Task-space Velocity Research Articles

The “Fluid Jacobian”: Modeling force-motion relationships in fluid-driven soft robots

In this paper, we introduce the concept of the Fluid Jacobian, which provides a description of the power transmission that operates between the fluid and mechanical domains in soft robotic systems. It can be understood as a generalization of the traditional kinematic Jacobian that relates the joint space torques and velocities to the task space forces and velocities of a robot. In a similar way, the Fluid Jacobian relates fluid pressure to task space forces and fluid flow to task space velocities. In addition, the Fluid Jacobian can also be regarded as a generalization of the piston cross-sectional area in a fluid-driven cylinder that extends to complex geometries and multiple dimensions. In the following, we present a theoretical derivation of this framework, focus on important special cases, and illustrate the meaning and practical applicability of the Fluid Jacobian in four brief examples.

Task-Space Cooperative Tracking Control for Networked Uncalibrated Multiple Euler–Lagrange Systems

Task-space cooperative tracking control of the networked multiple Euler–Lagrange systems is studied in this paper. On the basis of establishing kinematic and dynamic modeling of a Euler–Lagrange system, an innovative task-space coordination controller is designed to deal with the time-varying communicating delays and uncertainties. First, in order to weaken the influence of the uncertainty of kinematic and dynamic parameters on the control error of the system, the product of the Jacobian matrix and the generalized spatial velocity are linearly parameterized; thus, the unknown parameters are separated from known parameters. The online estimation of uncertain parameters is realized by designing parameters and by proposing new adaptive laws for the dynamic and kinematic parameters. Furthermore, to describe the transmission of time-varying delay errors among networked agents, a new error term is introduced, obtained by adding the observation error and tracking error, and the coefficient of the network mutual coupling term related to the time-varying delay rate is added with reference to the generalized space velocity and task-space velocity of the Lagrange systems. In the end, the influence of the time-varying delay on the cooperative tracking control error of the networked multiple Euler–Lagrange systems is eliminated. With the help of Lyapunov stability theory, the tracking errors and synchronization errors of this system are calculated by introducing the Lyapunov–Krasovskii functional; the asymptotic convergence results rigorously prove the stability of the adaptive cooperative control systems. The simulation results verify the excellent performance of the controller.

Superiority of q-Chlodowsky operators versus fuzzy systems and neural networks: Application to adaptive impedance control of electrical manipulators

This paper introduces a novel application of q-Chlodowsky operators in the approximation of unknown nonlinear functions including uncertainties, un-modeled dynamics, and external disturbances. In fact, q-Chlodowsky operators play the role of basis functions with unknown coefficients. Furthermore, an effective model-free observer is designed for estimation of the task-space velocity signals of the end-effector. The results illustrate that the performances of both radial basis functions neural networks (RBFNN) and the q-Chlodowsky-based approach are nearly the same due to the universal approximation property of both estimators, while the adaptive fuzzy controller needs optimal tuning which is time consuming. Therefore, compared with fuzzy systems and neural networks, the proposed scheme is superior in terms of simplicity and is less computational due to the state-free basis functions in the regressor vector. Simulation results on a 2-DOF electrical manipulator effectively verify the efficiency of the proposed strategy.

Adaptive Neural Task Space Control for Robot Manipulators With Unknown and Closed Control Architecture Under Random Vibrations

Robot manipulators are now used in various domains and environments, where they can be subjected to random vibrations. Random vibrations mainly affect the torque control signal, and a torque controller is therefore required to be designed for stabilization purposes. However, for security or intellectual property protection reasons, most commercialized robots are manufactured with unknown and inaccessible torque controller interface such that the user can only design a position/velocity controller. This paper proposes an adaptive task-space velocity controller free from the inner controller’s structure and exhibiting stochastic and deterministic disturbances rejection to deal with these issues. To deal with the unknown inner controller, the paper exploits the fact that most torque controllers use a velocity feedback term, and it considers the other terms as an unknown functions vector. To cope with random disturbances, it is demonstrated that the random excitation matrix can be linearly parameterized, and therefore, a direct adaptive method is constructed. Using radial basis function neural network (RBF NN), an indirect adaptive method is developed to cope with deterministic uncertainties. Through Lyapunov theory, the paper proves that all the closed-loop signals are bounded in probability. The effectiveness of the proposed approach is further demonstrated through simulation comparisons.

Collision-Free Compliance Control for Redundant Manipulators: An Optimization Case.

Force control of manipulators could enhance compliance and execution capabilities, and has become a key issue in the field of robotic control. However, it is challenging for redundant manipulators, especially when there exist risks of collisions. In this paper, we propose a collision-free compliance control strategy based on recurrent neural networks. Inspired by impedance control, the position-force control task is rebuilt as a reference command of task-space velocities, by combing kinematic properties, the compliance controller is then described as an equality constraint in joint velocity level. As to collision avoidance strategy, both robot and obstacles are approximately described as two sets of key points, and the distances between those points are used to scale the feasible workspace. In order to save unnecessary energy consumption while reducing impact of possible collisions, the secondary task is chosen to minimize joint velocities. Then a RNN with provable convergence is established to solve the constraint-optimization problem in realtime. Numerical results validate the effectiveness of the proposed controller.

Bearing-based formation control of networked robotic systems with parametric uncertainties

Abstract In this paper, the distributed bearing-based formation control problem for networked robotic systems with parametric uncertainties is investigated. Firstly, under the consideration that the task-space velocity is measurable, a reference control input is designed to achieve a bearing constrained target formation. For the unmeasurable task-space velocity case, an observer-based reference velocity scheme is proposed and only the local relative task-space position measurement is needed to achieve globally bearing-based formation stabilization. By designing a velocity feedback in proportional-integral reference velocity control scheme, at least two leaders can handle the leader–follower formation tracking problem, in which the followers do not need any global information. Finally, some simulation results are provided to demonstrate the effectiveness of the proposed control laws.

Adaptive task-space control of robot manipulators using the Fourier series expansion without task-space velocity measurements

Many control approaches presented in the field of robotics require velocity signals, which are not usually provided by many commercial robots. The novelty of this paper is designing an adaptive model-free observer for robot manipulators in the task-space without the use of task-space velocity measurements. To compensate for the uncertainties and nonlinearities in the observer and controller, the Fourier series are utilized. Using Lyapunov stability theorem and Barbalat’s lemma, it is guaranteed that the tracking error and also the observer estimation error converge to zero. The case study is an articulated robot manipulator driven by permanent magnet DC motors. Simulation results and comparison with an extended state observer and linear observer verify the effectiveness of the proposed algorithm.

Task-space fully distributed tracking control of networked uncertain robotic manipulators without velocity measurements

ABSTRACTThis paper investigates the task-space synchronised tracking problem of uncertain networked manipulators interconnected on directed graphs, where the dynamic leader is available to only a subset of followers and followers have only local interaction. A fully distributed tracking controller is proposed, which is composed of a distributed desired trajectory estimator, a joint-space velocity observer and an adaptive cooperative control algorithm. Specifically, the proposed controller allows each manipulator to track the dynamic leader solely using local task-space position measurements. Besides, in the presence of both dynamic and kinematic uncertainties, the adaptive cooperative control algorithm indeed improves the system's robustness. Furthermore, it is strictly proved that the proposed control scheme ensures that both task-space position and velocity tracking errors converge to zero as time tends to infinity. In the end, simulation results are provided to demonstrate the effectiveness of the proposed controller.

Adaptive Control for Nonlinear Teleoperators With Uncertain Kinematics and Dynamics

The problem of controlling bilateral teleoperation systems in the presence of uncertain kinematics and dynamics is studied in this paper. Control algorithms and adaptive laws are developed to address the impediment of imprecise measurement resulting from when the slave robot grips a tool with unknown grasping point and orientation. We first demonstrate that with the utilization of the proposed adaptive laws, the teleoperation system is stable and the position tracking is guaranteed even if there are dynamic and kinematic uncertainties. Due to the end-effector velocity being difficult to obtain, an alternative control algorithm that does not incorporate task-space velocity information is developed. The issue of asymmetric constant communication delays in the teleoperation system is studied by Lyapunov–Krasovskii theorem. In the presence of external forces, we prove that all signals in the proposed teleoperation systems are bounded, and that force feedback is proportional to the tracking errors. Numerical simulations and experiments are performed to demonstrate the efficacy of the developed teleoperation systems.

Adaptive Task-Space Cooperative Tracking Control of Networked Robotic Manipulators Without Task-Space Velocity Measurements.

In this paper, the task-space cooperative tracking control problem of networked robotic manipulators without task-space velocity measurements is addressed. To overcome the problem without task-space velocity measurements, a novel task-space position observer is designed to update the estimated task-space position and to simultaneously provide the estimated task-space velocity, based on which an adaptive cooperative tracking controller without task-space velocity measurements is presented by introducing new estimated task-space reference velocity and acceleration. Furthermore, adaptive laws are provided to cope with uncertain kinematics and dynamics and rigorous stability analysis is given to show asymptotical convergence of the task-space tracking and synchronization errors in the presence of communication delays under strongly connected directed graphs. Simulation results are given to demonstrate the performance of the proposed approach.

General-Weighted Least-Norm Control for Redundant Manipulators under Time-Dependent Constraint

Previous research dealing with constrained kinematic redundancy problems focuses on manipulators with time-independent constraints. This paper extends the general-weighted least-norm (GWLN) method to manipulators with time-dependent constraints by introducing time-dependent virtual joints. In the virtual joint space, corresponding task space velocity is revised to encapsulate the effects of time-dependent parameters of constraints. This is done so that an intermediate kinematic control problem with only joint limit is obtained. Then, the inverse kinematic problem is solved in the virtual joint space. A new inverse-weighted matrix setting criterion is proposed to replace the one-step prediction that originally complicated implementation of the GWLN method. To demonstrate the efficacy of the method, simulations and experiments are carried out on a five-link welding manipulator to track the welding trajectory. Time-dependent orientation constraint and preventing joint limits is guaranteed using this method.

Adaptive task-space synchronisation of networked robotic agents without task-space velocity measurements

In this paper, we investigate the problem of task-space synchronisation of multiple robotic agents in the presence of uncertain kinematics and dynamics. Our control objective is to realise synchronisation without the measurements of task-space velocity. The communication topology is assumed to be directed graphs containing a spanning tree. A decentralised task-space observer with kinematic parameter updating is proposed to avoid the reliance of task-space velocity. Based on the observer, we propose the distributed adaptive synchronisation controller for two cases: (1) the leaderless consensus case and (2) the leader-follower case, where all the followers track the convex hull spanned by the virtual leaders and for each follower, it is required that there exists at least one leader that has a directed path to the follower. The asymptotic synchronisation is proved with Lyapunov analysis and input–output stability analysis tools. Simulations with multiple robotic agents are performed to show the effectiveness of the proposed schemes.

Distributed Task-space Synchronization of Networked Robotic Agents without Task-space Velocity Measurements

In this paper, we investigate the problem of task-space synchronization of multiple robotic agents in the presence of uncertain kinematics and dynamics. Our control objective is to realize synchronization without the measurements of task-space velocity. The communication topology is assumed to be directed graphs containing a spanning tree. A decentralized task-space observer with kinematic parameter updating is proposed to avoid the reliance of task-space velocity. Based on the observer, we propose the distributed adaptive synchronization controller for two cases: 1) The leaderless consensus case; 2) The leader-follower case, where all the followers track the convex hull spanned by the virtual leaders and for each follower, it is required that there exists at least one leader that has a directed path to the follower. The asymptotic synchronization is proved with Lyapunov analysis and input-output stability analysis tools. Simulations with multiple robotic agents are performed to show the effectiveness of the proposed schemes.

An optimal regulator for stabilization of multi-joint reaching movements under DOF redundancy: a challenge to the Bernstein problem from a control-theoretic viewpoint

An optimal regulator problem for multi-joint reaching movements of redundant manipulators is solved from the non-linear control-theoretic viewpoint. Given a target point that the manipulator endpoint should reach, a task-space position feedback with joint damping is introduced, which enables stabilization of reaching movements even if the degrees-of-freedom of the manipulator is greater than the dimension of task space and the inverse kinematics is ill-posed. Usually, the speed of convergence is slow, depending on choice of feedback gains for joint damping. Hence, to speed up the convergence without incurring further energy consumption, an optimal control design for minimizing the integral of a quadratic form of task-space control input and velocity output for an interval [ t0, t1] plus a quadratic function at t = t1 are introduced. This leads to the derivation of a Hamilton–Jacobi–Bellman equation that is solvable in control variables. It is shown that, in the case of infinite time horizon [ t0, ∞), the optimal control reduces to a task-space velocity feedback, and the Hamilton–Jacobi equation becomes solvable in an explicit quadratic form. Finally, a functional relationship of the optimal regulator with the passivity of the closed-loop dynamics is presented.

On-Line Robotic Interception Planning Using a Rendezvous-Guidance Technique

A novel method for online, robotic interception of moving objects using visual feedback is proposed in this paper. No prior knowledge of the motion of the object is assumed. Since such objects might depart quickly from the workspace of the robot, fast interception is a critical issue. Thus, a novel time-optimal rendezvous-guidance technique that takes the dynamic limitations of the robot into account has been developed. In the proposed methodology, first, a parallel-navigation rule, originally introduced in the missile-guidance literature, is applied to generate a set of instantaneous task-space velocity commands, which, if executed, would keep the end-effector on a collision course with the object. Subsequently, a rendezvous-guidance method is utilized to reduce the original command set to one with velocity-matching capability. Finally, the fastest velocity command in the reduced set is chosen such that the dynamic limitations of the actuators of the robot are not violated. The proposed algorithm results in a fast and robust interception as shown by several simulation examples in 2D and 3D workspace.

Task-space adaptive control of robotic manipulators with uncertainties in gravity regressor matrix and kinematics

Thus far, most research in adaptive control of robotic manipulators has assumed that models of regressor matrix and kinematics are known exactly. To overcome these drawbacks, we propose in this paper a task-space adaptive law for setpoint control of robots with uncertainties in gravity regressor matrix and kinematics. In addition, we investigate the stability problem when an estimated task-space velocity is used in the feedback loop. Sufficient conditions for choosing the feedback gains, gravity regressor, and Jacobian matrix are presented to guarantee the stability.

Velocity workspace analysis for multiple arm robot systems

In this paper, the analysis of manipulability of robotic systems comprised of multiple cooperating arms is considered. Given bounds on the capabilities of joint actuators for each robot, the purpose of this study is to derive the bounds for task velocity achievable by the system. Since bounds on each joint velocity form a polytope in joint-velocity space and the task space velocity is connected with joint velocity through Jacobian matrices of each robot, the allowable task velocity space, i.e. velocity workspace, for multiple cooperating robot system is also represented as a polytope which is called manipulability polytope throughout this paper. Based on the fact that the boundaries of the manipulability polytope are mapped from the boundaries of allowable joint-velocity space, slack variables are introduced in order to transform given inequality constraint given on joint velocities into a set of normal linear equalities in which the unknowns of the equation are composed of the vertices of manipulability polytope, vectors spanning the null space of the Jacobian matrix, and the slack variables. Either redundant or nonredundant cooperating robot systems can be handled with the proposed technique. Several different application examples including simple SCARA-type robots as well as complex articulated robot manipulators are included, and, under the assumption of firm grip, it will be shown that the calculated manipulability polytope for cooperating robot system is actually the intersection of all the manipulability polytopes of every single robot which is hard to be derived through geometrical manipulation.

A Differential-Geometric Analysis of Singularities of Point Trajectories of Serial and Parallel Manipulators

In this paper, we present a differential-geometric approach to analyze the singularities of task space point trajectories of two and three-degree-of-freedom serial and parallel manipulators. At non-singular configurations, the first-order, local properties are characterized by metric coefficients, and, geometrically, by the shape and size of a velocity ellipse or an ellipsoid. At singular configurations, the determinant of the matrix of metric coefficients is zero and the velocity ellipsoid degenerates to an ellipse, a line or a point, and the area or the volume of the velocity ellipse or ellipsoid becomes zero. The degeneracies of the velocity ellipsoid or ellipse gives a simple geometric picture of the possible task space velocities at a singular configuration. To study the second-order properties at a singularity, we use the derivatives of the metric coefficients and the rate of change of area or volume. The derivatives are shown to be related to the possible task space accelerations at a singular configuration. In the case of parallel manipulators, singularities may lead to either loss or gain of one or more degrees-of-freedom. For loss of one or more degrees-of-freedom, the possible velocities and accelerations are again obtained from a modified metric and derivatives of the metric coefficients. In the case of a gain of one or more degrees-of-freedom, the possible task space velocities can be pictured as growth to lines, ellipses, and ellipsoids. The theoretical results are illustrated with the help of a general spatial 2R manipulator and a three-degree-of-freedom RPSSPR-SPR parallel manipulator.

Task Compatibility of Manipulator Postures

In performing a manipulation task, humans tend to adopt arm postures that most effectively utilize the motion and strength capabilities of the arm. Selecting arm postures that are compatible with the task requirements has become almost instinctive to humans. By mimicking this approach in robotic manipulation, we can exploit the full capability of a manipu lator in performing a task. An index is proposed for measur ing the compatibility of manipulator postures with respect to a generalized task description. The manipulator is viewed as a mechanical transformer, with joint space velocity and force as input and task space velocity and force as output. Optimi zation of the index corresponds to matching the velocity and force transmission characteristics to the task requirements. The applications of this index to manipulator redundancy utilization and workspace design are also discussed.