Uncertain Kinematics Research Articles

Adaptive Control of Robot Manipulators With Uncertain Kinematics and Dynamics

In this paper, we investigate the adaptive control problem for robot manipulators with both the uncertain kinematics and dynamics. We propose two adaptive control schemes to realize the objective of task-space trajectory tracking irrespective of the uncertain kinematics and dynamics. The proposed controllers have the desirable separation property, and we also show that the first adaptive controller with appropriate modifications can yield improved performance, without the expense of conservative gain choice. The performance of the proposed controllers is shown by numerical simulations.

Task Space Trajectory Tracking Control of Robot Manipulators with Uncertain Kinematics and Dynamics

To improve the tracking precision of robot manipulators’ end-effector with uncertain kinematics and dynamics in the task space, a new control method is proposed. The controller is based on time delay estimation and combines with the nonsingular terminal sliding mode (NTSM) and adaptive fuzzy logic control scheme. Kinematic parameters are not exactly required with the consideration of kinematic uncertainties in the controller. No dynamic models or numerous parameters of the robot manipulator system are required with the use of TDE. Thus, the controller is simple structure and suitable for practical applications. Furthermore, errors caused by time delay estimation are compensated by the adaptive fuzzy nonsingular terminal sliding mode scheme. The simulation is performed on a 2-DOF robot manipulator with three cases in the task space. The results show that the proposed controller provides faster convergence rate and higher tracking precision than TDE based NTSM and improved TDE based NTSM controller.

Multilateral Telecoordinated Control of Multiple Robots With Uncertain Kinematics.

This paper addresses the telecoordinated control of multiple robots in the simultaneous presence of asymmetric time-varying delays, nonpassive external forces, and uncertain kinematics/dynamics. To achieve the control objective, a neuroadaptive controller with utilizing prescribed performance control and switching control technique is developed, where the basic idea is to employ the concept of motion synchronization in each pair of master-slave robots and among all slave robots. By using the multiple Lyapunov-Krasovskii functionals method, the state-independent input-to-output practical stability of the closed-loop system is established. Compared with the previous approaches, the new design is straightforward and easier to implement and is applicable to a wider area. Simulation results on three pairs of three degrees-of-freedom robots confirm the theoretical findings.

Tracking Control of Robotic Manipulators With Uncertain Kinematics and Dynamics

This paper investigates a difficult problem of tracking control for robotic manipulations with guaranteed high accuracy. Uncertain kinematics, unknown torques including unknown gravitational torque, unknown friction torque, and uncertain dynamics induced by uncertain moment of inertia and disturbance, are addressed. The approach is developed in the framework of observer-based control design. Two sliding-mode observers are proposed to handle uncertain kinematics and to estimate unknown torques, respectively. Using the estimated information, a control law is then synthesized to guarantee that the desired trajectory can be followed after finite-time with zero tracking error. Experimental results are presented to show the performance of the proposed control approach.

Robust Task Space Trajectory Tracking Control of Robotic Manipulators

This work deals with the problem of the accurate task space trajectory tracking subject to finite-time convergence. Kinematic and dynamic equations of a redundant manipulator are assumed to be uncertain. Moreover, globally unbounded disturbances are allowed to act on the manipulator when tracking the trajectory by the end-effector. Furthermore, the movement is to be accomplished in such a way as to reduce both the manipulator torques and their oscillations thus eliminating the potential robot vibrations. Based on suitably defined task space non-singular terminal sliding vector variable and the Lyapunov stability theory, we propose a class of chattering-free robust controllers, based on the estimation of transpose Jacobian, which seem to be effective in counteracting both uncertain kinematics and dynamics, unbounded disturbances and (possible) kinematic and/or algorithmic singularities met on the robot trajectory. The numerical simulations carried out for a redundant manipulator of a SCARA type consisting of the three revolute kinematic pairs and operating in a two-dimensional task space, illustrate performance of the proposed controllers as well as comparisons with other well known control schemes.

Adaptive control for space debris removal with uncertain kinematics, dynamics and states

As the Tethered Space Robot is considered to be a promising solution for the Active Debris Removal, a lot of problems arise in the approaching, capturing and removing phases. Particularly, kinematics and dynamics parameters of the debris are unknown, and parts of the states are unmeasurable according to the specifics of tether, which is a tough problem for the target retrieval/de-orbiting. This work proposes a full adaptive control strategy for the space debris removal via a Tethered Space Robot with unknown kinematics, dynamics and part of the states. First we derive a dynamics model for the retrieval by treating the base satellite (chaser) and the unknown space debris (target) as rigid bodies in the presence of offsets, and involving the flexibility and elasticity of tether. Then, a full adaptive controller is presented including a control law, a dynamic adaption law, and a kinematic adaption law. A modified controller is also presented according to the peculiarities of this system. Finally, simulation results are presented to illustrate the performance of two proposed controllers.

Robust Task Space Finite-Time Chattering-Free Control of Robotic Manipulators

This work deals with the problem of the accurate task space control subject to finite-time convergence. Kinematic and dynamic equations of a rigid robotic manipulator are assumed to be uncertain. Moreover, unbounded disturbances, i.e., such structures of the modelling functions that are generally not bounded by construction, are allowed to act on the manipulator when tracking the trajectory by the end-effector. Based on suitably defined task space non-singular terminal sliding vector variable and the Lyapunov stability theory, we derive a class of absolutely continuous (chattering-free) robust controllers based on the estimation of a Jacobian transpose matrix, which seem to be effective in counteracting uncertain both kinematics and dynamics, unbounded disturbances and (possible) kinematic and/or algorithmic singularities met on the robot trajectory. The numerical simulations carried out for a 2DOF robotic manipulator with two revolute kinematic pairs and operating in a two-dimensional task space, illustrate performance of the proposed controllers.

Constraint finite-time control of redundant manipulators

Summary This work addresses the problem of the accurate task-space control subject to finite-time convergence. Dynamic equations of a redundant manipulator are assumed to be uncertain. Moreover, globally unbounded disturbances are allowed to act on the manipulator when tracking the trajectory by the end effector. Furthermore, the movement is to be accomplished in such a way as to optimize some performance index. Based on suitably defined task-space non-singular terminal sliding vector variable and the Lyapunov stability theory, we derive a class of inverse-free robust controllers consisting of a Jacobian transpose component plus a compensating term, which seem to be effective in counteracting uncertain dynamics, unbounded disturbances and (possible) kinematic singularities met on the robot trajectory. The numerical simulations carried out for a redundant manipulator of a Selective Compliant Articulated Robot for Assembly (SCARA) type consisting of three revolute kinematic pairs and operating in a two-dimensional task space illustrate performance of the proposed controllers. Copyright © 2016 John Wiley & Sons, Ltd.

Adaptive zero reaction motion control for free-floating space manipulators

This paper investigates adaptive zero reaction motion control for free-floating space manipulators with uncertain kinematics and dynamics. The challenge in deriving the adaptive reaction null-space (RNS) based control scheme is that it is difficult to obtain a linear expression, which is the basis of the adaptive control. The main contribution of this paper is that we skillfully obtain such a linear expression, based on which, an adaptive version of the RNS-based controller (referred to as the adaptive zero reaction motion controller in the sequel) is developed at the velocity level, taking into account both the kinematic and dynamic uncertainties. It is shown that the proposed controller achieves both the spacecraft attitude regulation and end-effector trajectory tracking. The performance of the proposed adaptive controller is shown by numerical simulations with a planar 3-DOF (degree-of-freedom) space manipulator.

Constrained Multilegged Robot System Modeling and Fuzzy Control With Uncertain Kinematics and Dynamics Incorporating Foot Force Optimization

This paper studies the optimal distribution of feet forces and control of multilegged robots with uncertainties in both kinematics and dynamics. First, a constrained dynamics for multilegged robots and the constrained environment model are established by considering both kinematic and dynamic uncertainties. Under an external wrench for multilegged robots, the foot forces and moments of the supporting legs can be formulated as quadratic programming problems subject to linear and nonlinear constraints. The neurodynamics of recurrent neural network is developed for foot force optimization. For the obtained optimized tip-point force and the motion of legs, we propose a hybrid task-space trajectory and force tracking based on fuzzy system and adaptive mechanism that are used to compensate for the external perturbation, kinematics, and dynamics uncertainties. The tracking of task-space trajectory and constraint force is achieved under unknown dynamical parameters, constraints, and disturbances. Extensive simulations have been provided to verify the effectiveness of the proposed scheme.

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.

Note: Model-based identification method of a cable-driven wearable device for arm rehabilitation.

Cable-driven exoskeletons have used active cables to actuate the system and are worn on subjects to provide motion assistance. However, this kind of wearable devices usually contains uncertain kinematic parameters. In this paper, a model-based identification method has been proposed for a cable-driven arm exoskeleton to estimate its uncertainties. The identification method is based on the linearized error model derived from the kinematics of the exoskeleton. Experiment has been conducted to demonstrate the feasibility of the proposed model-based method in practical application.

Adaptive Jacobian force/position tracking for space free-flying robots with prescribed transient performance

This paper presents a tracking control with guaranteed prescribed performance (PP) for space free-flying robots with uncertain kinematics (Jacobian matrix) and dynamics, uncertain normal force parameter, and bounded disturbances in a compliant contact with a planar surface. Given the orientation of the surface and a nonlinear model of the elastic force, a controller is designed requiring no information on the robot parameters and the disturbances. This controller will guarantee that the tracking errors satisfy PP indexes such as the maximum steady-state errors and overshoots, and the minimum convergence rates. Thus, contact maintenance can be ensured as prescribed. An approximation of the Jacobian is utilized in the presence of uncertain robot kinematics, and PP position/attitude tracking of the free-flying base is achieved in addition to the PP force/position tracking of the manipulator’s fingertip. The proposed controller is based on an error transformation technique, and a directly tunable gain for the transformed error feedback is introduced in the control to trade off between the tracking performance and control effort. Numerical simulations and comparisons demonstrate the effectiveness and superiority of the proposed controller.

An adaptive non-linear constraint control of mobile manipulators

This paper addresses the problem of position control of mobile manipulators operating in the task space with state constraints. Motivated in part by the energy shaping and damping injection methodology, we first propose a class of non-linear model-based constraint task space regulators which, by the fulfilment of a reasonable condition, are shown both to be asymptotically stable and to provide an optimal solution at the desired end-effector location. This methodology is then generalized to a class of both parametrically uncertain kinematic and dynamic equations of the mobile manipulators. The position control problem in the presence of kinematic and dynamic uncertainties and (unknown) environment (obstacles) is solved herein based on the Lyapunov stability theory, the exterior penalty function approach and by using the sensory feed-back of the end-effector and the sensors, in which the mobile manipulator is equipped. Novel adaptive laws, extending the capability of the classic algorithms to deal with both holonomic and nonholonomic kinematic uncertainties and obstacles, are proposed.

Distributed synchronization for heterogeneous robots with uncertain kinematics and dynamics under switching topologies

In this paper, the problems related to control for a network of heterogeneous robots, to achieve task-space synchronization in the presence of uncertainties in kinematic and dynamic models have been reported. Based on the proposed control algorithms and adaptive laws, networked robot systems can be ensured to synchronize with imprecise measurement of system parameters and communication delays. Three different connection scenarios, namely, strongly connected graphs, switching regular graphs, and jointly connected regular graphs have been considered in this paper. With the use of weighted storage function, attempts have been made in this paper to demonstrate that a multi-robot system, interconnected over a strongly connected graph with time delays, can be stabilized with guaranteed position and velocity synchronization. Since it is difficult to set up a fixed communication network between robots, an alternative synchronization controller was developed through switching topologies. Additionally, for interconnections between robots that are time-varying and agents that are disconnected at certain time intervals, the stability and synchronous behaviors of the networked system were studied using Lyapunov theory and switching control theory. Numerical examples were also provided to demonstrate the performance of the proposed multi-robot system.

Distributed adaptive image‐based consensus of networked robotic manipulators without visual velocity measurements

In this paper, the authors study the fixed-camera visual servoing consensus problem of multiple robotic manipulators with uncertain robotic dynamics, kinematics and camera parameters. The communication graph is assumed to be directed graphs containing a spanning tree. Our control objective is to achieve image-space consensus without the measurements of visual velocity. A novel decentralised image-space position observer with online parameter updating is presented to avoid the reliance on visual velocity and to handle the uncertain robotic kinematics and camera parameters. Based on the observed visual information, we perform the distributed adaptive controller design in a cascade framework. The asymptotic convergence of consensus error is proved by use of Lyapunov analysis tool and input–output stability analysis tool. Finally, simulations with networked robotic manipulators are performed to validate the effectiveness of the proposed strategy.

Robust assessment of collapse resistance of structures under uncertain loads based on Info-Gap model

The paper proposes a pair of novel mathematical programming based approaches which directly determine the worst collapse load limit in one case, and the best limit in the other case of rigid perfectly-plastic structures subjected to uncertain-but-bounded applied loads using an Info-Gap model. The methods take advantage of the important properties in which the worst collapse load limit defined for an uncertain static formulation is equivalent to the most favourable solution of the uncertain kinematic limit analysis problem, and vice versa for the best collapse load limit. The formulation for capturing the worst collapse load limit (robust worst case solution) takes the form as a mathematical program with equilibrium constraints that is processed using a penalty algorithm, whilst that for the best collapse load limit is a standard linear programming problem. The efficiency and robustness of the proposed schemes are evidenced from a number of successfully solved examples.

Adaptive synchronised tracking control for multiple robotic manipulators with uncertain kinematics and dynamics

In this study, a new adaptive synchronised tracking control approach is developed for the operation of multiple robotic manipulators in the presence of uncertain kinematics and dynamics. In terms of the system synchronisation and adaptive control, the proposed approach can stabilise position tracking of each robotic manipulator while coordinating its motion with the other robotic manipulators. On the other hand, the developed approach can cope with kinematic and dynamic uncertainties. The corresponding stability analysis is presented to lay a foundation for theoretical understanding of the underlying issues as well as an assurance for safely operating real systems. Illustrative examples are bench tested to validate the effectiveness of the proposed approach. In addition, to face the challenging issues, this study provides an exemplary showcase with effectively to integrate several cross boundary theoretical results to formulate an interdisciplinary solution.

Task-Space Synchronization of Networked Robotic Systems With Uncertain Kinematics and Dynamics

In this technical note, we investigate the task-space synchronization for networked robots interconnected on strongly connected graphs with both the uncertain kinematics and dynamics. A cascade framework is proposed to facilitate the synchronization controller design for networked robotic systems. Under this framework, we propose an adaptive task-space synchronization scheme with indirect/direct kinematic parameter adaptations and a direct dynamic parameter adaptation for the networked robots. We employ the passive decomposition approach to show the asymptotic task-space synchronization of the networked system, and we demonstrate that the proposed control is capable of ensuring the weighted average consensus of the networked uncertain robots. Simulation results are provided to demonstrate the performance of the proposed control approach.