New inverse kinematic algorithms for redundant robots

New inverse kinematic algorithms for generating redundant robot joint trajectories are proposed. The algorithms utilize the kinematic redundancy to improve robot motion performance (in joint space or Cartesian space) as specified by certain objective functions. The algorithms are based on the extension of the existing “joint-space command generator” technique in which a null space vector is introduced which optimizes a specific objective function along the joint trajectories. In this article, the algorithms for generating the joint position and velocity (PV) trajectories are extensively developed. The case for joint position, velocity, and acceleration (PVA) generation is also addressed. Application of the algorithms to a four-link revolute planar robot manipulator is demonstrated through simulation. Several motion performance criteria are considered and their results analyzed.     

Manipulator motion control in operational space using joint velocity inner loops

This paper addresses the operational space motion control—trajectory tracking—of robot manipulators endowed with joint velocity feedback inner loops. A general structure for model-based joint velocity controllers is proposed for the inner loop. The required joint velocity reference is provided by an outer loop inspired from the robot kinematic control approach. It is shown that above two-loops control schemes lead to a nice cascade structure for the corresponding closed-loop systems. A stability result adapted for analysis of this particular kind of systems is developed in the paper; sufficient conditions for global exponential stability of this class of cascade systems are obtained. The effectiveness of the proposed control approach is evaluated on a direct-drive mechanical arm, and compared with a typical control strategy based on inverse kinematics resolution for computation of the desired motion in joint space, and the use of the computed-torque technique. The experimental evidences show better performance of the proposed two-loops controller.     

Neural-network-based two-loop control of robotic manipulators including actuator dynamics in task space

A neural-network-based motion controller in task space is presented in this paper. The proposed controller is addressed as a two-loop cascade control scheme. The outer loop is given by kinematic control in the task space. It provides a joint velocity reference signal to the inner one. The inner loop implements a velocity servo loop at the robot joint level. A radial basis function network （RBFN） is integrated with proportional-integral （PI） control to construct a velocity tracking control scheme for the inner loop. Finally, a prototype technology based control system is designed for a robotic manipulator. The proposed control scheme is applied to the robotic manipulator. Experimental results confirm the validity of the proposed control scheme by comparing it with other control strategies.     

空间机器人随机故障容错规划的蜜蜂算法

本文为解决复杂的随机规划问题设计了一种基于随机模拟的混沌量子蜜蜂算法,证明了该算法的收敛 性,并分析了算法的收敛速度．分析6 自由度空间机器人系统的不确定性,采用基于微分变换法进行误差分析,建 立了随机数学规划模型．为涉及故障前后运动学与动力学约束限制的容错轨迹规划,以加权最小驱动力矩为优化性 能指标,采用混沌量子蜜蜂算法求解全部工作时间中机械臂故障前后的最优轨迹．通过降低异常关节的运动速度来 降低故障关节力矩,保证机械臂在发生故障后具有较高的操作能力．案例研究验证了该算法的有效性、稳定性及准 确性．     

一种基于测地线的机器人轨迹规划方法

提出了一种基于测地线的机器人轨迹规划方法.该方法克服了传统的轨迹规划方法的某些不足,其规划是在关节空间(黎曼空间)内进行的,规划目标是直角坐标空间内的直线,即两点之间的最短路径,也可以是系统动能最小,或某项综合指标最优.该规划方法直接得到机器人的各关节的转角和角速度,无需进行运动学反解和多项式插值.本文的基于测地线的轨迹规划是以轨迹弧长作为参考变量的,因此它还具有非时间参考的机器人轨迹规 划的优点.􀁱     

A natural redundancy‐resolution for 3‐D multi‐joint reaching under the gravity effect

A simple control method for 3‐dimensional multi‐joint reaching movements under redundancy of degrees of freedom (DOF) is proposed, which need neither introduce any performance index to solve inverse kinematics uniquely nor calculate pseudo‐inverse of the Jacobian matrix of task coordinates with respect to joint coordinates. The proposed control signal is composed of linear superposition of three terms: (1) angular‐velocity feedback for damping shaping, (2) task‐space position error feedback with a single stiffness parameter, and (3) compensation for gravity force on the basis of estimates for uncertain parameters of the potential energy without calculation any inverse joint position to the target in task space. Through a theoretical analysis of the closed‐loop dynamics and a variety of computer simulations by using a whole arm model with five DOFs, the importance of synergistic adjustments of damping factors as well as its relation to selection of the stiffness parameter is pointed out. It is shown that if damping factors are chosen synergistically corresponding to the inertia matrix at the initial time and the stiffness parameter then the endpoint converges asymptotically to the target position and reaches it smoothly without incurring any self‐motion. © 2005 Wiley Periodicals, Inc.     

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。     

A Bayesian approach to joint tracking and identification of geometric shapes in video sequences

A Bayesian approach is proposed for joint tracking and identification. These two problems are often addressed independently in the literature, leading to suboptimal performance. In a Bayesian approach, a prior distribution is set on both the hypothesis space and the associated parameter space. Although this is straightforward from a conceptual viewpoint, it is typically impossible to perform inference in closed-form. We discuss an advanced particle filtering approach to solve this computational problem and apply this algorithm to joint tracking and identification of geometric forms in video sequences.     

Feedback control for robotic manipulator with an uncertain Jacobian matrix

In most applications of robots, a desired path for the end‐effector is usually specified in task space such as Cartesian space. One way to move the robot along this path is to solve the inverse kinematics problem to generate the desired angles in joint space. However, it is a very time consuming task to solve the inverse kinematics problem. Furthermore, in the presence of uncertainty in kinematics, it is impossible to derive the desired joint angle from the desired end‐effector path and the Jacobian matrix of the mapping from joint space to task space. In this article, a feedback control law using an uncertain Jacobian matrix is proposed for setpoint control of robots. Sufficient conditions for the bound of the estimated Jacobian matrix and stability conditions for the feedback gains are presented to guarantee the stability and passivity of the robots. A gravity regressor with an uncertain Jacobian matrix is also proposed for gravitational force compensation when the gravitational force is uncertain. Simulation results are presented to illustrate the performance of the proposed controllers. ©1999 John Wiley & Sons, Inc.     

Real-Time Motion Tracking of Robot Manipulators Using Adaptive Genetic Algorithms

The paper presents a genetic algorithm approach to real-time motion tracking of redundant and non-redundant manipulators. The joint angle trajectories are found by applying genetic operators to a set of suitably generated configurations so that the end-effector follows a desired workspace trajectory accurately. The probability of applying a particular genetic operator is adapted on-line to achieve fast convergence to the solution. The adaptation is based on two measures, namely, diversity and fitness of the generated configurations. In order to achieve real time tracking, special provisions are made so that only an appropriate small region in the joint space is searched. The tracking problem is solved at the position level rather the then velocity level. As such the proposed method does not use the manipulator Jacobian inverse or pseudo-inverse matrix and is shown to be free from problems such as excessive joint velocities due to singularities. Simulation results are presented for the 6-DOF Puma and the 7-DOF Robotic Research arm that demonstrate good tracking accuracy and reasonable joint velocities.     

Force,orientation and position control in redundant manipulators in prioritized scheme with null space compliance

This paper addresses the problem of executing multiple prioritized tasks for robot manipulators with compliant behavior in the remaining null space. A novel controller–observer is proposed to ensure accurate accomplishment of various tasks based on a predefined hierarchy using a new priority assignment approach. Force control, position control and orientation control are considered. Moreover, a compliant behavior is imposed in the null space to handle physical interaction without using joint torque measurements. Asymptotic stability of the task space error and external torque estimation error during executing multiple tasks are shown. The performance of the proposed approach is evaluated on a 7R light weight robot arm by several case studies.     

Duty-cycle analysis of a human-controlled manipulator

The duty cycles of a human-controlled servomanipulator system have been experimentally measured revealing how humans use manipulators to perform tasks. The use of the kinematic ranges, in both joint and Cartesian space is valuable to engineers in the kinematic design of servomanipulators. The working volume of human manipulation presented here is also of interest to designers of prosthetic systems. These results illuminate the relative merits of various system drive configurations. A graphical representation of mechanical power usage, which displays the total operation time as a function of torque and velocity, is presented for each manipulator joint. These data are compared with data representing idealized joint performance resulting in design criteria for quantitative improvements in joint torque and velocity capacities. A generalized method for applying this representation to any robotic system is discussed.     

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.     

Reactive navigation of multiple moving agents by collaborative resolution of conflicts

In navigation that involves several moving agents or robots that are not in possession of each other's plans, a scheme for resolution of collision conflicts between them becomes mandatory. A resolution scheme is proposed in this paper specifically for the case where it is not feasible to have a priori the plans and locations of all other robots, robots can broadcast information between one another only within a specified communication distance, and a robot is restricted in its ability to react to collision conflicts that occur outside of a specified time interval called the reaction time interval. Collision conflicts are resolved through velocity control by a search operation in the robot's velocity space. The existence of a cooperative phase in conflict resolution is indicated by a failure of the search operation to find velocities in the individual velocity space of the respective robots involved in the conflict. A scheme for cooperative resolution of conflicts is modeled as a search in the joint velocity space of the robots involved in conflict when the search in the individual space yields a failure. The scheme for cooperative resolution may further involve modifying the states of robots not involved in any conflict. This phenomenon is characterized as the propagation phase where cooperation spreads to robots not directly involved in the conflict. Apart from presenting the methodology for the resolution of conflicts at various levels (individual, cooperative, and propagation), the paper also formally establishes the existence of the cooperative phase during real‐time navigation of multiple mobile robots. The effect of varying robot parameters on the cooperative phase is presented and the increase in requirement for cooperation with the scaling up of the number of robots in a system is also illustrated. Simulation results involving several mobile robots are presented to indicate the efficacy of the proposed strategy. © 2005 Wiley Periodicals, Inc.     

自由飞行空间机器人的关节驱动力矩递推算法及其仿真

由于空间特有的微重力环境和卫星本体重心不固定,机械手和卫星本体之间存在运动学和动力学耦合作用,已有针对地面机器人提出的计算关节力矩的 Ｎｅｗ ｔｏｎ Ｅｕｌｅｒ 法和地面机器人的控制策略不能直接应用于自由飞行空间机器人（ Ｆ Ｆ Ｓ Ｒ）的研究报告．文中首先分析了 Ｆ Ｆ Ｓ Ｒ 的速度和加速度关系,在此基础上建立了计算 Ｆ Ｆ Ｓ Ｒ机械手各链杆的速度和加速度的递推公式;其次基于已有的针对地面机器人提出的 Ｎｅｗ ｔｏｎ Ｅｕｌｅｒ 动力学算法,开发了适用于 Ｆ Ｆ Ｓ Ｒ 的关节驱动力矩的递推算法;最后,用计算机仿真验证了文中提出的关节力矩算法的有效性     

Force-guided motions of a 6-d.o.f. industrial robot with a joint space approach

This article deals with the interaction between humans and industrial robots, more specifically with the new design and implementation of an algorithm for force-guided motions of a 6-d.o.f. robot. It may be used to comfortably teach positions without using any teaching pendant or for some assistance tasks. For this purpose, from readings of the force/torque sensor mounted in the robot wrist, the gravity forces and torques first have to be eliminated. To control the robot in joint space, it is then convenient to transform the external force and torque values from Cartesian space into joint space using the manipulator transposed Jacobian. This is why with the present approach the Jacobian matrix of the robot used was calculated. Now, from the computed joint torques, suitable position commands of the robot arm can be generated to obtain the desired behavior. A suggestion for this desired behavior is also included in this article. It is based on the impedance control approach in joint space. The proposed algorithm was implemented with the standard Stäubli RX90B industrial robot.     

基于hp自适应伪谱法的空间机器人路径规划

针对空间机器人运动过程中基座姿态产生较大扰动的问题,基于hp自适应高斯伪谱法提出了一种以基座所受反作用力矩最小为目标函数的空间机器人路径规划方法.首先,综合考虑空间机器人运动过程中存在的关节角度约束、关节角速度约束、控制力矩约束及初始状态和终端状态约束等约束条件,将空间机器人路径规划问题看成满足一系列约束条件和边界条件并实现特定性能指标最优的最优控制问题.其次,结合hp自适应高斯伪谱法（hp-AGPM）与非线性规划技术,求解带有边界约束和路径约束的优化控制问题,得到满足约束且性能指标最优的空间机器人运动轨迹.最后,以平面2自由度空间机械臂为例对所设计方法进行仿真验证,并与其他伪谱法进行对比分析.仿真结果表明：本文算法能在10.6 s的时间内规划出满足各约束条件且容许偏差低于10^-6的最优运动轨迹,并且在计算速度和配点数量上都优于其他伪谱法.     

基于二次型规划的平面冗余机械臂的自运动

提出一种基于二次型性能指标的方法,用于规划平面冗余机械臂的自运动轨迹．鉴于实际的机械臂都存在关节物理约束,该自运动规划方案考虑了关节极限和关节速度极限的躲避．提出了基于线性变分不等式的原对偶神经网络,并将其作为所对应的二次型规划方案的实时求解器．仿真结果证实了该基于神经网络的自运动规划方案的有效性．     

An online collision-free trajectory generation algorithm for human–robot collaboration

The premise of human–robot collaboration is that robots have adaptive trajectory planning strategies in hybrid work cell. The aim of this paper is to propose a new online collision avoidance trajectory planning algorithm for moderate dynamic environments to insure human safety when sharing collaborative tasks. The algorithm contains two parts: trajectory generation and local optimization. Firstly, based on empirical Dirichlet Process Gaussian Mixture Model (DPGMM) distribution learning, a neural network trajectory planner called Collaborative Waypoint Planning network (CWP-net) is proposed to generate all key waypoints required for dynamic obstacle avoidance in joint space according to environmental inputs. These points are used to generate quintic spline smooth motion trajectories with velocity and acceleration constraints. Secondly, we present an improved Stochastic Trajectory Optimization for Motion Planning (STOMP) algorithm which locally optimizes the generated trajectories of CWP-net by constraining the trajectory optimization range and direction through the DPGMM model. Simulations and real experiments from an industrial use case of human–robot collaboration in the field of aircraft assembly testing show that the proposed algorithm can smoothly adjust the nominal path online and effectively avoid collisions during the collaboration.