Redundancy Resolution Scheme Research Articles

A Single Network Adaptive Critic-Based Redundancy Resolution Scheme for Robot Manipulators

This paper proposes an adaptive critic-based real-time redundancy resolution scheme for kinematic control of a redundant manipulator. The kinematic control of the redundant manipulator is formulated as a discrete-time input affine system, and then, an optimal real-time redundancy resolution scheme is proposed. The optimal control law is derived in real time using an adaptive critic framework. The proposed single network adaptive critic-based methodology defines the additional task in terms of integral cost function which results in global optimal solution. With adaptive critic-based optimal control scheme, the optimal redundancy resolution is achieved in real time without the computation of inverse, which makes the method computationally efficient. The problem formulation as proposed in this paper is first of its kinds. Furthermore, the real-time optimal redundancy resolution using an integral cost function has been comprehensively solved, which is also a novel contribution. The proposed scheme is tested in both simulation and experiment on a seven-degree-of-freedom PowerCube manipulator from Amtec Robotics.

Effective parameter range for equivalence of velocity-level and acceleration-level redundancy resolution schemes

This Letter shows the equivalence of the velocity-level and acceleration-level redundancy resolution schemes by using so-called Zhang et al.ʼs neural-dynamic method. In addition, the equivalence requires that a design parameter be sufficiently large. But how large should it be? The effective range of such a design parameter is thus determined by means of the 2%-difference rule and the runtime of the computer-simulations.

Automated Milling Path Tracking and CAM-ROB Integration for Industrial Redundant Manipulators

The present paper explores the industrial capabilities of a CAM-ROB system implementation based on a commercial CAD/CAM system (NX™) for an industrial robotic workcell of eight joints, committed to the rapid prototyping of 3D CAD-defined models. The workcell consists of a KUKA™ KR15/2 manipulator assembled on a linear track and synchronized with a rotary table. A redundancy resolution scheme is developed to deal with the redundancies due to the additional joints of the robot, plus the one from the symmetry axis of the milling tool. During the path tracking, the use of these redundancies is optimized by adjusting two performance criterion vectors related to singularity avoidance and maintenance of a preferred reference posture, as secondary tasks to be done. In addition, two suitable fuzzy inference engines adjust the weight of each joint in these tasks. The developed system is validated in a real prototyping of a carving.

CAM-Rob postprocessor based on a fuzzified redundancy resolution scheme

This work highlights the applicability of different redundancy resolution schemes to the postprocessing stage from a computer-aided manufacturing (CAM) system to an industrial redundant workcell. The inverse kinematic problem for redundant manipulators is not straightforward and, therefore, it is commonly solved using an iteratively approach based on redundant resolution schemes at the velocity level. In this work, two conceptions of redundancy resolution schemes are evaluated and a novel fuzzy inference system is developed to improve the performance during the toolpath tracking in order to avoid singularities and to maintain a preferred reference posture. For this purpose, the fuzzy inference engine properly adjusts the weight of each joint in the calculation of the performance criterion vectors. The proposed approach is validated in the real prototyping of a windmill blade mold using a KUKA KR15/2 manipulator mounted on a linear track and synchronized with a rotary table. To the authors’ knowledge, the proposed method and the results shown are novel in the context of postprocessing techniques from CAM systems to industrial robots devoted to milling works. With the same guidelines, the postprocessor programmed inside the CAM system is expected to be easily applicable not only to other industrial robots, but also for different applications such as welding or painting labors.

Two/Infinity Norm Criteria Resolution of Manipulator Redundancy at Joint-Acceleration Level Using Primal-Dual Neural Network

A two/infinity norm criteria (termed bi-criteria) weighting scheme is proposed in this paper for resolving manipulator redundancy at the joint-acceleration level. This bi-criteria scheme is aimed at remedying discontinuity-points and torque-instability problems which arise in pure infinity-norm acceleration-minimization schemes. By incorporating joint physical limits, the proposed bi-criteria redundancy-resolution scheme can finally be formulated as a quadratic program (QP) subject to equality constraint, inequality constraint and bound constraint simultaneously. As a real-time QP solver with simple piecewise-linear dynamics and higher computational efficiency, the primal-dual neural network based on linear variational inequalities (LVI) is presented in this paper to solve online such a bi-criteria weighting scheme. Computer-simulation results based on a PMUA560 robot arm illustrate the advantages and efficacy of such a neural weighting scheme.

An Analytic-Iterative Redundancy Resolution Scheme for Cable-Driven Redundant Parallel Manipulators

In this paper, redundancy resolution of a cable-driven parallel manipulator is performed through an analytic-iterative scheme. The redundancy resolution scheme is formulated as a convex optimization problem with inequality constraints that are imposed by manipulator structure and cable dynamics. The Karush-Kuhn-Tucker theorem is used to analyze the optimization problem and to draw an analytic-iterative solution for it. Subsequently, a tractable and iterative search algorithm is proposed to implement the redundancy resolution of such redundant manipulators. Furthermore, it is shown through simulations that the worst case and average elapsed time that is required to implement the proposed redundancy resolution scheme in a closed-loop implementation is considerably less than that of other numerical optimization methods.

Implementation and testing of a CAM postprocessor for an industrial redundant workcell with evaluation of several fuzzified Redundancy Resolution Schemes

This paper describes the implementation of a postprocessor to adapt the toolpath generated by a CAM system (NXTM) to a complex workcell of eight joints (namely, a KUKA KR15/2 manipulator mounted on a linear track and synchronized with a rotary table), devoted to the rapid prototyping of 3D CAD-defined products. Previously, it evaluates several Redundancy Resolution Schemes at the joint-rate level for the configuration of the postprocessor, dealing not only with the additional joints but also with the redundancy due to the symmetry on the milling tool. The use of these redundancies is optimized by adjusting two performance criterion vectors related to both singularity avoidance and maintenance of a preferred reference posture, as secondary tasks to be done during the path tracking. In addition, two proper fuzzy inference engines actively adjust the weight of each joint in these tasks. The postprocessor is validated in a real prototyping of a Valencian Falla.

A supervisory loop approach to fulfill workspace constraints in redundant robots

An approach based on geometric invariance and sliding mode ideas is proposed for redundancy resolution in robotic systems to fulfill configuration and workspace constraints caused by robot mechanical limits, collision avoidance, industrial security, etc. Some interesting features of the proposal are that: (1) it can be interpreted as a limit case of the classical potential field-based approach for collision avoidance which requires using variable structure control concepts, (2) it allows reaching the limit surface of the constraints smoothly, depending on a free design parameter, and (3) it can be easily added as a supervisory block to pre-existing redundancy resolution schemes. The algorithm is evaluated in simulation on a 6R planar robot and on the freely accessible 6R robot model PUMA-560, for which the main features of the method are illustrated.

Calibration and control of a redundant robotic workcell for milling tasks

This article deals with the tuning of a complex robotic workcell of eight joints devoted to milling tasks. It consists of a KUKA™ manipulator mounted on a linear track and synchronised with a rotary table. Prior to any machining, the additional joints require an in situ calibration in an industrial environment. For this purpose, a novel planar calibration method is developed to estimate the external joint configuration parameters by means of a laser displacement sensor and avoiding direct contact with the pattern. Moreover, a redundancy resolution scheme on the joint rate level is integrated within a computer aided manufacturing system for the complete control of the workcell during the path tracking of a milling task. Finally, the whole system is tested in the prototyping of an orographic model.

Remedy scheme and theoretical analysis of joint-angle drift phenomenon for redundant robot manipulators

A quadratic programming (QP)-based method, as a remedy for joint angle drifts, is employed for redundant robot manipulators with physical constraints (e.g., joint-angle limits and joint-velocity limits) considered. By using the QP-based redundancy-resolution scheme, real-time repetitive motion planning (RMP) can be achieved in a drift-free manner. Theoretical analyses based on gradient-descent and neural-dynamic methods are also conducted. Based on analyses, the efficacy of the presented QP-based RMP scheme for redundant manipulators is successfully explained. To demonstrate the effectiveness of the RMP scheme, different kinds of redundant robot manipulators, such as PA10, PUMA560, and a six-link planar robot arm, are tested in order to perform circular and straight line end-effector trajectories by using computer simulations. Both theoretical analysis and computer simulation results have demonstrated the efficacy of the QP-based RMP scheme.

Novel reaction control techniques for redundant space manipulators: Theory and simulated microgravity tests

This paper presents two novel redundancy resolution schemes aimed at locally minimizing the reaction torque transferred to the spacecraft during manipulator manoeuvres. The subject is of particular interest in space robotics because reduced reactions result in reduced energy consumption and longer operating life of the attitude control system. The first presented solution is based on a weighted Jacobian pseudoinverse and is derived by using Lagrangian multipliers. The weight matrix is defined by means of the inertia matrix which appears in the spacecraft reaction torque dynamics. The second one is based on a least squares formulation of the minimization problem. In this formulation the linearity of the forward kinematics and of the reaction torque dynamics equations with respect to the joint accelerations is used. A closed-form solution is derived for both the presented methods, and their equivalence is proven analytically. Moreover, the proposed solutions, which are suitable for real-time implementation, are extended in order to take into account the physical limits of the manipulator joints directly inside the solution algorithms. A software simulator has been developed in order to simulate the performance of the presented solutions for the selected test cases. The proposed solutions have then been experimentally tested using a 3D free-flying robot previously tested in an ESA parabolic flight campaign. In the test campaign the 3D robot has been converted in a 2D robot thanks to its modularity in order to perform planar tests, in which the microgravity environment can be simulated without time constraints. Air-bearings are used to sustain the links weight, and a dynamometer is used to measure the reaction torque. The experimental validation of the presented inverse kinematics solutions, with an insight on the effect of joint flexibility on their performance, has been carried out, and the experimental results confirmed the good performance of the proposed methods. In particular, two test cases have been analyzed in order to validate and evaluate the performance of both the unconstrained solution and the solution which takes into account the robot physical limits.

Redundancy resolution for underwater mobile manipulators

A new fault-tolerant redundancy resolution scheme is presented that allows a single six degree of freedom (DOF) command to be distributed over a small remotely operated underwater vehicle–manipulator (ROVM) system. ROVM systems are composed of a remotely operated underwater vehicle (ROV) and serial manipulator. The combined system is often kinematically redundant for the six-DOF end-effector command, and such a ROVM system admits an infinite number of joint-space solutions for a commanded end-effector state. In the current work, the primary objective is to follow the desired end-effector velocities commanded by a human pilot. The primary objective is realized using the right Moore–Penrose pseudoinverse solution that minimizes the two-norm of the collective joint velocities. Secondary objectives considered are: avoiding manipulator joint limits, avoiding singularities and high joint velocities, keeping the end-effector in sight of the on-board camera, minimizing the ROV motion, and minimizing the drag-forces on the ROV. Each criterion is defined within the framework of the gradient projection method (GPM). The hierarchy for the secondary tasks is established by a low-level artificial pilot that determines a weighting factor for each criterion based on if–then-type fuzzy rules that reflect an expert human pilot's knowledge. The resulting weight schedule yields a self-motion (null-space motion) that emulates how a skilled operator would utilize the redundancy of the ROVM to achieve the secondary objectives. In addition, the proposed method has a fault-tolerant property that enforces joint-velocity limits and also redistributes the end-effector velocity command in the case of faulty joints. To demonstrate the efficacy of the proposed scheme, a numerical simulation case study is performed. The results illustrate that complex spatial end-effector manoeuvres that are otherwise not possible with a stationary ROV can be accomplished in real-time via the coordination of the ROV and the manipulator. The on-line nature of the proposed scheme makes it suitable for remote systems where the desired end-effector state is not known a priori.

A Robust Position and Force Control Strategy for 7-DOF Redundant Manipulators

This paper is concerned with robust position and contact force control for 7-DOF redundant robot arms. An outer-inner loop controller, called the augmented hybrid impedance control scheme is developed. A 6-DOF force/torque sensor is used to measure the interaction forces. These are fed back to the outer-loop controller that implements either a force or an impedance controller in each of the 6 DOF of the tool frame. The force controller is provided with a force set point, and desired inertia and damping are introduced in the force control loop to improve transient performance. The inner loop consists of a Cartesian-level potential difference controller, a redundancy resolution scheme at the acceleration level, and a joint-space inverse dynamics controller. Experimental results for two 7-DOF robot arms (redundant, dextrous, isotropically enhanced, seven-turning pair robot (REDIESTRO) and Mitsubishi PA10-7C) are given to illustrate the performance of the force control strategy. A successful application of the proposed scheme to a surface cleaning task is described using the REDIESTRO, while position and force tracking experiments are described for the Mitsubishi PA10-7C robot.

Equivalence of velocity-level and acceleration-level redundancy-resolution of manipulators

The equivalence of velocity-level and acceleration-level redundancy resolution of robot manipulators is investigated in this Letter. Theoretical analysis based on gradient-descent method and computer simulations based on PUMA560 robot manipulator both demonstrate the equivalence of redundancy-resolution schemes at different levels.

Bi‐criteria optimal control of redundant robot manipulators using LVI‐based primal‐dual neural network

AbstractIn this paper, a bi‐criteria weighting scheme is proposed for the optimal motion control of redundant robot manipulators. To diminish the discontinuity phenomenon of pure infinity‐norm velocity minimization (INVM) scheme, the proposed bi‐criteria redundancy‐resolution scheme combines the minimum kinetic energy scheme and the INVM scheme via a weighting factor. Joint physical limits such as joint limits and joint‐velocity limits could also be incorporated simultaneously into the scheme formulation. The optimal kinematic control scheme can be reformulated finally as a quadratic programming (QP) problem. As the real‐time QP solver, a primal‐dual neural network (PDNN) based on linear variational inequalities (LVI) is developed as well with a simple piecewise‐linear structure and global exponential convergence to optimal solutions. Since the LVI‐based PDNN is matrix‐inversion free, it has higher computational efficiency in comparison with dual neural networks. Computer simulations performed based on the PUMA560 manipulator illustrate the validity and advantages of such a bi‐criteria neural optimal motion‐control scheme for redundant robots. Copyright © 2009 John Wiley & Sons, Ltd.

Repetitive motion planning of PA10 robot arm subject to joint physical limits and using LVI-based primal–dual neural network

In this paper, a primal–dual neural network based on linear variational inequalities (LVI) is presented for the online repetitive motion planning of PA10 robot arm, a kinematically redundant manipulator. To do this, a drift-free criterion is exploited. In addition, the physical constraints such as joint limits and joint velocity limits are incorporated into the problem formulation of such a redundancy-resolution scheme. The scheme is finally reformulated as a quadratic-programming (QP) problem. As a QP real-time solver, the LVI-based primal–dual neural network is designed based on the QP-LVI conversion and Karush–Kuhn–Tucker (KKT) condition. With simple piecewise-linear dynamics and global exponential convergence to optimal solutions, it can handle general QP and linear programming (LP) problems in the same inverse-free manner. The repetitive motion planning scheme and the LVI-based primal–dual neural network are simulated successfully based on PA10 robot arm, with effectiveness demonstrated.

DEXTEROUS TASK-PRIORITY BASED REDUNDANCY RESOLUTION FOR UNDERWATER MANIPULATOR SYSTEMS

The problem of redundancy resolution for underwater remote vehicle-manipulator systems (URVM) is addressed in the current work. In URVM applications, it is beneficial to have the underwater remote vehicle (URV) hold station using its thrusters while a human pilot operates the serial manipulator. This provides a stable platform for the manipulator and eases the pilot’s job drastically when current and/or tether disturbances are present. However, when following this objective, the redundancy of the URVM as a whole is wasted; the four actively controlled motions of the URV are not used to improve the efficacy of the manipulator task. In fact, this standard operating procedure frequently puts the manipulator into near singular configurations. This is not desirable from the manipulator controller standpoint since near singular configurations result in undesirably high joint velocities and oscillations. In this work, a new heuristic approach based on the task-priority redundancy resolution scheme is applied to the URVM. The proposed approach provides a means to avoid singular configurations of the manipulator, and provides dexterous manipulation by using the URV’s mobility in an optimal, coordinated manner. This scheme is particularly useful for remote systems where an a priori trajectory generator is not applicable. Numerical case studies are developed to demonstrate the effectiveness of the technique.

Dynamic redundancy resolution in a nonholonomic wheeled mobile manipulator

SUMMARYWheeled Mobile Manipulators (WMM) possess many advantages over fixed-base counterparts in terms of improved workspace, mobility and robustness. However, the combination of the nonholonomic constraints with the inherent redundancy limits effective exploitation of end-effector payload manipulation capabilities. The dynamic-level redundancy-resolution scheme presented in this paper decomposes the system dynamics into decoupled task-space (end-effector motions/forces) and a dynamically consistent null-space (internal motions/forces) component. This simplifies the subsequent development of a prioritized task-space control (of end-effector interactions) and a decoupled but secondary null-space control (of internal motions) in a hierarchical WMM controller. Various aspects of the ensuing novel capabilities are illustrated using a series of simulation results.

GENERATION OF POSTURE AND HUMAN MOVEMENT FOR WORKSPACE DESIGN

This paper deals with modelling of human movement in order to provide an analysis and simulation tool which could be used for workspace design. The goal of this work is to generate postures and displacements in an automatic way thanks to the state of the art on the human movement. We are interested in systematic generation of human motion and postures that correspond to working tasks defined by grasps or, more generally, by locations of particular frames linked to hands, head or another body of interest. These tasks are reaching — point to point — tasks or tasks with imposed cartesian path. So the problem is: how to control global posture when frames attached to some bodies are imposed? For that, kinematic models resulting from robotics are used and a redundancy resolution scheme is proposed that makes possible to take into account the articular limits.

A Unified Quadratic-Programming-Based Dynamical System Approach to Joint Torque Optimization of Physically Constrained Redundant Manipulators

In this paper, for joint torque optimization of redundant manipulators subject to physical constraints, we show that velocity-level and acceleration-level redundancy-resolution schemes both can be formulated as a quadratic programming (QP) problem subject to equality and inequality/bound constraints. To solve this QP problem online, a primal-dual dynamical system solver is further presented based on linear variational inequalities. Compared to previous researches, the presented QP-solver has simple piecewise-linear dynamics, does not entail real-time matrix inversion, and could also provide joint-acceleration information for manipulator torque control in the velocity-level redundancy-resolution schemes. The proposed QP-based dynamical system approach is simulated based on the PUMA560 robot arm with efficiency and effectiveness demonstrated.