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.     

基于伪逆的导轨机械臂关节速度纠偏运动规划方案

针对导轨机械臂在任务执行过程中出现的关节速度偏离期望值的问题，提出了一种基于伪逆算法的导轨机械臂关节速度纠偏运动规划方案。首先，根据机械臂的关节角状态和末端执行器的运动状态，运用伪逆算法对导轨机械臂在速度层上进行冗余度解析。然后，设计时变函数对关节速度进行约束调整，使偏离后的关节速度收敛于期望值。接着，针对末端执行器出现的位置误差设计了误差修正方法以保证轨迹跟踪任务的顺利执行。最后，将运动规划方案在Matlab软件上以基座直线移动和弧形移动的四连杆冗余度机械臂为例进行了仿真实验。仿真结果表明了该方案能纠正导轨机械臂在任务执行过程中偏离期望值的关节速度，且能使末端执行器的轨迹跟踪达到较高的精度。     

基于伪逆的导轨机械臂关节速度纠偏运动规划方案

针对导轨机械臂在任务执行过程中出现的关节速度偏离期望值的问题,提出了一种基于伪逆算法的导轨机械臂关节速度纠偏运动规划方案。首先,根据机械臂的关节角状态和末端执行器的运动状态,运用伪逆算法对导轨机械臂在速度层上进行冗余度解析。然后,设计时变函数对关节速度进行约束调整,使偏离后的关节速度收敛于期望值。接着,针对末端执行器出现的位置误差设计了误差修正方法以保证轨迹跟踪任务的顺利执行。最后,将运动规划方案在Matlab软件上以基座直线移动和弧形移动的四连杆冗余度机械臂为例进行了仿真实验。仿真结果表明了该方案能纠正导轨机械臂在任务执行过程中偏离期望值的关节速度,且能使末端执行器的轨迹跟踪达到较高的精度。     

Redundant robot control using task based performance measures

The joint velocities required to move the end-effector of a redundant robot with a desired linear and angular velocity depend on its configuration. Similarly, the joint torques produced due to the force and moment at the end-effector also depend on its configuration. When the robot is near a singular configuration, the joint velocities required to attain the end-effector velocity in certain directions are extremely high. Similarly, in some configurations the joint torque produced at certain joints may be high for a relatively small magnitude of external force. An infinite number of trajectories in the joint space can be used to achieve a desired end-effector trajectory for redundant robots. However, a joint trajectory resulting in robot configurations requiring lower joint velocities or joint torques is desired. This may be achieved through a proper utilization of redundancy. Local performance measures for redundant robots are defined in this article as indicators of their ability to follow a desired end-effector trajectory and their ability to apply desired forces at the end-effector. Thus, these performance measures depend on the task to be performed. Control algorithms which can be efficiently applied to redundant robots to improve these performance measures are presented. These control algorithms are based on the gradient projection method. Gradients of the performance measures used in the control schemes result in simple symbolic expressions for “real world” robots'. Feasibility and effectiveness of these control schemes is demonstrated through the simulation of a seven-degree-of-freedom redundant robot derived from the PUMA geometry.     

A fast approach for the robust trajectory planning of redunant robot manipulators

In this article, a fast approach for robust trajectory planning, in the task space, of redundant robot manipulators is presented. The approach is based on combining an original method for obstacle avoidance by the manipulator configuration with the traditional potential field approach for the motion planning of the end-effector. This novel method is based on formulating an inverse kinematics problem under an inexact context. This procedure permits dealing with the avoidance of obstacles with an appropriate and easy to compute null space vector; whereas the avoidance of singularities is attained by the proper pseudoinverse perturbation. Furthermore, it is also shown that this formulation allows one to deal effectively with the local minimum problem frequently associated with the potential field approaches. The computation of the inverse kinematics problem is accomplished by numerically solving a linear system, which includes the vector for obstacle avoidance and a scheme for the proper pseudoinverse perturbation to deal with the singularities and/or the potential function local minima. These properties make the proposed approach suitable for redundant robots operating in real time in a sensor-based environment. The developed algorithm is tested on the simulation of a planar redundant manipulator. From the results obtained it is observed that the proposed approach compares favorably with the other approaches that have recently been proposed. © 1995 John Wiley & Sons, Inc.     

Path following by the end-effector of a redundant manipulator operating in a dynamic environment

This paper addresses the problem of generating at the control-loop level a collision-free trajectory for a redundant manipulator operating in dynamic environments which include moving obstacles. The task of the robot is to follow, by the end-effector, a prescribed geometric path given in the work space. The control constraints resulting from the physical abilities of robot actuators are also taken into account during the robot movement. Provided that a solution to the aforementioned robot task exists, the Lyapunov stability theory is used to derive the control scheme. The numerical simulation results for a planar manipulator whose end-effector follows a prescribed geometric path, given in both an obstacle-free work space and a work space including the moving obstacles, illustrate the trajectory performance of the proposed control scheme.     

Path-constrained control of a redundant manipulator in a task space

This study addresses the problem of controlling a redundant manipulator with both state and control dependent constraints. The task of the robot is to follow by the end-effector a prescribed geometric path given in the task space. The control constraints resulting from the physical abilities of robot actuators are also taken into account during the robot movement. Provided that a solution to the aforementioned robot task exists, the Lyapunov stability theory is used to derive the control scheme. The numerical simulation results, carried out for a planar manipulator whose end-effector follows a prescribed geometric path given in a task space, illustrate the trajectory performance of the proposed control scheme.     

Adaptive control of redundant multiple robots in cooperative motion

A redundant robot has more degrees of freedom than what is needed to uniquely position the robot end-effector. In practical applications the extra degrees of freedom increase the orientation and reach of the robot. Also the load carrying capacity of a single robot can be increased by cooperative manipulation of the load by two or more robots. In this paper, we develop an adaptive control scheme for kinematically redundant multiple robots in cooperative motion.In a usual robotic task, only the end-effector position trajectory is specified. The joint position trajectory will therefore be unknown for a redundant multi-robot system and it must be selected from a self-motion manifold for a specified end-effector or load motion. In this paper, it is shown that the adaptive control of cooperative multiple redundant robots can be addressed as a reference velocity tracking problem in the joint space. A stable adaptive velocity control law is derived. This controller ensures the bounded estimation of the unknown dynamic parameters of the robots and the load, the exponential convergence to zero of the velocity tracking errors, and the boundedness of the internal forces. The individual robot joint motions are shown to be stable by decomposing the joint coordinates into two variables, one which is homeomorphic to the load coordinates, the other to the coordinates of the self-motion manifold. The dynamics on the self-motion manifold are directly shown to be related to the concept of zero-dynamics. It is shown that if the reference joint trajectory is selected to optimize a certain type of objective functions, then stable dynamics on the self-motion manifold result. The overall stability of the joint positions is established from the stability of two cascaded dynamic systems involving the two decomposed coordinates.     

Optimal path planning of redundant free-floating revolute-jointed space manipulators with seven links

The path planning of free-floating manipulators is of great interest in space operations. The manipulators in the free-floating mode exhibit nonholonomic characteristics due to the nonintegrability of the angular momentum, which makes the problem complicated. This paper analyzes the path planning of redundant, free-floating space manipulators with revolute joints and 7 degrees of freedom. The primary task of manipulators is to move the manipulator arms so that the desired end-effector position and orientation can be achieved. The motion of the manipulators can produce an attitude disturbance of the base, which has an adverse impact on the spacecraft operation. Thus, it is necessary to minimize the base attitude disturbance in order to reduce the fuel consumption for attitude maintenance. Practically, the path planning of redundant free-floating manipulators with higher degrees of freedom (7 degrees of freedom in this paper) in three-dimensional space is more complicated than path planning with fewer degrees of freedom, including planar or fixed base cases. This paper provides a tractable planning method to solve this problem, which could avoid the pseudo inverse of the Jacobian matrix. The sine functions, whose arguments are the polynomial functions with unknown coefficients, are used to specify the joint paths. The PSODE algorithm (particle swarm optimization combined with differential evolution) is applied to optimize the unknown coefficients of the polynomials in order to achieve the desired end-effector position and orientation and simultaneously minimize the base attitude disturbance. The simulations demonstrate that this method could provide satisfactory smooth paths for redundant free-floating space manipulators.     

空间机器人最优能耗捕获目标的自适应跟踪控制

提出了一种能够引导末端执行器以期望速度跟踪目标的轨迹规划方法。该方法可以实现避障并满足关节限制要求。基于轨迹规划方法,设计了一种利用自由飘浮空间机器人跟踪与捕获章动自旋卫星的自适应控制策略。此外,该控制策略还考虑了最优能耗、测量误差和优化误差。首先,为了使执行器的跟踪误差和机械臂的能耗最小,将空间机器人的控制策略描述为一个关于关节速度、力矩和避障距离的不等式约束优化问题。然后,推导出一个系数为下三角矩阵的显式状态方程,并对目标函数进行解耦和线性化。设计了一种关节速度和力矩分段优化方法去代替传统的凸二次规划方法求解最优问题,这种方法具有较高的计算效率。最后,利用李雅普诺夫稳定性理论验证了所提控制方法的收敛性。     

Direct adaptive impedance control of robot manipulators

This article presents an adaptive scheme for controlling the end-effector impedance of robot manipulators. The proposed control system consists of three subsystems: a simple “filter” that characterizes the desired dynamic relationship between the end-effector position error and the end-effector/environment contact force, an adaptive controller that produces the Cartesian-space control input required to provide this desired dynamic relationship, and an algorithm for mapping the Cartesian-space control input to a physically realizable joint-space control torque. The controller does not require knowledge of either the structure or the parameter values of the robot dynamics and is implemented without calculation of the robot inverse kinematic transformation. As a result, the scheme represents a general and computationally efficient approach to controlling the impedance of both nonredundant and redundant manipulators. Furthermore, the method can be applied directly to trajectory tracking in free-space motion by removing the impedance filter. Computer simulation results are given for a planar four degree-of-freedom redundant robot under adaptive impedance control. These results demonstrate that accurate end-effector impedance control and effective redundancy utilization can be achieved simultaneously by using the proposed controller.     

Optimization of layout and path planning of surgical robotic system

Positioning a surgical robot for optimal operation in a crowded operating room is a challenging task. In the robotic-assisted surgical procedures, the surgical robot’s end-effector must reach the patient’s anatomical targets because repositioning of the patient or surgical robot requires additional time and labor. This paper proposes an optimization algorithm to determine the best layout of the operating room, combined with kinematics criteria and optical constraints applied to the surgical assistant robot system. A new method is also developed for trajectory of robot’s end-effector for path planning of the robot motion. The average deviations obtained from repeatability tests for surgical robot’s layout optimization were 1.4 and 4.2 mm for x and y coordinates, respectively. The results of this study show that the proposed optimization method successfully solves the placement problem and path planning of surgical robotic system in operating room.

     

自由漂浮空间机器人避奇异规划—跟踪算法

针对路径相关空间内自由漂浮空间机器人无法进行有效跟踪控制的问题,设计了一种避奇异轨迹规划—跟踪算法,用于完成路径相关空间机械臂末端轨迹跟踪控制的任务．首先,分析奇异条件并设定安全边界曲线,求解回避奇异的基座姿态角阈值,从而得到避奇异参考轨迹及初始状态值．接着,利用自由漂浮空间机器人非线性动力学模型具有状态依赖参数的类线性结构特点,基于状态依赖Riccati方程设计跟踪控制器对末端速度进行跟踪,保证闭环系统的局部渐近稳定性．所提方法克服了传统方法将工作空间约束在路径无关空间的缺点．仿真结果表明,该算法具有比比例微分（proportional derivative,PD）控制更高的跟踪精度．同时,在存在输入干扰的情况下仍然能够实现有效跟踪．     

空间机器人抓捕目标后基于任务相容性的消旋策略

针对双臂空间机器人抓捕自旋目标后的镇定操作,在考虑机器人系统输入约束的条件下,提出了一种基于任务相容性的消旋规划与控制方法。首先,给出空间机器人抓捕目标后的组合系统的动力学模型,作为规划与控制的基础。然后,根据动力学可操作度和任务相容性设计了目标的快速消旋策略,其期望加速度的方向和大小分别取作速度的反方向和机器人系统输入约束允许的最大值。最后,基于所推导的运动学和动力学模型,通过对目标和机械臂末端分别建立柔顺度等式,提出了一种跟踪期望运动轨迹同时对末端接触力进行调节的柔顺控制方法。通过双臂7自由度空间机器人消除目标自旋运动的仿真结果,验证了所提方法的有效性。     

Optimal trajectory planning for a space robot docking with a moving target via homotopy algorithms

The mathematical formulation of optimal trajectory planning for a space robot docking with a moving target is derived. The calculus of variations is applied to the problem so that the optimal robot trajectory can be obtained directly from the target information without first planning the trajectory of the end-effector. The nonlinear two-point boundary value problem resulting from the problem formulation is solved numerically by a globally convergent homotopy algorithm. The algorithm guarantees convergence to a solution for an arbitrarily chosen initial guess. Numerical simulation for three examples demonstrates the approach. © 3995 John Wiley & Sons, Inc.     

双臂空间机器人的避自碰轨迹规划研究*

本文针对自由漂浮的双臂空间机器人系统研究了一种基于危险域的避自碰轨迹规划方案。首先,引入危险域的概念,用来评估两个机械臂之间发生碰撞的危险程度。其次,在路径规划的基础之上,利用危险域的反馈信息,设计了一种安全避自碰的轨迹规划方案,用以保证两个机械臂可以运动在安全位型,从而避免发生自碰。最后,针对一个双臂冗余空间机器人系统进行运动仿真,仿真结果验证了本文方法的有效性。     

Path planning with general end-effector constraints

In this paper, we address the path planning problem with general end-effector constraints (PPGEC) for robot manipulators. Two approaches are proposed. The first approach is the Adapted-RGD method, which is adapted from an existing randomized gradient descent (RGD) method for closed-chain robots. The second approach is radically different. We call it ATACE, Alternate Task-space And Configuration-space Exploration. Unlike the first approach which searches purely in C-space, ATACE works in both task space and C-space. It explores the task space for end-effector paths satisfying given constraints, and utilizes trajectory tracking technique(s) as a local planner(s) to track these paths in the configuration space. We have implemented both approaches and compared their relative performances in different scenarios. ATACE outperforms Adapted-RGD in the majority (but not all) of the scenarios. We outline intuitive explanations for the relative performances of these two approaches.     

A recurrent neural network for minimum infinity-norm kinematiccontrol of redundant manipulators with an improved problem formulationand reduced architecture complexity

This paper presents an improved neural computation where scheme for kinematic control of redundant manipulators based on infinity-norm joint velocity minimization. Compared with a previous neural network approach to minimum infinity-non kinematic control, the present approach is less complex in terms of cost of architecture. The recurrent neural network explicitly minimizes the maximum component of the joint velocity vector while tracking a desired end-effector trajectory. The end-effector velocity vector for a given task is fed into the neural network from its input and the minimum infinity-norm joint velocity vector is generated at its output instantaneously. Analytical results are given to substantiate the asymptotic stability of the recurrent neural network. The simulation results of a four-degree-of-freedom planar robot arm and a seven-degree-of-freedom industrial robot are presented to show the proposed neural network can effectively compute the minimum infinity-norm solution to redundant manipulators.     

Online trajectory planning of robot arms for interception of fast maneuvering object under torque and velocity constraints

This paper presents a novel approach to an online trajectory planning of robot arms for the interception of a fast-maneuvering object under torque and velocity constraints. A body axis is newly introduced as a trajectory-planning coordinate in order to meet the position and the velocity matching conditions for a smooth grasp of the fast-maneuvering object. Using the position of the object and the end-effector in the inertia axis, the acceleration commands are generated in the X-, Y-, and Z-directions of the body axis and the acceleration commands are modified considering the torque and the velocity constraints. The trajectory planning in the X-direction becomes the speed planning to achieve the maximum speed, whereas the trajectory planning in the Y- and Z-directions becomes the direction planning where a missile-guidance algorithm is employed to intercept the maneuvering object. Finally, the acceleration commands in the body axis are transformed into the angle commands of the end-effector in the joint axis, which is used as the actual trajectory commands in robot arms.     

A Neural Network Adaptive Controller for End-effector Tracking of Redundant Robot Manipulators

In this paper we propose a neural network adaptive controller to achieve end-effector tracking of redundant robot manipulators. The controller is designed in Cartesian space to overcome the problem of motion planning which is closely related to the inverse kinematics problem. The unknown model of the system is approximated by a decomposed structure neural network. Each neural network approximates a separate element of the dynamical model. These approximations are used to derive an adaptive stable control law. The parameter adaptation algorithm is derived from the stability study of the closed loop system using Lyapunov approach with intrinsic properties of robot manipulators. Two control strategies are considered. First, the aim of the controller is to achieve good tracking of the end-effector regardless the robot configurations. Second, the controller is improved using augmented space strategy to ensure minimum displacements of the joint positions of the robot. Simulation examples are also presented to verify the effectiveness of the proposed approach.