A Sequential Bi-criteria Search Algorithm for Robot Path Planning in the Box Pushing Problem

The collision-free trajectory planning method subject to control constraints for mobile manipulators is presented. The robot task is to move from the current configuration to a given final position in the workspace. The motions are planned in order to maximise an instantaneous manipulability measure to avoid manipulator singularities. Inequality constraints on state variables i.e. collision avoidance conditions and mechanical constraints are taken into consideration. The collision avoidance is accomplished by local perturbation of the mobile manipulator motion in the obstacles neighbourhood. The fulfilment of mechanical constraints is ensured by using a penalty function approach. The proposed method guarantees satisfying control limitations resulting from capabilities of robot actuators by applying the trajectory scaling approach. Nonholonomic constraints in a Pfaffian form are explicitly incorporated into the control algorithm. A computer example involving a mobile manipulator consisting of nonholonomic platform (2,0) class and 3DOF RPR type holonomic manipulator operating in a three-dimensional task space is also presented.     

The SDRE control of mobile base cooperative manipulators: Collision free path planning and moving obstacle avoidance

This work proposes application of a state-dependent Riccati equation (SDRE) controller for wheeled mobile cooperative manipulators. Implementation of the SDRE on a wheeled mobile manipulator (WMM) considering holonomic and non-holonomic constraints is difficult and leads to instability of the system. The present study introduces a method of controlling the WMMs including: a general formulation, state-dependent coefficient parameterization, and control structure of the SDRE. Overcoming the problem of instability of the WMM resulted in control design for a system of cooperative manipulators mounted on a wheeled mobile platform. Optimal load distribution (OLD) was employed to distribute the load between the cooperative arms. The presence of obstacles and the probability of a collision between multiple robots in a workspace are the motivations behind employment of the artificial potential field (APF) approach. Two cooperative manipulators mounted on a mobile platform retrieved from Scout robot were modeled and simulated for situations such as controlling multiple mobile bases (collision avoidance), a cooperative system of manipulators, and moving obstacle avoidance. The OLD improved the load capacity, precision, and stability in motion of the cooperative system. Compatibility of the APF within the structure of the SDRE controller is another promising aspect of this research.     

Endogenous configuration space approach to mobile manipulators: A derivation and performance assessment of Jacobian inverse kinematics algorithms

By a mobile manipulator we mean a robotic system composed of a non-holonomic mobile platform and a holonomic manipulator fixed to the platform. A taskspace of the mobile manipulator includes positions and orientations of its end effector relative to an inertial coordinate frame. The kinematics of a mobile manipulator are represented by a driftless control system with outputs. Admissible control functions of the platform along with joint positions of the manipulator constitute the endogenous configuration space. Endogenous configurations have a meaning of controls. A map from the endogenous configuration space into the taskspace is referred to as the instantaneous kinematics of the mobile manipulator. Within this framework, the inverse kinematic problem for a mobile manipulator amounts to defining an endogenous configuration that drives the end effector to a desirable position and orientation in the taskspace. Exploiting the analogy between stationary and mobile manipulators we present in the paper a collection of regular and singular Jacobian inverse kinematics algorithms. Their performance is evaluated on the basis of intense computer simulations.     

Hybrid adaptive control laws solving a path following problem for non-holonomic mobile manipulators

In this paper a general solution to the path following problem for mobile manipulators with non-holonomic mobile platform has been presented. New proposed control algorithms — for mobile manipulators with fully known dynamics or with parametric uncertainty in the dynamics — take into considerations the kinematics as well as the dynamics of the non-holonomic mobile manipulator. The convergence of the control algorithms is proved using the LaSalle's invariance principle.     

Dynamically consistent Jacobian inverse for mobile manipulators

By analogy to the definition of the dynamically consistent Jacobian inverse for robotic manipulators, we have designed a dynamically consistent Jacobian inverse for mobile manipulators built of a non-holonomic mobile platform and a holonomic on-board manipulator. The endogenous configuration space approach has been exploited as a source of conceptual guidelines. The new inverse guarantees a decoupling of the motion in the operational space from the forces exerted in the endogenous configuration space and annihilated by the dual Jacobian inverse. A performance study of the new Jacobian inverse as a tool for motion planning is presented.     

A novel formulation for determining joint constraint loads during optimal dynamic motion of redundant manipulators in DH representation

The kinematic representations of general open-loop chains in many robotic applications are based on the Denavit–Hartenberg (DH) notation. However, when the DH representation is used for kinematic modeling, the relative joint constraints cannot be described explicitly using the common formulation methods. In this paper, we propose a new formulation of solving a system of differential-algebraic equations (DAEs) where the method of Lagrange multipliers is incorporated into the optimization problem for optimal motion planning of redundant manipulators. In particular, a set of fictitious joints is modeled to solve for the joint constraint forces and moments, as well as the optimal dynamic motion and the required actuator torques of redundant manipulators described in DH representation. The proposed method is formulated within the framework of our earlier study on the generation of load-effective optimal dynamic motions of redundant manipulators that guarantee successful execution of given tasks in which the Lagrangian dynamics for general external loads are incorporated. Some example tasks of a simple planar manipulator and a high-degree-of-freedom digital human model are illustrated, and the results show accurate calculation of joint constraint loads without altering the original planned motion. The proposed optimization formulation satisfies the equivalent DAEs.     

Fuzzy logic-based optimization for redundant manipulators

Redundant manipulators have more degrees of freedom (DOF) than the DOF of the task space. This implies that the number of joint position variables is greater than the number of variables specifying the task. The problem of solving the kinematic equations for the joint variables is underspecified unless additional equations/constraints are introduced to obtain a well-posed problem. A dynamic level redundancy resolution is proposed. The joint space model is transformed to a reduced-order model in the pseudovelocity space. The elements of the foregoing transformation matrix indirectly determine the contribution of each joint to the total motion. These elements are selected using two fuzzy logic-based methods so as to minimize the instantaneous manipulator power: (1) in the velocity method, a space vector in the velocity relationship between the two spaces is determined by imposing a constraint on the continuity of the joint velocities at the time instant when the elements of the transformation matrix experience a discontinuity and (2) in the torque method, an alternative approach introduced to reduce the computational complexity, the changes in the transformation matrix are made continuous with respect to time by the appropriate choice of a space vector in the joint torque expression. Simulations are given.     

Fault-tolerant motion planning and control of redundant manipulator

One important issue in the motion planning of a kinematic redundant manipulator is fault tolerance. In general, if the motion planner is fault tolerant, the manipulator can achieve the required path of the end-effector even when its joint fails. In this situation, the contribution of the faulty joint to the end-effector is required to be compensated by the healthy joints to maintain the prescribed end-effector trajectory. To achieve this, this paper proposes a fault-tolerant motion planning scheme by adding a simple fault-tolerant equality constraint for the faulty joint. Such a scheme is then unified into a quadratic program (QP), which incorporates joint-physical constraints such as joint limits and joint-velocity limits. In addition, a numerical computing solver based on linear variational inequalities (LVI) is presented for the real-time QP solving. Simulative studies and experimental results based on a six degrees-of-freedom (DOF) redundant robot manipulator with variable joint-velocity limits substantiate the effectiveness of the proposed fault-tolerant scheme and its solution.     

Disturbance rejection for space‐based manipulators

Most industrial manipulators operate from a fixed base. Hence, there are no disturbances from the environment to alter the position of the end‐effector. On the other hand, manipulators that are mounted on mobile platforms are subject to disturbances emerging from unwanted motion at the base. Similarly, manipulators that perform delicate operations in space while on board in‐orbit spacecraft experience disturbances. This article describes the design and implementation of a disturbance rejection controller for a 6 degree‐of‐freedom (DOF) programable universal manipulator for assembly (PUMA) manipulator mounted on a 3‐DOF platform. A control algorithm is designed to track the desired position and attitude of the end‐effector in inertial space, subject to unknown disturbances in the platform axes. Experimental results are presented for step, sinusoidal, and random disturbances in the platform rotational axis and in the neighborhood of kinematic singularities. ©1999 John Wiley & Sons, Inc.     

On Multiple Secondary Task Execution of Redundant Nonholonomic Mobile Manipulators

This paper investigates self-motion control of redundant nonholonomic mobile manipulators, to execute multiple secondary tasks including tip-over prevention, singularity removal, obstacle avoidance and physical limits escape. An extended gradient projection method (EGPM) is proposed to determine self-motion directions, and a real-time fuzzy logic self-motion planner (FLSMP) is devised to generate the corresponding self-motion magnitudes. Unlike the task-priority allocation method and the extended Jacobian method, the proposed scheme is simple to implement and is free from algorithm singularities. The proposed dynamic model is established with consideration of nonholonomic constraints of the mobile platform, interactive motions between the mobile platform and the onboard manipulator, as well as self-motions allowed by redundancy of the entire robot. Furthermore, a robust adaptive neural-network controller (RANNC) is developed to accomplish multiple secondary tasks without affecting the primary one in the workspace. The RANNC does not rely on precise prior knowledge of dynamic parameters and can suppress bounded external disturbance effectively. In addition, the RANNC does not require any off-line training and can ensure the control performance by online adjusting the neural-network parameters through adaptation laws. The effectiveness of the proposed algorithm is verified via simulations on a three-wheeled redundant nonholonomic mobile manipulator.     

Encoder based online motion planning and feedback control of redundant manipulators

This paper proposes and investigates an online motion planning and feedback control (OMPFC) scheme for redundant manipulators via techniques of quadratic programming and rotary encoder. The proposed OMPFC scheme is performed on a planar six degrees-of-freedom (DOF) manipulator. This robotic scheme incorporates the feedback of task-space position error. The joint state is obtained in real time via rotary encoders equipped on the physical manipulator. The original scheme is finally reformulated as a unified quadratic program (QP). The QP is solved online during the joint motion by employing an efficient numerical algorithm. Simulation and experimental results validate the physical realizability, online property, and efficacy of the proposed OMPFC scheme (including the employed numerical algorithm).     

Modeling of tracked mobile manipulators with consideration of track–terrain and vehicle–manipulator interactions

This paper presents a systematic method to establish the kinematics model for a tracked mobile manipulator on firm grounds, with consideration of the interactive motions between the tracks and the terrain, as well as those between the tracked vehicle and the onboard manipulator. Kinematics analysis is essential for real-time pose estimation and online autonomous navigation of tracked mobile manipulators. Furthermore, to improve the effectiveness of motion planning, and to simulate or control tracked mobile manipulators, a reliable kinematics model is required. However, kinematics modeling for a tracked mobile manipulator is complicated by the fact that there are infinite number of contact points between the tracks and the terrain, which makes slippage unavoidable. The track–terrain and vehicle–manipulator interactions make the problem even more complicated as the motion of the onboard manipulator and the centrifugal forces during moderate or high speed motion give rise to transfer of the load distribution, which will affect the longitudinal and lateral tractive forces and the resistance. Also, the motion of the mobile platform contributes to the inertial forces of the manipulator, and the track–terrain interactive forces help balance the gravity as well as the manipulation forces. The developed kinematics modeling approach is presented on the basis of a tracked mobile manipulator in our laboratory, but the forward kinematics analysis method, and the track–terrain and vehicle–manipulator interaction analysis algorithm are general, and can be used for any tracked mobile manipulators with little modification. This work lays a solid foundation for autonomous control, online slippage estimation, real-time traction optimization as well as tip-over prediction and prevention of tracked mobile manipulators.     

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.     

Virtual joint method for kinematic modeling of wheeled mobile manipulators

In this paper, we propose a virtual joint method that better utilizes quasi-velocities for the kinematic modeling of wheeled mobile manipulators. By identifying quasi-velocities as motions of imaginary revolute and prismatic kinematic pairs, our method enables one to regard a mobile manipulator as an ordinary articulated manipulator for the purposes of velocity analysis. We also propose an inverse kinematic scheme for the mobile manipulators along the line with the virtual joint based kinematic framework. Details are worked out for mobile manipulators with representative differential-drive and car-like mobile platforms.     

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.     

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。     

Analysis and Verification of Repetitive Motion Planning and Feedback Control for Omnidirectional Mobile Manipulator Robotic Systems

Mobile manipulator robotic systems (MMRSs) composed of a manipulator and a mobile platform are investigated in this paper. In order for the mobile manipulator robotic system (MMRS) to return to its initial state when the manipulator’s end-effector is requested to execute cyclical tasks, a quadratic program (QP) based repetitive motion planning and feedback control (RMPFC) scheme is proposed and analyzed. Such an RMPFC scheme can not only mix motion planning and reactive control, but also consider the physical limits of the robotic system. Mathematically, the efficacy of the RMPFC scheme is verified via gradient dynamics analysis. To further demonstrate the effectiveness of the RMPFC scheme, a kinematically redundant MMRS composed of a three degrees-of-freedom (DOF) planar manipulator and an omnidirectional mobile platform is designed, modeled and analyzed. Then, repetitive motion planning and feedback control for the designed omnidirectional MMRS is studied. Besides, a numerical algorithm is developed and presented to solve the QP and resolve the redundancy of the robotic system. Moreover, computer simulations are comparatively performed on such an omnidirectional MMRS, and simulation results substantiate the effectiveness, accuracy and superiority of the proposed RMPFC scheme.     

Theoretical Investigation of a Time-Suboptimal Control Method for Rotational Motions of Industrial Manipulators End-Effectors

A time suboptimal control method is developed for rotational motions of industrial manipulators end-effectors. A set of nonlinear equations is obtained and linearized at each time step of the motion. A method which yields the time suboptimal joint angular velocities as functions of time is developed by considering constraints on joint velocities as well as joint and tool center point frame accelerations. The method is demonstrated on a six-degree-of-freedom elbow-type manipulator.     

一种基于矢量分析的视觉伺服冗余机器人运动规划方法

本文提出了一种适用于视觉伺服冗余机器人的运动规划方法．针对大多数具有三轴 相交手腕的操作臂,文章把操作臂的运动规划分解为两个方面．一方面,采用腕部速度矢量 在操作臂关节空间极小最小二乘分解的方法规划操作臂关节速度．另一方面,用欧拉角矢量 递推的方法规划操作臂手爪的姿态．该方法的特点是物理意义明确,算法简单．同时具有一 定的运动学鲁棒性．文中还采用该方法对8R操作臂进行了仿真研究．     

An inverse kinematic solution for kinematically redundant robot manipulators

An inverse kinematic analysis addresses the problem of computing the sequence of joint motion from the Cartesian motion of an interested member, most often the end effector. Although the rates and accelerations are related linearly through the Jacobian, the positions go through a highly nonlinear transformation from one space to another. Hence, the closed-form solution has been obtained only for rather simple manipulator configurations where joints intersect or where consecutive axes are parallel or perpendicular. For the case of redundant manipulators, the number of joint variables generally exceeds that of the constraints, so that in this case the problem is further complicated due to an infinite number of solutions. Previous approaches have been directed to minimize a criterion function, taking into account additional constraints, which often implies a time-consuming optimization process. In this article, a different approach is taken to these problems. A Newton-Raphson numerical procedure has been developed based on a composite Jacobian which now includes rows for all members under constraint. This procedure may be applied to solve the inverse kinematic problem for a manipulator of any mechanical configuration without having to derive beforehand a closed-form solution. The technique is applicable to redundant manipulators since additional constraints on other members as well as on the end effector may be imposed. Finally, this approach has been applied to a seven degree-of-freedom manipulator, and its ability to avoid obstacles is demonstrated.