Task-space Control Research Articles

Stiff and safe task-space position and attitude controller for robotic manipulators

This paper proposes a stiff and safe task-space position and attitude control scheme for robotic manipulators. This study extends the work of Kikuuwe et al’s. (2006) velocity-bounding proxy-based sliding mode control by explicitly addressing the attitude part. The proposed controller has a Jacobian-based structure, which realizes smooth trajectories when the desired attitude is far rotated from the actual attitude. It also imposes arbitrary magnitude limits on the end-effector velocity, angular velocity, and each actuator force without sacrificing a stiffness, which is the same level as a high-gain PID position control below the limits. The benefit of the proposed controller becomes apparent after the robot yields to external forces due to force saturations, when the robot makes contact with obstacles. In such a situation, if the external forces disappear, the controller generates overdamped resuming motion from large tracking errors. The proposed controller can be expected to enhance the safety of robotic applications for the human–robot interaction. The proposed method is validated by experiments employing a six-degree of freedom industrial manipulator.

Adaptive tracking control of robot manipulators with input saturation and time‐varying output constraints

AbstractThis paper investigates adaptive tracking control in task space for robot manipulators with uncertain system dynamics, input saturation, and time‐varying output constraints simultaneously. An auxiliary system is constructed to compensate the effect of the input saturation, and an asymmetric barrier Lyapunov function (BLF) is applied to tackle time‐varying output constraints, while radial basis function (RBF) neural networks (NN) are used to approximate the unknown closed‐loop dynamics. By introducing a disturbance observer (DO), unknown external disturbances from humans and environment are estimated, and NN approximation errors are compensated. A novel adaptive NN tracking controller is designed to guarantee all signals in the closed‐loop system are semi‐globally uniformly ultimately bounded (UUB), while the tracking errors and observer errors converge to a small neighborhood of zero, and the time‐varying output constraints are not violated. Moreover, the adaptive tracking control of redundant robot manipulators is studied, and the subtask and task space tracking of redundant robot manipulators are realized simultaneously, while the stability of the system is proved by Lyapunov stability theory. Finally, some simulation results are presented to verify the effectiveness and superiority of the proposed control scheme.

Sagittal SLIP-anchored task space control for a monopode robot traversing irregular terrain

As a well-explored template that captures the essential dynamical behaviors of legged locomotion on sagittal plane, the spring-loaded inverted pendulum (SLIP) model has been extensively employed in both biomechanical study and robotics research. Aiming at fully leveraging the merits of the SLIP model to generate the adaptive trajectories of the center of mass (CoM) with maneuverability, this study presents a novel two-layered sagittal SLIP-anchored (SSA) task space control for a monopode robot to deal with terrain irregularity. This work begins with an analytical investigation of sagittal SLIP dynamics by deriving an approximate solution with satisfactory apex prediction accuracy, and a two-layered SSA task space controller is subsequently developed for the monopode robot. The higher layer employs an analytical approximate representation of the sagittal SLIP model to form a deadbeat controller, which generates an adaptive reference trajectory for the CoM. The lower layer enforces the monopode robot to reproduce a generated CoM movement by using a task space controller to transfer the reference CoM commands into joint torques of the multi-degree of freedom monopode robot. Consequently, an adaptive hopping behavior is exhibited by the robot when traversing irregular terrain. Simulation results have demonstrated the effectiveness of the proposed method.

Model Predictive Control With Integral Compensation for Motion Control of Robot Manipulator in Joint and Task Spaces

The motion control of robot manipulators is a crucial problem concerning automatically controlled robots. In this work, the model predictive control method with an integral compensation (MPC-I), which compensates for the matched uncertainties due to unmodeled dynamics, is proposed to solve the trajectory tracking problem of robot manipulators in joint and task spaces. First, this paper decouples the joint variables of the robot manipulator using a computed torque control method. The MPC-I method is, thereafter, derived to realize the motion control of the robot manipulators in joint space. To realize the motion control of the robot manipulator in task space, the task space is, thereafter, converted into the joint space, in which the MPC-I method is executed, afterward, to control the robot. Furthermore, an MPC-I variation, in which the inverse kinematics is calculated indirectly, is proposed to achieve the motion control in task space. The novelty of this paper is to propose the MPC-I method and the method of converting task space to joint space with indirect inverse kinematics calculation. The former is suitable for the dynamic control of the robot manipulators in the joint space, and the latter can extend the MPC-I method to dynamic control in task space. To evaluate the performance of the proposed control method, motion control simulations are performed in the task and joint spaces, respectively. Simulation results and comparisons verify the effectiveness of the proposed control approach for the dynamic control of the UR5 robot manipulator.

Task Space Position Control of Slider-Crank Mechanisms Using Simple Tuning Techniques Without Linearization Methods

In this work, a position control in task space for slider-crank mechanisms is presented. In order to apply linear controllers it is required to linearize the mechanism dynamics at an equilibrium point. However, complete dynamic knowledge is needed and the linearization technique gives an oversimplified model that affects the control performance. In this work, it is proposed a novel method to design task space controllers without using the complete knowledge of the mechanism dynamics and linearization methods. From the extended dynamic model of parallel robots, it can be seen that the end-effector (slider) dynamics is expressed as a linear system that can be used directly for the control design instead of the complete mechanism linear dynamics. The approach requires a minimal knowledge of the mechanism dynamics and avoids linearization methods. To verify our approach, it is used pole placement and sliding mode controllers whose gains are tuned according to the slider dynamics. A linear sensor is mounted at the slider to measure its position and avoids considering noise and disturbances at links before the slider. Simulations and experiments are presented to validate our approach using two kinds of slider-crank mechanisms.

Cooperative r-Passivity Based Control for Mechanical Systems

In this work we consider the problem of cooperative end-effector control between heterogeneous fully actuated agents when varying-time delays and/or packet loss are present. We couple agents via outputs encoded with task-space coordinates and velocities that are transformed into wave-variables to overcome the destabilising effects of the communication network. The scheme poses dynamic requirements on the agents which are locally satisfied with feedback control that integrates subtasks, such as joint-limit avoidance or local tracking, when there are redundant degrees-of-freedom. The proposed approach extends existing methods to task-space control. The approach is robust to network effects, applies to nonlinear systems and is scalable by design. The tuning task is simplified considerably by separation of the cooperative and non-cooperative control terms. We demonstrate the efficacy of the proposed approach experimentally.

A cooperative paradigm for task-space control of multilateral nonlinear teleoperation with bounded inputs and time-varying delays

In this article, a novel multilateral teleoperation structure is presented for cooperative control of a redundant remote robot in the task-space. In the structure, each local robot is assigned a real number between zero and one, as its dominance factor. The sum of all the assigned factors is equal to one, and a greater dominance factor implies that its corresponding operator will have more power in controlling the remote robot. The time-varying delays in the communication channels, the actuators saturation, and the nonlinear dynamics are incorporated into the controller development. Using Barbalat’s lemma and a Lyapunov-Krasovskii functional, the asymptotic stability analysis of the closed-loop dynamics are shown, and the performance claims are delivered. Simulation and experimental results are provided to verify the theoretical findings.

Dynamic Modularity Approach to Adaptive Control of Robotic Systems With Closed Architecture

Modern applications of robotics typically involve a robot control system with an inner PI (proportional-integral) or PID (proportional-integral-derivative) control loop and an outer user-specified control loop. The existing outer loop controllers, however, do not take into consideration the dynamic effects of robots and their effectiveness relies on the ad hoc assumption that the inner PI or PID control loop is fast enough, and other torque-based control algorithms cannot be implemented in robotics with closed architecture. This paper investigates the adaptive control of robotic systems with an inner/outer loop structure, taking into full account the effects of the dynamics and the system uncertainties, and both the task-space control and joint-space control are considered. We propose a dynamic modularity approach to resolve this issue, and a class of adaptive outer loop control schemes is proposed and their role is to dynamically generate the joint velocity (or position) command for the low-level joint servoing loop. Without relying on the ad hoc assumption that the joint servoing is fast enough or the modification of the low-level joint controller structure, we rigorously show that the proposed outer loop controllers can ensure the stability and convergence of the closed-loop system. We also propose the outer loop versions of several standard joint-space direct/composite adaptive controllers for rigid or flexible-joint robots, and a promising conclusion may be that most torque-based adaptive controllers for robots can be designed to fit the inner/outer loop structure by using the new definition of the joint velocity (or position) command. Simulation results are provided to show the performance of various adaptive outer loop controllers, using a three-DOF (degree-of-freedom) manipulator, and experiment results using the UR10 robotic system are also presented.

Closed Loop Control of an MR-Conditional Robot with Wireless Tracking Coil Feedback.

This paper presents a hardware and software system to implement the task space control of an MR-conditional robot by integrating inductively coupled wireless coil based tracking feedback into the control loop. The main motivation of this work is to increase the accuracy performance and address the system uncertainties in the practical scenarios. We present the MR-conditional robot hardware design, wireless tracking method, and custom-designed communication software for real-time tracking data transfer. Based on these working principles, we fabricate the robot platform and evaluate the complete system with respect to various performance indices, i.e. data communication speed, targeting accuracy, tracking coil resolution, image quality, temperature variation, and task space control accuracy for static and dynamic targeting inside MRI scanner. The in-scanner targeting results show that the MR-conditional robot with wireless tracking coil feedback achieves the targeting error of 0.17 ± 0.08mm, while the error calculated from the joint space optical encoder feedback is 0.68 ± 0.19mm.

A note on the ‘task-space control of robots using an adaptive Taylor series uncertainty estimator’

This note points out some errors in the above paper that presents an indirect adaptive Taylor series control approach for the asymptotic tracking task-space control of electrically driven robots. In the proposed approach, Taylor series estimator is designed to approximate the lumped uncertainties (a real-valued function of several variables) in a decentralised form. However, in this note, it is proven that according to Stone–Weierstrass theorem, such an approximation is not technically true, and consequently, the obtained results in the above-mentioned paper are not correct.

Coordination Control of a Dual-Arm Exoskeleton Robot Using Human Impedance Transfer Skills

This paper has developed a coordination control method for a dual-arm exoskeleton robot based on human impedance transfer skills, where the left (master) robot arm extracts the human limb impedance stiffness and position profiles, and then transfers the information to the right (slave) arm of the exoskeleton. A computationally efficient model of the arm endpoint stiffness behavior is developed and a co-contraction index is defined using muscular activities of a dominant antagonistic muscle pair. A reference command consisting of the stiffness and position profiles of the operator is computed and realized by one robot in real-time. Considering the dynamics uncertainties of the robotic exoskeleton, an adaptive-robust impedance controller in task space is proposed to drive the slave arm tracking the desired trajectories with convergent errors. To verify the robustness of the developed approach, a study of combining adaptive control and human impedance transfer control under the presence of unknown interactive forces is conducted. The experimental results of this paper suggest that the proposed control method enables the subjects to execute a coordination control task on a dual-arm exoskeleton robot by transferring the stiffness from the human arm to the slave robot arm, which turns out to be effective.

Toward Global Complex Systems Control The Autonomous Intelligence Challenge

<p align="justify"><strong><span>Complex systems are the emerging new scientific frontier with modern technology advance and new parametric domains study in natural systems. An important challenge is, contrary to classical systems studied so far, the great difficulty in predicting their future behaviour from initial time because, by their very structure, interactions strength between system components is shielding completely their specific individual features. Independent of clear existence of strict laws complex systems are obeying like classical systems, it is however possible today to develop methods allowing to handle dynamical properties of such systems and to master their evolution.</span></strong><span>�</span><strong><span>So the methods should be imperatively adapted to representing system self organization when becoming complex. This rests upon the new paradigm of passing from classical trajectory space to more abstract trajectory manifolds associated to natural system invariants characterizing complex system dynamics. The methods are basically of qualitative nature, independent of system state space dimension and, because of its generic impreciseness, privileging robustness to compensate for not well known system parameters and functional variations. This points toward the importance of </span></strong><strong><em><span>control approach</span></em></strong><strong><span>�for complex system study in adequate function spaces, the more as for industrial applications there is now evidence that transforming a complicated man made system into a complex one is extremely beneficial for overall performance improvement</span></strong><span>. </span><strong><span>But this last step requires larger intelligence delegation to the system </span></strong><strong><span>requiring more autonomy for exploiting its full potential.</span></strong><strong><span>�A well defined, meaningful and explicit control law should be set by using equivalence classes within which system dynamics are forced to stay, so that a complex system described in very general terms can behave in a prescribed way for fixed system parameters value</span></strong><span>. </span><strong><span>Along</span></strong><strong><span>�the line traced by Nature for living creatures, the delegation is expressed at lower level by a change from regular trajectory space control to task space control following system reassessment into its complex stage imposed by the high level of interactions between system constitutive components. Aspects of this situation with coordinated action on both power </span></strong><strong><em><span>and</span></em></strong><strong><span>�information fluxes are handled in a new and explicit control structure derived from application of Fixed Point Theorem which turns out to better perform than (also explicit) extension of Popov criterion to more general nonlinear monotonically upper bounded potentials bounding system dynamics discussed here.</span></strong><span>�</span><strong><span>An interesting observation is that</span></strong><span>�</span><strong><span>when correctly amended as proposed here, complex systems are </span></strong><strong><em><span>not</span></em></strong><strong><span>�as commonly believed a counterexample to reductionism so strongly influential in Science with Cartesian method supposedly only valid for complicated systems.</span></strong><strong></strong></p>

Designing a Robust Control Scheme for Robotic Systems with an Adaptive Observer

This paper introduces a robust task-space control scheme for a robotic system with an adaptive observer. The proposed approach does not require the availability of the system states and an adaptive observer is developed to estimate the state variables. These estimated states are then used in the control scheme. First, the dynamic model of a robot is derived. Next, an observer-based robust control scheme is designed to compensate the uncertainties occurring in the control system. Moreover, upper bound of the lumped uncertainty is essential in the design of the robust controller. However, the upper bound of the lumped uncertainty is difficult to obtain in practical applications. Therefore, an adaptive law is derived to adapt the value of the lumped uncertainty, and an adaptive observer-based robust task-space controller is obtained. In this paper, we proved that the proposed adaptive observer-based controller can guarantee that the task-space tracking error and also the observation error converge to zero. To demonstrate the effectiveness of the proposed method, simulation results are illustrated in this paper.

Task-Space Control of Articulated Mobile Robots With a Soft Gripper for Operations

A task-space method is presented for the control of a head-raising articulated mobile robot, allowing the trajectory tracking of a tip of a gripper located on the head of the robot in various operations, e.g., picking up an object and rotating a valve. If the robot cannot continue moving because it reaches a joint angle limit, the robot moves away from the joint limit and changes posture by switching the allocation of lifted/grounded wheels. An articulated mobile robot with a gripper that can grasp objects using jamming transition was developed, and experiments were conducted to demonstrate the effectiveness of the proposed controller in operations.

A Synergy-Based Motor Control Framework for the Fast Feedback Control of Musculoskeletal Systems.

This paper presents a computational framework for the fast feedback control of musculoskeletal systems using muscle synergies. The proposed motor control framework has a hierarchical structure. A feedback controller at the higher level of hierarchy handles the trajectory planning and error compensation in the task space. This high-level task space controller only deals with the task-related kinematic variables, and thus is computationally efficient. The output of the task space controller is a force vector in the task space, which is fed to the low-level controller to be translated into muscle activity commands. Muscle synergies are employed to make this force-to-activation (F2A) mapping computationally efficient. The explicit relationship between the muscle synergies and task space forces allows for the fast estimation of muscle activations that result in the reference force. The synergy-enabled F2A mapping replaces a computationally heavy nonlinear optimization process by a vector decomposition problem that is solvable in real time. The estimation performance of the F2A mapping is evaluated by comparing the F2A-estimated muscle activities against the measured electromyography (EMG) data. The results show that the F2A algorithm can estimate the muscle activations using only the task-related kinematics/dynamics information with ∼70% accuracy. An example predictive simulation is also presented, and the results show that this feedback motor control framework can control arbitrary movements of a three-dimensional (3D) musculoskeletal arm model quickly and near optimally. It is two orders-of-magnitude faster than the optimal controller, with only 12% increase in muscle activities compared to the optimal. The developed motor control model can be used for real-time near-optimal predictive control of musculoskeletal system dynamics.

Networked Euler-Lagrangian Systems Synchronization under Time-Varying Communicating Delays

This paper investigates the problem of the task-space synchronization control for networked Euler-Lagrange systems. In the considered systems, there are time-varying delays existing in the networking links and every subsystem contains uncertainties in both kinematics and dynamics. By adding new time-varying coupling gains, the negative effects caused by time-varying delays are eliminated. Moreover, to address the difficulties of parametric calibration, an adaptively synchronous protocol and adaptive laws are designed to online estimate kinematics and dynamic uncertainties. Through a Lyapunov candidate and a Lyapunov-Krasovskii functional, the asymptotic convergences of tracking errors and synchronous errors are rigorously proved. The simulation results demonstrate the proposed protocol guaranteeing the cooperative tracking control of the uncalibrated networked Euler-Lagrange systems in the existence of time-varying delays.

Self-tuning Fuzzy Task Space Controller for Puma 560 Robot

Since in most robot applications the desired paths are determined in task space or Cartesian space, it is important to control the robot arm in task space. In this paper a fuzzy controller with modifiable scaling factors is proposed to control the robot end-effector in task space. The controller is a fuzzy system with a mechanism to change the scaling factors when the error is bounded under a predetermined value. The controller is designed in joint space and is developed to work space by using inverse Jacobian strategy. The simulations results on Puma 560 robot manipulator illustrate the high performance of presented control method.

Wave Correction Scheme for Task Space Control of Time-Varying Delayed Teleoperation Systems

This brief presents a novel method in wave variable approach for controlling the $SE(3)$ task space manipulation of the teleoperation system over time-varying delayed communication. The scheme modulates typical wave commands using corrective waves to address the motion/effort mismatch largely caused by time-varying delay and environmental impedance. These corrections are computed based on the difference between the desired and fictitious poses obtained from integrating/propagating nondistorted wave variables. Resulting waves ensure the pose and, moreover, effort tracking of the teleoperation system under appropriate conditions. Passivity of the system is guaranteed by the nonnegative power dissipation constraint on the corrective wave signals, or by the help of dissipative elements in the controllers. Therefore, the scheme may be integrated to the master/slave robots controlled with passive motion/force controllers. Specific application to the teleoperation system with the proportional–derivative controllers is studied.

Singularity Resolution in Equality and Inequality Constrained Hierarchical Task-Space Control by Adaptive Nonlinear Least Squares

We propose a robust method to handle kinematic and algorithmic singularities of any kinematically redundant robot under task-space hierarchical control with ordered equalities and inequalities. Our main idea is to exploit a second order model of the nonlinear kinematic function, in the sense of the Newton's method in optimization. The second order information is provided by a hierarchical BFGS algorithm omitting the heavy computation required for the true Hessian. In the absence of singularities, which is robustly detected, we use the Gauss-Newton algorithm that has quadratic convergence. In all cases, we keep a least-squares formulation enabling good computation performances. Our approach is demonstrated in simulation with a simple robot and a humanoid robot, and compared to state-of-the-art algorithms.

Disturbance estimator based non-singular fast fuzzy terminal sliding mode control of an autonomous underwater vehicle

In this paper, a robust finite time trajectory tracking control approach is proposed for autonomous underwater vehicle (AUV), which belongs to the class of highly nonlinear, coupled dynamics with motion in 6-degrees-of-freedom (DOF). The finite-time error convergence and robust control task is accomplished by designing a non-singular fast fuzzy terminal sliding mode controller (NFFTSMC) with disturbance estimator for the 6-DOF dynamics of an AUV. The proposed NFFTSMC incorporates a non-singular fast terminal sliding mode controller (NFTSMC) which not only assures faster and finite convergence of the tracking errors to the equilibrium from anywhere in the phase portrait but also eliminates the issue of singularity dilemma appeared in conventional terminal sliding mode controller (TSMC); a fuzzy logic control (FLC) tool is employed to generate the hitting control signal in order to reduce chattering in control inputs, which commonly occur in conventional TSMC, and an estimated uncertainty term to compensate for the un-modeled dynamics, external disturbances, and time-varying parameters. Furthermore to investigate the effectiveness of the proposed method, it has been extended to task space control problem of an AUV - manipulator system (AUVMS) employed for underwater manipulation tasks. Simulation studies confirms the potency of the proposed method.