Trajectory Planning with Collision Avoidance for Redundant Robots Using Jacobian and Artificial Potential Field-based Real-time Inverse Kinematics

This study proposes an algorithm for combining the Jacobian-based numerical approach with a modified potential field to solve real-time inverse kinematics and path planning problems for redundant robots in unknown environments. With an increase in the degree of freedom (DOF) of the manipulator, however, the problems in realtime inverse kinematics become more difficult to solve. Although the analytical and geometrical inverse kinematics approach can obtain the exact solution, it is considerably difficult to solve as the DOF increases, and it necessitates recalculations whenever the robot arm DOF or Denavit-Hartenberg (D-H) parameters change. In contrast, the numerical method, particularly the Jacobian-based numerical method, can easily solve inverse kinematics irrespective of the aforementioned changes including those in the robot shape. The latter method, however, is not employed in path planning for collision avoidance, and it presents real-time calculation problems. This study accordingly proposes the Jacobian-based numerical approach with a modified potential field method that can realize real-time calculations of inverse kinematics and path planning with collision avoidance irrespective of whether the case is redundant or non-redundant. To achieve this goal, the use of a judgment matrix is proposed for obstacle condition identification based on the obstacle boundary definition; an approach for avoiding the local minimum is also proposed. After the obstacle avoidance path is generated, a trajectory plan that follows the path and avoids the obstacle is designed. Finally, the proposed method is evaluated by implementing a motion planning simulation of a 7-DOF manipulator, and an experiment is performed on a 7-DOF real robot.

     

A fast procedure for manipulator inverse kinematics computation and singularities prevention

In this article, a fast procedure for numerical manipulator inverse kinematics computation and singularities prevention is presented. The approach is based upon solving a linear system and automatically calculating some parameters. These parameters are properly used in either one of two original schemes that are also proposed to induce robustness to the pseudoinverse. Furthermore, here it is also shown how to properly implement one of these schemes in conjunction with a recently developed approach for the singularities prevention of redundant manipulators. The resultant algorithms are tested on the simulation of a planar redundant manipulator. From the results obtained, it is observed that the proposed approach compares favorably with the approaches using a Gaussian elimination procedure and with pseudoinverse robustness based on a manipulability measure.     

Procedure for manipulator inverse kinematics computation and proper pseudoinverse perturbation

In this article, an efficient procedure for the proper pseudoinverse perturbation and the numerical inverse kinematics computation of robot manipulators is presented. The approach is based on solving a linear system of equations and using an original scheme for the appropriate perturbation of the pseudoinverse matrix in the next iteration. The resultant algorithm is tested on the simulation of an industrial robot manipulator. From the results obtained, it is observed that the proposed approach compares favorably with the approaches using a Gaussian elimination procedure and with pseudoinverse robustness based on a manipulability measure.     

Inverse kinematics and geometrically bounded singularities prevention of redundant manipulators: An Artificial Neural Network approach

This article presents an Artificial Neural Network (ANN) approach for fast inverse kinematics computation and effective geometrically bounded singularities prevention of redundant manipulators. Here, some bounded geometrical concepts are properly utilized to establish some characterizing matrices, to yield a simple performance index, and a null space vector for singularities avoidance/prevention and safe path generation. Then, a properly trained ANN is used in a novel scheme for the computation of inverse kinematics. This scheme includes the proposed null space vector being also computed by another properly trained ANN. The efficiency of the proposed ANN approach is demonstrated in the successful singularities prevention of a planar redundant manipulator performing a benchmark test.     

基于解析法和遗传算法的机械手运动学逆解

研究优化机械手轨迹规划问题,机械手运动时要具有稳定性避障性能。针对平面3自由度冗余机械手优化控制问题,建立机械手的结构模型。提出用解析法和遗传算法相结合满足具有计算量小和适应性强的特点。在给定机械手末端执行器的运动轨迹,按着机械手冗余自由度,运动轨迹上每个点对应的关节角有无穷多个解。而通过算法可以找到一组最优的关节角,可得到优化机械手运动过程中柔顺性和避障点。仿真结果表明,该算法可以快速收敛到全局最优解,可用于计算冗余机械手运动学逆解,并可实现机器人的轨迹规划和避障优化控制。     

Obstacle avoidance of redundant manipulators using neural networks based reinforcement learning

This paper proposes a new approach for solving the problem of obstacle avoidance during manipulation tasks performed by redundant manipulators. The developed solution is based on a double neural network that uses Q-learning reinforcement technique. Q-learning has been applied in robotics for attaining obstacle free navigation or computing path planning problems. Most studies solve inverse kinematics and obstacle avoidance problems using variations of the classical Jacobian matrix approach, or by minimizing redundancy resolution of manipulators operating in known environments. Researchers who tried to use neural networks for solving inverse kinematics often dealt with only one obstacle present in the working field. This paper focuses on calculating inverse kinematics and obstacle avoidance for complex unknown environments, with multiple obstacles in the working field. Q-learning is used together with neural networks in order to plan and execute arm movements at each time instant. The algorithm developed for general redundant kinematic link chains has been tested on the particular case of PowerCube manipulator. Before implementing the solution on the real robot, the simulation was integrated in an immersive virtual environment for better movement analysis and safer testing. The study results show that the proposed approach has a good average speed and a satisfying target reaching success rate.     

An efficient local approach for the path generation of robot manipulators

In this article an efficient local approach for the path generation of robot manipulators is presented. The approach is based on formulating a simple nonlinear programming problem. This problem is considered as a minimization of energy with given robot kinematics and subject to the robot requirements and a singularities avoidance constraint. From this formulation a closed form solution is derived which has the properties that allows to pursue both singularities and obstacle avoidance simultaneously; and that it can incorporate global information. These properties enable the accomplishment of the important task that while a specified trajectory in the operational space can be closely followed, also a desired joint configuration can be attained accurately at a given time. Although the proposed approach is primarily developed for redundant manipulators, its application to nonredundant manipulators is examplified by considering a particular commercial manipulator.     

A global approach for the optimal path generation of redundant robot manipulators

In this article the optimal path generation of redundant robot manipulators is considered as an optimization problem, with given kinematics and subject to the robot requirements and a singularities avoidance constraint. This problem is formulated as a constrained continuous optimal control problem, which allows to consider joints and velocities constraints and/or manipulator dynamics. This approach is exemplified for a planar redundant manipulator and the resultant state constrained problem is solved by an efficient iterative numerical technique.     

An Artificial Neural Network Approach for Inverse Kinematics Computation and Singularities Prevention of Redundant Manipulators

In this article an Artificial Neural Network (ANN) approach for fast inverse kinematics computation and effective singularities prevention of redundant robot manipulators is presented. The approach is based on establishing some characterizing matrices, representing some geometrical concepts, in order to yield a simple performance index and a null space vector for singularities avoidance/prevention and safe path generation. Here, this null space vector is computed using a properly trained ANN and included in the computation of the inverse kinematics being performed also by another properly trained ANN.     

A Robust Method for the Concurrent Motion Planning of Multi-Manipulators Systems

In this article a robust and simple procedure for the on-line concurrent motion planning of multi-manipulators is presented. The approach is based on solving for each manipulator a linear system of equations taking into account a vector for motion planning, and an original scheme for the appropriate perturbation of the pseudoinverse matrix. This method can pursue simultaneously both motion coordination and singularities prevention in real time in a sensor based environment. These properties make it suitable for fully autonomous or telerobotic systems operations.     

Obstacle avoidance for kinematically redundant manipulators using a dual neural network.

One important issue in the motion planning and control of kinematically redundant manipulators is the obstacle avoidance. In this paper, a recurrent neural network is developed and applied for kinematic control of redundant manipulators with obstacle avoidance capability. An improved problem formulation is proposed in the sense that the collision-avoidance requirement is represented by dynamically-updated inequality constraints. In addition, physical constraints such as joint physical limits are also incorporated directly into the formulation. Based on the improved problem formulation, a dual neural network is developed for the online solution to collision-free inverse kinematics problem. The neural network is simulated for motion control of the PA10 robot arm in the presence of point and window-shaped obstacle.     

冗余自由度机械手的避障控制

避障碍物一直是冗余自由度机械手的主要应用，本文采用伪逆矩阵法，以障碍物和 机械手之间的距离的函数作为性能指标函数来解冗余自由度机械手逆解，进行避障控制，并 提出一种简单的计算机械手和障碍物之间的距离方法，通过对一个三自由度的平面机械手进 行仿真，验证了算法的正确性．     

基于遗传算法的机械臂实时避障路径规划研究

针对模块化机械臂在运行时可能与工作空间中的障碍物发生碰撞的问题, 提出一种基于遗传算法的避障路径规划算法。首先采用D-H(Denavit-Hartenberg)表示法对机械臂进行建模, 并进行运动学和动力学分析, 建立机械臂运动学和动力学方程。在此基础上, 利用遗传算法分别在单/多个障碍物工作环境中, 以运动的时间、移动的空间距离和轨迹长度作为优化指标, 实现机械臂避障路径规划的优化。通过仿真验证了基于遗传算法的机械臂避障路径规划算法的有效性与可行性, 该算法提高了运行中的机械臂有效避开工作空间中障碍物的效率。     

A Fast Approach for Robot Motion Planning

This paper describes a new approach to robot motion planning that combines the end-point motion planning with joint trajectory planning for collision avoidance of the links. Local and global methods are proposed for end-point motion planning. The joint trajectory planning is achieved through a pseudoinverse kinematic formulation of the problem. This approach enables collision avoidance of the links by a fast null-space vector computation. The power of the proposed planner derives from: its speed; the good properties of the potential function for end-point motion planning; and from the simultaneous avoidance of the links collision, kinematic singularities, and local minima of the potential function. The planner is not defined over computationally expensive configuration space and can be applied for real-time applications. The planner shows to be faster than many previous planners and can be applied to robots with many degrees of freedom. The effectiveness of the proposed local and global planning methods as well as the general robot motion planning approach have been experimented using the computer-simulated robots. Some of the simulation results are included in this paper.     

Collision-avoidance for redundant robots through control of the self-motion of the manipulator

A new method to on-line collision-avoidance of the links of redundant robots with obstacles is presented. The method allows the use of redundant degrees of freedom such that a manipulator can avoid obstacles while tracking the desired end-effector trajectory. It is supposed that the obstacles in the workspace of the manipulator are presented by convex polygons. The recognition of collisions of the links of the manipulator with obstacles results on-line through a nonsensory method. For every link of the redundant manipulator and every obstacle a boundary ellipse is defined in workspace such that there is no collision if the robot joints are outside these ellipses. In case a collision is imminent, the collision-avoidance algorithm compute the self-motion movements necessary to avoid the collision. The method is based on coordinate transformation and inverse kinematics and leads to the favorable use of the abilities of redundant robots to avoid the collisions with obstacles while tracking the end-effector trajectory. This method has the advantage that the configuration of the manipulator after collision-avoidance can be influenced by further requirements such as avoidance of singularities, joint limits, etc. The effectiveness of the proposed method is discussed by theoretical considerations and illustrated by simulation of the motion of three-and four-link planar manipulators between obstacles.     

Inverse kinematics of variable-geometry truss manipulators

A new class of robotic arm consists of a periodic sequence of truss substructures, each of which has several variable-length members. Such variable-geometry truss manipulators (VGTMs) are inherently highly redundant and promise a significant increase in dexterity over conventional anthropomorphic manipulators. This dexterity may be exploited for both obstacle avoidance and controlled deployment in complex workspaces. The inverse kinematics problem for such unorthodox manipulators, however, becomes complex because of the large number of degrees of freedom, and conventional solutions to the inverse kinematics problem become inefficient because of the high degree of redundancy. This paper presents a solution to this problem based on a spline-like reference curve for the manipulator's shape. Such an approach has a number of advantages: (1) direct, intuitive manipulation of shape; (2) reduced calculation time; and (3) direct control over the effective degree of redundancy of the manipulator. Furthermore, although the algorithm has been developed primarily for variable-geometry-truss manipulators, it is general enough for application to other manipulator designs.     

空间冗余机械臂路径规划方法研究

针对空间站遥操作7DOF冗余机械臂路径规划的安全性、可靠性问题,提出了基于臂型角逆运动学的优化A*路径规划算法.本文根据臂型角参数化完善了逆运动学方法,得到了32组完备逆解集,增加了路径规划时逆解选择的灵活性;通过臂型角搜索和最小奇异值优化A*路径规划算法,提高机械臂避障、避奇异能力,机械臂操作的灵活性和路径的安全可靠性;同时根据路径优化策略,有效平滑了路径,减少了机械臂的磨损.仿真结果说明了该方法的有效性.     

Kinematic control of a redundant manipulator using an inverse-forward adaptive scheme with a KSOM based hint generator

This paper proposes an online inverse-forward adaptive scheme with a KSOM based hint generator for solving the inverse kinematic problem of a redundant manipulator. In this approach, a feed-forward network such as a radial basis function (RBF) network is used to learn the forward kinematic map of the redundant manipulator. This network is inverted using an inverse-forward adaptive scheme until the network inversion solution guides the manipulator end-effector to reach a given target position with a specified accuracy. The positioning accuracy, attainable by a conventional network inversion scheme, depends on the approximation error present in the forward model. But, an accurate forward map would require a very large size of training data as well as network architecture. The proposed inverse-forward adaptive scheme effectively approximates the forward map around the joint angle vector provided by a hint generator. Thus the inverse kinematic solution obtained using the network inversion approach can take the end-effector to the target position within any arbitrary accuracy.In order to satisfy the joint angle constraints, it is necessary to provide the network inversion algorithm with an initial hint for the joint angle vector. Since a redundant manipulator can reach a given target end-effector position through several joint angle vectors, it is desirable that the hint generator is capable of providing multiple hints. This problem has been addressed by using a Kohonen self organizing map based sub-clustering (KSOM-SC) network architecture. The redundancy resolution process involves selecting a suitable joint angle configuration based on different task related criteria.The simulations and experiments are carried out on a 7 DOF PowerCube? manipulator. It is shown that one can obtain a positioning accuracy of 1 mm without violating joint angle constraints even when the forward approximation error is as large as 4 cm. An obstacle avoidance problem has also been solved to demonstrate the redundancy resolution process with the proposed scheme.     

Kinematic aspects of a robot-positioner system in an arc welding application

This paper focuses on the kinematic control of a redundant robotic system taking into account particularities of the arc welding technology. The considered system consists of a 6-axis industrial robot (welding tool manipulator) and a 2-axis welding positioner (workpiece manipulator) that is intended to optimise a weld joint orientation during the technological process. The particular contribution of the paper lies in the area of the positioner inverse kinematics, which is a key issue of such system off-line programming and control. It has been proposed a novel formulation and a closed-form solution of the inverse kinematic problem that deals with the explicit definition of the weld joint orientation relative to the gravity. Similar results have also been obtained for the known problem statement that is based on a unit vector transformation. For both the cases, a detailed investigation of the singularities and uniqueness-existence topics have been carried out. The presented results are implemented in a commercial software package and verified for real-life applications in the automotive industry.     

Reliability-based approach to the inverse kinematics solution of robots using Elman's networks

The solution of inverse kinematics problem of redundant manipulators is a fundamental problem in robot control. The inverse kinematics problem in robotics is the determination of joint angles for a desired cartesian position of the end effector. For the solution of this problem, many traditional solutions such as geometric, iterative and algebraic are inadequate if the joint structure of the manipulator is more complex. Furthermore, many neural network approaches have been done to this problem. But the neural network-based solutions are not much reliable due to the error at the end of learning. Therefore, a reliability-based neural network inverse kinematics solution approach has been presented, and applied to a six-degrees of freedom (dof) robot manipulator in this paper. The structure of the proposed method is based on using three networks designed parallel to minimize the error of the whole system. Elman network, which has a profound impact on the learning capability and performance of the network, is chosen and designed according to the proposed solution method. At the end of parallel implementation, the results of each network are evaluated using direct kinematics equations to obtain the network with best result.