poor performance. In conventional adaptive computed torque control methods, updating the parameters of the system is generally discussed, but updating the control coefficients of vital importance in the control of the system is not considered. In the proposed method, an adaptation rule has been created to update uncertain parameters. In addition, the gray wolf optimization algorithm, one of the current optimization algorithms, has been proposed and applied to obtain the control coefficients of the system. The position tracking stability of the system was examined by using Lyapunov stability analysis method. As a result, both simulation and real-time optimal adaptive computational torque control method were used and bilateral position and force control was performed and the performance results of the system are obtained graphically and examined. Optimal adaptive computed torque control method obtained using the gray wolf optimization algorithm was used first in the literature search and success results have been obtained. In this regard, the authors have the idea that this work is an innovative aspect of both simulation and real time with the optimal adaptive computed torque control method.

Model-based joint and task space control strategies for a kinematically redundant parallel manipulator

AbstractOne alternative to overcome the presence of singularities within Parallel Manipulators’ workspace is kinematic redundancy. This design alternative can be realized by adding an extra active joint to a kinematic chain. Due to this addition, the IKM presents an infinite number of solutions requiring a redundancy resolution scheme. Moreover, Parallel Manipulators’ control may require complex strategies due to their coupled and complex dynamic and kinematic relations. In this work, a model-free, a joint space computed torque, and a hybrid joint-task-space computed torque control strategies are experimentally compared for a kinematically redundant parallel manipulator. The latter is a novel strategy that requires the measurement of the end-effector’s pose, which is performed by an eye-to-hand limited frame rate camera. The impact of up to three kinematic redundancy levels is also experimentally evaluated using prepositioning and ongoing positioning redundancy resolution schemes. The data are assessed by evaluating a prescribed trajectory executed using a planar kinematically redundant parallel manipulator. These results indicate that kinematic redundancy can not only be used as an alternative design for reducing the presence of singular regions, as claimed in the literature, but also be used along with model-based control strategies for improving dynamic performance and accuracy of parallel manipulators.

Robust Control Based Stability Analysis and Trajectory Tracking of Triple Link Robot Manipulator

In this paper the stability and tracking control for robot manipulator subjected to known parameters is proposed using robust control technique. The modelling of robot manipulator is obtained using Euler- Lagrange technique. Three link manipulators have been taken for the study of robust control techniques. Lyapunov based approach is used for stability analysis of triple link robot manipulator. The Ultimate upper bound parameter (UUBP) is estimated by the worst-case uncertainties subject to bounded conditions. The proposed robust control is also compared with computer torque control to show the superiority of the proposed control law.

Hybrid force/position control in workspace of robotic manipulator in uncertain environments based on adaptive fuzzy control

In this study, a novel hybrid force/position controller in workspace of robotic manipulator based on adaptive fuzzy control is developed to improve the controlling performance of force and position in contact with uncertain environments. The dynamic model of the robotic manipulator in joint space is converted to a dynamic model in workspace, which is consisted of the model of position-controlled subsystem and model of force-controlled subsystem. Furthermore, in the position-controlled subsystem, an adaptive fuzzy computed torque control is proposed by considering adaptive fuzzy control and conventional computed torque control (AFCTC), for compensating deviations caused by the presence of structured uncertainty and unstructured uncertainty. In the force-controlled subsystem, a fuzzy proportional integral control method (FPI) is proposed by fuzzy logic and conventional proportional integral method to improve the control performance. The asymptotic stability of the developed controller is proved by Lyapunov theorem. The simulation results show the preferable performance of the proposed controller (AFCTC-FPI) by comparison with adaptive fuzzy sliding mode control (AFSMC), adaptive network-based fuzzy inference system with proportion differential and integral (ANFIS-PD+I), computed torque control-proportion integral (CTC-PI), fuzzy proportional integral derivative (FPID), and proportional integral derivative (PID) in uncertain environments. Furthermore, in the experimental study, average position error with AFCTC-FPI is decreased by 87.14 % than that with PID, meanwhile, range of interaction force with AFCTC-FPI is reduced by 70.31% than that with PID. In summary, the experimental results also show the superior control accuracy of the proposed controller in real environment.

Research on a 3-DOF Planar Cable-Driven Parallel Robot Based on Fuzzy Adaptive PD Computed Torque Control

Cable-driven parallel robots (CDPR) with spatial configuration are widely used while ones with plannar configuration are rarely applied. Therefore, this paper studies the modeling and control characteristics of a three degree-of-freedom cable-driven planar parallel robot with great application prospects. Aiming at the shortcomings of the existing control methods towards CDPR, a new method based on fuzzy adaptive PD computing torque control is proposed which contains a reasonable optimal distribution of cable forces. To validate the method, the tracking control simulation research and analysis are carried out for the trajectory of high-order interpolation planning, the results of which show that the control method has favorable dynamic tracking accuracy and mechanical properties. Moreover, compared with the fixed-gain computed torque control, the proposed control method can overcome the influence of model inaccuracy more effectively.

Experimental and Simulation-Based Performance Analysis of a Computed Torque Control (CTC) Method Running on a Double Rotor Aeromechanical Testbed

Concept of closed loop control appears in many fields of engineering sciences, where the output quantity of some physical system must be forced to follow some prescribed function over time, e.g., when a robotic arm endpoint must track a desired trajectory or path given as timed series of spatial coordinates. The classic approach for solving this kind of problem involves a PID compensation block, and the necessary input signal for keeping the controlled process in the vicinity of the desired trajectory is calculated as the weighted sum of momentary deviation, deviation integral, and deviation derivative relative to the reference path. However, despite the obvious advantages, practical usability, and simplicity of the PID controllers, their performance is limited when they are utilized for controlling nonlinear systems. Even with linear systems, their proper operation requires an accurate system model and precise tuning process for finding the best weight values for the proportional, integral, and derivative effects, and the planned closed loop behavior might change significantly as the parameters of the controlled plant change over time. In this article, a computed torque-based controller is presented, which has only one adjustable parameter ensuring precise trajectory tracking even with significantly alternated model constants. The practical usability of the offered algorithm is evaluated and verified by simulations and experiments performed on a simple mechanical bi-rotor testbed playing the role of controlled plant.

Tracking and vibration control of a free-floating space manipulator system with flexible links and joints

The problem of modeling and controlling of a free-floating space manipulator with flexures in both links and joints is addressed in this study. A mathematical model of the system is developed by combining Lagrange’s equations and momentum conservation. The finite element method is introduced to discretize multi-links with complex cross-sections. In order to reduce the dimensions and maintain the precision of a rigid-flexible coupled system, an iterated improved reduction system method is adopted. Then, a novel composite control scheme for the reduced system is presented that uses the concept of integral manifolds and singular perturbation theory. Finally, an augmented computed torque controller is applied to the under-actuated slow subsystem to realize trajectory tracking in joint space, while a linear-quadratic controller is designed to damp out the vibration of joints and links. Numerical simulation results verified that the proposed hybrid controller can successfully suppress vibration and track trajectory at the same time.

Robust control of a cable-driven rehabilitation robot for lower and upper limbs

In this research, a redundant cable-driven robust rehabilitation robot has been proposed for helping and automating the proper function of the patient’s lower and upper limbs in the presence of uncertainties, disturbances, noise, and time delay using a new control algorithm to derive the best tracking with the least deviations. A new joint limit avoidance path-planning method is exerted while maintaining the bounds of upper and lower angles. Also, a new robust motion controller, namely computed-torque-like controller with a variable-structure compensator was applied to the system and compared with computed-torque controller outputs. Thus, showing the efficiency of the mentioned control algorithm in the presence of uncertainties, disturbances, noise, and time delay and its superior performance and robustness in spatial motions are the goals of this paper as well as taking advantage of a new path-planning approach.Firstly, the kinematic formulation of the cables is obtained. Then, a joint limit avoidance theory is used to apply upper and lower bounds for the joint angles. In the next step, Lagrangian dynamic equations for the 3D motions are derived. Subsequently, the positive and unilateral tension conditions in cable-driven systems are applied using null-space solutions. To have precise tracking and robustness with the existence of uncertainties, disturbances, noise, and time delay, a computed-torque control and robust computed-torque-like controller with a variable-structure compensator are utilized for the system. Stability analyses of the controllers are presented and the obtained results are compared for tracking a spatial reference trajectory.Ultimately, this controller witnessed an improvement in the lower limb with the existence of uncertainties and disturbances in terms of the robustness of the given method about 19.5 percent, and in cable forces about 17.1 percent. Improvements for the tracking errors and the control inputs were 10.8 and 7.3 percent in the presence of noise, and 7.3 and 8.6 percent in the presence of the time delay respectively. Similar results were obtained for the upper limb with 21 percent improvement in control inputs and 21.1 percent improvement in tracking performance respectively.

Identification and Control of a 3-X Cable-Driven Manipulator Inspired From the Bird’s Neck

AbstractThis paper is devoted to the control and identification of a manipulator with three anti-parallelogram joints in series, referred to as X-joints. Each X-joint is a tensegrity one-degree-of-freedom mechanism antagonistically actuated with cables and springs in parallel. As compared to manipulators built with simple revolute joints in series, manipulators with tensegrity X-joint offer a number of advantages, such as an intrinsic stability, variable stiffness, and lower inertia. This design was inspired by the musculosleketon architecture of the bird’s neck, which is known to be very dextrous. A test-bed prototype is presented and used to test computed torque control laws. Friction and cable elasticity are modeled and identified. Their effect on the performance of control laws is analyzed. It is shown that in the context of antagonistic actuation and lightweight design, friction plays a leading role and the significance of modeling cable elasticity is discussed.

Fault tolerant control for robotic manipulator using fractional-order backstepping fast terminal sliding mode control

In this paper, the problems of tracking control and finite-time stabilization of a high nonlinear system such as a robotic manipulator in the presence of actuator faults, uncertainties, and external disturbances are explored. In order to improve the performance of the system in the presence of actuator faults, uncertainties and external disturbances a novel fault tolerant control system based on fractional-order backstepping fast terminal sliding mode control is developed in this paper. The control system is developed by employing the results obtained from studies in the fields of fractional-order calculus, backstepping, sliding mode control, Mittag–Leffler stability, and finite-time Lyapunov stability. The performance of the suggested controller is then tested for a PUMA560 robot in which the first three joints are used. The simulation results validate the usefulness of the developed control approach in terms of accuracy of tracking, and convergence speed in the presence of disturbances, uncertainties and actuator faults. The trajectory tracking performance of the developed method is compared with other state of the art approaches such as conventional computed torque control, proportional integral derivative control and nonsingular fast terminal sliding mode control. The simulation results show that the proposed control approach performed better as compared to other control approaches in the presence of actuator faults, uncertainties, and disturbances.

Predictive Trajectory Tracking Algorithm of Underactuated Systems Based on the Calculus of Variations

Abstract The tracking control of underactuated systems is a challenging problem due to the structural differences compared to fully actuated systems. Contrarily to fully actuated systems, resolving the inverse kinematics problem of underactuated systems is not possible independently from the dynamic equations. Instead, the inverse dynamics must be addressed. It is common to extend the computed torque control (CTC) technique with servoconstraints. Besides the CTC's clearness, the stability of the system cannot be always guaranteed. A novel predictive controller (PC) is presented in this paper. Our PC applies the variational principle to design the motion of the system in order to achieve a stable motion with the lowest possible tracking error. To demonstrate the applicability and the performance of the PC method, a numerical study is presented for a planar manipulator resulting in about 20% RMS error compared to the CTC method from the literature.

Performance verification of different control schemes in human lower extremity rehabilitation robot

Many people experience temporary or permanent impairment sometime in their lifetime. Exoskeleton robot-based exercise machines for neurorehabilitation offer an attractive alternative for many disabled people. The performance of exoskeleton robot-based physiotherapy depends on the effectiveness of the robot control scheme. This paper examines the performance of three commonly used control algorithms in serial manipulators. Before examining the performance of the control schemes, it is essential to establish a model for plant dynamics. A dynamic model of the human lower extremity (HLE) is developed first. The Lagrange energy method is used for developing the HLE model. Since the dynamics of a serial manipulator is inherently nonlinear, a nonlinear control scheme would appear effective in dealing with the nonlinear robotic system. Two nonlinear control schemes (computed torque controller and sliding mode controller) and one linear controller (PID) are used to control the robot. The performance of the three control schemes is examined when disturbance torques and/or variations in robot parameters are present. The pros and cons of linear and nonlinear control schemes are discussed. Finally, a detailed discussion on controller selection criteria is presented, including how it can facilitate the selection of a suitable controller.

Nonlinear disturbance observer based flexible-boundary prescribed performance control for a lower limb exoskeleton

In this article, a nonlinear disturbance observer based flexible-boundary prescribed performance controller (NDOPPC) is proposed to achieve outstanding transient and steady-state tracking performance for a lower limb exoskeleton. To estimate and compensate the lumped disturbance consisting of unmodelled dynamics and interaction torques applied by the wearer, a nonlinear disturbance observer (NDO) is utilised. The prescribed performance of the trajectory tracking of the exoskeleton is guaranteed by constraining the tracking error between the preset upper and lower boundaries. The boundaries of the proposed NDOPPC can be asymmetric functions in various forms, which increases the flexibility of the prescribed performance. The proposed NDOPPC is designed based on backstepping and the stability is analysed with Lyapunov theorem. Comparative simulations have been conducted with MATLAB/Simulink. Compared to computed torque controller (CTC) and nonlinear disturbance observer based computed torque controller (NDOCTC), the obtained results of comparative simulations demonstrate the effectiveness and superiority of NDOPPC. Finally, different types of boundaries are considered to demonstrate the flexibility of the proposed NDOPPC.

A Non-Linear Continuous-Time Generalized Predictive Control for a Planar Cable-Driven Parallel Robot

This paper addresses a novel nonlinear algorithm for the trajectory tracking of a planar cable-driven parallel robot. In particular, we outline a nonlinear continuous-time generalized predictive control (NCGPC). The proposed controller design is based on the finite horizon continuous-time minimization of a quadratic predicted cost function. The tracking error in the receding horizon is approximated using a Taylor-series expansion. The main advantage of the proposed NCGPC is based on using an analytic solution, which can be truncated to a desired degree of order of the Taylor-series. This allows us to achieve a prediction horizon of NCGPC tracking performance. The description of the proposed NCGPC method is followed by a comparison between NCGPC and a conventional computed torque control (CTC) method. Robustness tests are performed by considering payload and parameter uncertainties for both controllers. Simulation results of NCGPC compared to the commonly used CTC prove the effectiveness and advantages of the proposed approach.