Coordinating mobility and manipulation using nonholonomic mobile manipulators

This paper deals with coordinated tasks for mobile nonholonomic manipulators. The systems are composed of a nonholonomic mobile platform and a simple kinematic chain holonomic arm. First, concepts such as redundancy and singular configurations are defined. Then, reduced differential models are introduced. It is then possible to work with a set of independent task coordinates. Applications follow for a planar system in the case of point-to-point and continuous path tasks.     

Extended Jacobian inverse kinematics algorithms for mobile manipulators

We consider the inverse kinematic problem for mobile manipulators consisting of a nonholonomic mobile platform and a holonomic manipulator on board the platform. The kinematics of a mobile manipulator are represented by a driftless control system with outputs together with the associated variational control system. The output reachability map of the driftless control system determines the instantaneous kinematics, while the output reachability map of the variational system plays the role of the analytic Jacobian of the mobile manipulator. Relying on a formal analogy between the kinematics of stationary and mobile manipulators we exploit the extended Jacobian construction in order to design a collection of extended Jacobian inverse kinematics algorithms for mobile manipulators. It has been proved mathematically and confirmed in computer simulations that these algorithms are capable of efficiently solving the inverse kinematic problem. Moreover, a choice of the Jacobian extension may lay down some guidelines for the platform‐manipulator motion coordination. © 2002 Wiley Periodicals, Inc.     

A Lagrangian network for kinematic control of redundant robotmanipulators

A recurrent neural network, called the Lagrangian network, is presented for the kinematic control of redundant robot manipulators. The optimal redundancy resolution is determined by the Lagrangian network through real-time solution to the inverse kinematics problem formulated as a quadratic optimization problem. While the signal for a desired velocity of the end-effector is fed into the inputs of the Lagrangian network, it generates the joint velocity vector of the manipulator in its outputs along with the associated Lagrange multipliers. The proposed Lagrangian network is shown to be capable of asymptotic tracking for the motion control of kinematically redundant manipulators.     

轮式移动机械臂的建模与仿真研究

移动机械臂系统一般由移动平台和机器臂组成,它既具有机器臂的操作灵活性,又具有移动机器人的可移动性,因此其应用范围要比单个系统宽得多。这篇文章主要研究了由非完整移动平台和完整机械臂组成的轮式移动机械臂系统的建模、跟踪控制及仿真问题。首先。利用拉格朗日动力学方程和非完整动力学罗兹方程建立了移动机械臂系统的精确数学模型;然后。利用非线性反馈将系统解耦。采用类PD控制器进行控制。在考虑了非完整约束及移动平台和机械臂的动态交互影响情况下,该控制算法保证系统同时跟踪给定的终端执行器和平台轨迹;最后,使用Maflah6．5对系统进行了仿真研究,仿真结果表明了其数学模型及控制方法的正确有效性。     

Dynamic Modeling and Tracking Control of a Nonholonomic Wheeled Mobile Manipulator with Dual Arms

This paper presents methodologies for dynamic modeling and trajectory tracking of a nonholonomic wheeled mobile manipulator (WMM) with dual arms. The complete dynamic model of such a manipulator is easily established using the Lagrange’s equation and MATHEMATICA. The structural properties of the overall system along with its subsystems are also well investigated and then exploited in further controller synthesis. The derived model is shown valid by reducing it to agree well with the mobile platform model. In order to solve the path tracking control problem of the wheeled mobile manipulator, a novel kinematic control scheme is proposed to deal with the nonholonomic constraints. With the backstepping technique and the filtered-error method, the nonlinear tracking control laws for the mobile manipulator system are constructed based on the Lyapunov stability theory. The proposed control scheme not only achieves simultaneous trajectory and velocity tracking, but also compensates for the dynamic interactions caused by the motions of the mobile platform and the two onboard manipulators. Simulation results are performed to illustrate the efficacy of the proposed control strategy.     

On controlling robots with redundancy

Recently there has been considerable interest in increasing the applicability and utility of robots by developing manipulators which possess kinematic and/or actuator redundancy. This paper presents a unified approach to controlling these redundant robots. The proposed control system consists of two subsystems: an adaptive position controller which generates the Cartesian-space control force FR^m required to track the desired end-effector position trajectory, and an algorithm that maps this control input to a robot joint torque vector TRⁿ. The F → T map is constructed so that the robot redundancy (kinematic and/or actuator) is utilized to improve the performance of the robot. The control scheme does not require knowledge of the complex robot dynamic model or parameter values for the robot or the payload. As a result, the controller is very general and is computationally efficient for on-line implementation. Computer simulation results are given for a kinematically redundant robot, for a robot with actuator redundancy, and for a robot which possesses both kinematic and actuator redundancy. In each case the results demonstrate that accurate end-effector trajectory tracking and effective redundancy utilization can be achieved simultaneously with the proposed scheme.     

Redundancy modelling and resolution for robotic mobile manipulators: a general approach

In this work the topic of kinematic redundancy modelling and resolution for robotic mobile manipulators is considered. A set of redundancy parameters is introduced to define a general inverse kinematic procedure for mobile manipulators. Then, redundancy is treated as a non-linear optimization problem with the purpose of finding robot configurations that maximize the designed metric measures. Some strategies to design the optimization objective function are introduced in order to achieve desirable redundant behaviours, such as obstacles avoidance, mobile base motions reductions and dexterity optimization. Moreover, the robot controller has been developed following an object-oriented software architecture principle that allows to keep it general and robot independent. As a prove of reliability and generality of our approach, the same controller has been used to control several different mobile manipulators in a simulation environment, as well as a real KUKA youBot robot.     

Overview of damped least-squares methods for inverse kinematics of robot manipulators

In this paper, we present a tutorial report of the literature on the damped-least squares method which has been used for computing velocity inverse kinematics of robotic manipulators. This is a local optimization method that can prevent infeasible joint velocities near singular configurations by using a damping factor to control the norm of the joint velocity vector. However, the exactness of the inverse kinematic solution has to be sacrificed in order to achieve feasibility.The damping factor is an important parameter in this technique since it determines the trade-off between the accuracy and feasibility of the inverse kinematic solution. Various methods that have been proposed to compute an appropriate damping factor are described.Redundant manipulators, possessing extra degrees of freedom, afford more choice of inverse kinematic solutions than do non-redundant ones. The damped least-squares method has been used in conjunction with redundancy resolution schemes to compute feasible joint velocities for redundant arms while performing an additional subtask. We outline the different techniques that have been proposed to achieve this objective. In addition, we introduce an iterative method to compute the optimal damping factor for one of the redundancy resolution techniques.     

Sliding Mode Adaptive Neural-Network Control for Nonholonomic Mobile Modular Manipulators

A general mobile modular manipulator can be defined as a m-wheeled holonomic/nonholonomic mobile platform combining with a n-degree of freedom modular manipulator. This paper presents a sliding mode adaptive neural-network controller for trajectory following of nonholonomic mobile modular manipulators in task space. Dynamic model for the entire mobile modular manipulator is established in consideration of nonholonomic constraints and the interactive motions between the mobile platform and the onboard modular manipulator. Multilayered perceptrons (MLP) are used as estimators to approximate the dynamic model of the mobile modular manipulator. Sliding mode control and direct adaptive technique are combined together to suppress bounded disturbances and modeling errors caused by parameter uncertainties. Simulations are performed to demonstrate that the dynamic modeling method is valid and the controller design algorithm is effective.     

Kinematic design of a redundant parallel mechanism for maskless lithography optical instrument manipulations

A new precision parallel mechanism having actuation redundancy will be introduced in this paper. Physical contribution of the actuation redundancy for the precision parallel mechanism is reviewed. In addition, several kinematic configurations have been analyzed for degrees of freedom verification and actuation redundancy. A new kinematic configuration which is 4-[P P]PS is suggested. The suggested 4-[P P]PS mechanism which has actuation redundancy provides six degrees of freedom to the mobile platform. For position control and path planning of the mobile platform, the inverse and the forward kinematics are solved for closed-form solutions. In order to verify the inverse and the forward kinematics, a numerical simulation result is presented. In addition to the inverse and forward accuracy proof, the numerical analysis provides other information such as independent translation motion, calibrated rotation arm at tilting motion, and symmetric motion at rotating motion.     

Criteria optimization using self-motion of a 9-R redundant robot

Using inverse kinematic solutions for self-motion of a class of 9-R redundant robots, a conjugate-gradient based constrained optimization scheme for incremental trajectory planning is formulated. The proposed scheme has been evaluated and proved to be an efficient optimization method for redundancy utilization. It can also be used for studying 7-R and 8-R manipulators by simply restricting to one-variable and two-variable optimization, respectively. In contrast with other approaches which are based on the Jacobian, our scheme exploits the availability of closed-form inverse kinematic solutions to give more effective and accurate results.     

Kinematic control of redundant robots with guaranteed joint limit avoidance

A novel approach for addressing the inverse differential kinematics of redundant manipulators in the presence of hard joint position constraints is presented. A prescribed performance signal for joint limit avoidance guarantees is proposed that can be utilized with both planned and on-line generated trajectories. In the first case, it is a null space velocity for the primary task velocity mapping while in the second case, it modifies the generated reference by acting on the whole velocity space producing a feasible path to the target. Experimental results utilizing a 7DOF KUKA LWR4+ arm demonstrate the performance of the proposed kinematic controller.     

Robust tracking control of nonholonomic dynamic systems with application to the bi-steerable mobile robot

A tracking controller for nonholonomic dynamic systems is proposed which allows global tracking of arbitrary reference trajectories and renders the closed loop system robust with respect to bounded disturbances. The controller is based on [Chwa, D. (2004). Sliding-mode tracking control of nonholonomic wheeled mobile robots in polar coordinates. IEEE Transactions on Control Systems Technology, 12(4), 637-644] and shows several generalizations and improvements. The control law for tracking of general nonholonomic systems using inverse kinematic models (IKM) and sliding surfaces is stated. Conditions are proven under which robust tracking is achieved for a specific system. Tracking control is applied to the bi-steerable mobile robot, and simulation results are presented.     

Stabilization of Nonholonomic Robotic Systems Using Adaptation and Homogeneous Feedback

This paper considers the problem of stabilizing nonholonomic robotic systems in the presence of uncertainty regarding the system dynamic model. It is proposed that a simple and effective solution to this problem can be obtained by combining ideas from homogeneous system theory and adaptive control theory. Thus each of the proposed control systems consists of two subsystems: a (homogeneous) kinematic stabilization strategy which generates a desired velocity trajectory for the nonholonomic system, and an adaptive control scheme which ensures that this velocity trajectory is accurately tracked. This approach is shown to provide arbitrarily accurate stabilization to any desired configuration and can be implemented without knowledge of the system dynamic model. Moreover, it is demonstrated that exponential rates of convergence can be achieved with this methodology. The efficacy of the proposed stabilization strategies is illustrated through extensive computer simulations with nonholonomic robotic systems arising from explicit constraints on the system kinematics and from symmetries of the system dynamics.     

Control-Based Solution to Inverse Kinematics for Mobile Manipulators Using Penalty Functions

This study offers the solution at the control feedback level to the inverse kinematics problem subject to state equality and inequality constraints for mobile manipulators. Based on the Lyapunov stability theory, a class of controllers generating the mobile manipulator trajectory whose attractor attained in a finite time, fulfills the above state constraints. The problem of both holonomic manipulability enforcement and collision avoidance is solved here based on an exterior penalty function approach which results in continuous mobile manipulator velocities near obstacles. The numerical simulation results carried out for a mobile manipulator consisting of a nonholonomic wheel and a holonomic manipulator of two revolute kinematic pairs, operating in both a constraint-free task space and task space including obstacles, illustrate the performance of the proposed controllers.     

Adaptive robust stabilization of dynamic nonholonomic chained systems

In this article, the stabilization problem is investigated for dynamic nonholonomic systems with unknown inertia parameters and disturbances. First, to facilitate control system design, the nonholonomic kinematic subsystem is transformed into a skew‐symmetric form and the properties of the overall systems are discussed. Then, a robust adaptive controller is presented in which adaptive control techniques are used to compensate for the parametric uncertainties and sliding mode control is used to suppress the bounded disturbances. The controller guarantees the outputs of the dynamic subsystem (the inputs to the kinematic subsystem) to track some bounded auxiliary signals which subsequently drive the kinematic subsystem to the origin. In addition, it can also be shown all the signals in the closed loop are bounded. Simulation studies on the control of a unicycle wheeled mobile robot are used to show the effectiveness of the proposed scheme. © 2001 John Wiley & Sons, Inc.     

A kinematically compatible framework for cooperative payload transport by nonholonomic mobile manipulators

In this paper, we examine the development of a kinematically compatible control framework for a modular system of wheeled mobile manipulators that can team up to cooperatively transport a common payload. Each individually autonomous mobile manipulator consists of a differentially-driven Wheeled Mobile Robot (WMR) with a mounted two degree-of-freedom (d.o.f) revolute-jointed, planar and passive manipulator arm. The composite wheeled vehicle, formed by placing a payload at the end-effectors of two (or more) such mobile manipulators, has the capability to accommodate, detect and correct both instantaneous and finite relative configuration errors. The kinematically-compatible motion-planning/control framework developed here is intended to facilitate maintenance of all kinematic (holonomic and nonholonomic) constraints within such systems. Given an arbitrary end-effector trajectory, each individual mobile-manipulator's bi-level hierarchical controller first generates a kinematically-feasible desired trajectory for the WMR base, which is then tracked by a suitable lower-level posture stabilizing controller. Two variants of system-level cooperative control schemes—leader-follower and decentralized control—are then created based on the individual mobile-manipulator control scheme. Both methods are evaluated within an implementation framework that emphasizes both virtual prototyping (VP) and hardware-in-the-loop (HIL) experimentation. Simulation and experimental results of an example of a two-module system are used to highlight the capabilities of a real-time local sensor-based controller for accommodation, detection and corection of relative formation errors.     

Adaptive stabilization of mobile manipulators

This paper considers the motion control problem for uncertain mobile manipulator systems comprised of a robotic arm mounted on a wheeled mobile platform. More specifically, we address the problem of stabilizing mobile manipulators in the presence of uncertainty regarding the system dynamic model. It is proposed that a simple and effective solution to this problem can be obtained by combining ideas from homogeneous system theory and adaptive control theory. Thus each of the proposed control systems consists of two subsystems: a (homogeneous) kinematic stabilization strategy, which generates a desired velocity trajectory for the mobile manipulator, and an adaptive control scheme, which ensures that this velocity trajectory is accurately tracked. This approach is shown to provide arbitrarily accurate stabilization to any desired configuration and can be implemented without knowledge of the details of the system dynamic model. Moreover, it is demonstrated that exponential rates of convergence can be achieved with this methodology. The efficacy of the proposed stabilization strategies is illustrated through computer simulations with two mobile manipulators. © 1998 John Wiley & Sons, Inc.     

一类不确定非完整移动机械臂的鲁棒镇定

讨论了一类带有未知惯性参数,未建模动态及外界干扰的非完整动力学系统的鲁棒镇定问题．基于滑模控制思想及非完整运动学系统的镇定策略,给出了该类系统的鲁棒镇定方法．将其用于一类不确定非完整移动机械臂的鲁棒镇定分析,仿真结果验证了所提出控制方法的正确有效性．     

Structural Properties of Inertia Matrix and Gravity Vector of Dynamics of Rigid Manipulators

In this paper, with the use of Euler‐Lagrange formalism, it has been proven which joint variables can influence entries of the inertia matrix and the gravity vector of dynamics of a manipulator relative to the kinematic structure of the manipulator. Some formulas, alternative to well‐known ones, are presented that allow us to compute the inertia matrix and the gravity vector without using a trace operator. These formulas are computationally inexpensive and provide an inspiration for interesting interpretations. Complexity indices are defined that are able to evaluate the complexity of dynamics of manipulators based on their kinematics. A key role of the accumulated pseudoinertia matrix of the manipulator has been shown. © 2002 Wiley Periodicals, Inc.