Mobile Manipulator Motion Planning for Multiple Tasks Using Global Optimization Approach

A mobile manipulator can perform various tasks efficiently by utilizing mobility and manipulation functions. The coupling of these two functions creates a particular kinematic redundancy introduced by mobility, which is different from that introduced by extra joints. This redundancy is quite desirable for dexterous motion in cluttered environments, but it also significantly complicates the motion planning and control problem. In this paper we propose a new motion planning method for mobile manipulators to execute a multiple task which consists of a sequence of tasks. The task considered in this paper is that the end-effector tracks a prespecified trajectory in a fixed world frame. In a multiple task, the final configuration of each task becomes the initial configuration of the next subsequent task. Such a configuration is known as a commutation configuration, which significantly affects the performance of the multiple task.We formulate the motion planning problem as a global optimization problem and simultaneously obtain the motion trajectory set and commutation configurations. In the formulation, we take account of the case that the platform has a non-holonomic constraint as well as the one that the platform has a holonomic constraint. Simulation results are demonstrated to verify the effectiveness of the proposed method.     

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.     

Visual Motor Control of a 7 DOF Robot Manipulator Using Function Decomposition and Sub-Clustering in Configuration Space

This paper deals with real-time implementation of visual-motor control of a 7 degree of freedom (DOF) robot manipulator using self-organized map (SOM) based learning approach. The robot manipulator considered here is a 7 DOF PowerCube manipulator from Amtec Robotics. The primary objective is to reach a target point in the task space using only a single step movement from any arbitrary initial configuration of the robot manipulator. A new clustering algorithm using Kohonen SOM lattice has been proposed that maintains the fidelity of training data. Two different approaches have been proposed to find an inverse kinematic solution without using any orientation feedback. In the first approach, the inverse Jacobian matrices are learnt from the training data using function decomposition. It is shown that function decomposition leads to significant improvement in accuracy of inverse kinematic solution. In the second approach, a concept called sub-clustering in configuration space is suggested to provide multiple solutions for the inverse kinematic problem. Redundancy is resolved at position level using several criteria. A redundant manipulator is dexterous owing to the availability of multiple configurations for a given end-effector position. However, existing visual motor coordination schemes provide only one inverse kinematic solution for every target position even when the manipulator is kinematically redundant. Thus, the second approach provides a learning architecture that can capture redundancy from the training data. The training data are generated using explicit kinematic model of the combined robot manipulator and camera configuration. The training is carried out off-line and the trained network is used on-line to compute the joint angle vector to reach a target position in a single step only. The accuracy attained is better than the current state of art.     

Task-based configuration control of redundant manipulators

This article establishes new goals for redundancy resolution based on manipulator dynamics and end-effector characteristics. These goals can be accomplished by employing the recently developed configuration control approach. Redundancy resolution is achieved by controlling the joint inertia matrix or the end-effector mass matrix that affect the inertial torques or by reducing the joint torques due to gravity loading and payload. The manipulator mechanical advantage and velocity ratio are also used as performance measures to be improved by proper utilization of redundancy. Furthermore, end-effector compliance, sensitivity, and impulsive force at impact are introduced as redundancy-resolution criteria. The new goals for redundancy resolution presented in this article allow a more efficient utilization of the redundant joints based on the desired task requirements. Simple case studies using computer simulations are described for illustration.     

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。     

On motion optimization of robotic manipulators with strong nonlinear dynamic coupling using support area level set algorithm

Aiming for a better dynamic performance from the robot beyond the physical limits set by the manufacturers, in this paper we propose to integrate the robot dynamics into motion planning and then to approximate the robot joint torques using parameterized B-splines. By introducing a high-dimensional non-linear fitness function, we transform the motion planning problem into an optimization of a non-linear fitness function, and then we develop the approach based on Support Area Level Set Algorithm (SALAS). It integrates dual-stage sampling strategies to avoid early convergence in a small search field and to improve the rate of convergence to the potential solution. The effectiveness of the proposed approach has been verified by the simulation of a two-link robotic manipulator.     

Inverse kinematics of binary manipulators by using the continuous-variable-based optimization method

Hyper redundancy, high reliability, and high task repeatability are the main advantages of binary manipulators over conventional manipulators with continuous joints, especially when manipulators are operated under tough and complex work conditions. The precise and complex movement of a binary manipulator necessitates many modules. In this case, numerically efficient inverse kinematics algorithms for binary manipulators usually require impractically large memory size for the real-time calculation of the binary states of all joints. To overcome this limitation by developing a new inverse kinematics algorithm is the objective of this research. The key idea of the proposed method is to formulate the inverse kinematics problem of a binary manipulator as an optimization problem with real design variables, in which the real variables are forced to approach the permissible binary values corresponding to two discrete joint displacements. Using the proposed optimization method, the inverse kinematics of 3-D binary manipulators with many modules can be solved almost in real time (say, less than a second for up to 16 modules) without requiring a large memory size. Furthermore, some manipulation considerations, such as operation power minimization, can be easily incorporated into the proposed formulation. The effectiveness of the proposed method is verified through several numerical problems, including 3-D inverse kinematics problems.     

Weighted hierarchical quadratic programming: assigning individual joint weights for each task priority

This paper proposes a novel method that computes the optimal solution of the weighted hierarchical optimization problem for both equality and inequality tasks. The method is developed to resolve the redundancy of robots with a large number of Degrees of Freedom (DoFs), such as a mobile manipulator or a humanoid, so that they can execute multiple tasks with differently weighted joint motion for each priority level. The proposed method incorporates the weighting matrix into the first-order optimality condition of the optimization problem and leverages an active-set method to handle equality and inequality constraints. In addition, it is computationally efficient because the solution is calculated in a weighted joint space with symmetric null-space projection matrices for propagating recursively to a low priority task. Consequently, robots that utilize the proposed method effectively show whole-body motions handling prioritized tasks with differently weighted joint spaces. The effectiveness of the proposed method was validated through experiments with a nonholonomic mobile manipulator as well as a humanoid.

     

Study and resolution of singularities for a 6-DOF PUMA manipulator

Upon solving the inverse kinematics problem of robot manipulators, the inherent singularity problem should always be considered. When a manipulator is approaching a singular configuration, a certain degree of freedom will be lost such that there are no feasible solutions of the manipulator to move into this singular direction. In this paper, the singularities of a 6-DOF PUMA manipulator are analyzed in detail and all the corresponding singular directions in task space are clearly identified. In order to resolve this singularity problem, an approach denoted Singularity Isolation Plus Compact QP (SICQP) method is proposed. The SICQP method decomposes the work space into achievable and unachievable (i.e., singular) directions. Then, the exactness in the singular directions are released such that extra redundancy is provided to the achievable directions. Finally, the Compact QP method is applied to maintain the exactness in the achievable directions, and to minimize the tracking errors in the singular directions under the condition that feasible joint solutions must be obtained. In the end, some simulation results for PUMA manipulator are given to demonstrate the effectiveness of the SICQP method.     

Well-conditioned configurations of fault-tolerant manipulators

Fault-tolerant motion of redundant manipulators can be obtained by joint velocity reconfiguration. For fault-tolerant manipulators, it is beneficial to determine the configurations that can tolerate the locked-joint failures with a minimum relative joint velocity jump, because the manipulator can rapidly reconfigure itself to tolerate the fault. This paper uses the properties of the condition numbers to introduce those optimal configurations for serial manipulators. The relationship between the manipulator’s locked-joint failures and the condition number of the Jacobian matrix is indicated by using a matrix perturbation methodology. Then, it is observed that the condition number provides an upper bound of the required relative joint velocity change for recovering the faults which leads to define the optimal fault-tolerant configuration from the minimization of the condition number. The optimization problem to obtain the minimum condition number is converted to three standard Eigen value optimization problems. A solution is for selected optimization problem is presented. Finally, in order to obtain the optimal fault-tolerant configuration, the proposed method is applied to a 4-DoF planar manipulator.     

空间机械臂全局反作用优化及其地面试验研究

针对空间机械臂在运动过程中对其基座产生力／力矩反作用这一问题进行了分析,并提出一种关节轨迹参数化的全局反作用优化方法,用于减小机械臂的反作用力／力矩．基于气浮轴承方法,建立了3自由度空间机械臂反作用优化地面实验系统．最后,采用3自由度机械臂验证了该方法的有效性．     

Selection of manipulator system for multiple-goal task by evaluating task completion time and cost with computational time constraints

The focus of this study is on the problem of manipulator system selection for a multiple-goal task by evaluating task completion time and cost with computational time constraints. An approach integrating system selection, structural configuration design, layout design, motion planning, and relative cost calculation is proposed to solve this problem within a reasonable computational time. In the proposed approach, multiple-objective particle swarm optimization (MOPSO) is utilized to search for the appropriate manipulator system with appropriate structural configuration from a set of candidate systems. Particle swarm optimization (PSO) and the nearest neighborhood algorithm are employed in layout design and motion planning due to their high convergence speed. Three methods involving a random search algorithm are compared to the proposed approach through a simulation. The simulation is done with a set of tasks and the result shows the effectiveness of the proposed approach.     

Practical Point-to-Point Multiple-Goal Task Realization in a Robot Arm with a Rotating Table

This study presents a multiple-goal task realization in a system composed of a 6-d.o.f. robot arm and a one-axis rotating table. The problem is complex due to the existence of multiple goals and the kinematic redundancy of the system. We propose a design approach integrating the base placement, task sequencing and motion coordination methods. We show that this approach reduces the task completion time of the robot arm; the motion planning is realized through straight-line paths in the configuration space despite collision occurrences. Furthermore, we introduce a hybrid graph-search method combining the greedy nearest-neighbor method and the Dijkstra method to solve the motion coordination of the robot arm and the table. We show the effectiveness of the design approach and the search method through a time-constrained simulation-based optimization.     

Optimal control of switched systems based on parameterization of the switching instants

This paper presents a new approach for solving optimal control problems for switched systems. We focus on problems in which a prespecified sequence of active subsystems is given. For such problems, we need to seek both the optimal switching instants and the optimal continuous inputs. In order to search for the optimal switching instants, the derivatives of the optimal cost with respect to the switching instants need to be known. The most important contribution of the paper is a method which first transcribes an optimal control problem into an equivalent problem parameterized by the switching instants and then obtains the values of the derivatives based on the solution of a two point boundary value differential algebraic equation formed by the state, costate, stationarity equations, the boundary and continuity conditions, along with their differentiations. This method is applied to general switched linear quadratic problems and an efficient method based on the solution of an initial value ordinary differential equation is developed. An extension of the method is also applied to problems with internally forced switching. Examples are shown to illustrate the results in the paper.     

A framework for large‐force task planning of mobile and redundant manipulators

A framework tackling the problem of large wrench application using robotic systems with limited force or torque actuators is presented. It is shown that such systems can apply a wrench to a limited set of Cartesian locations called force workspace (FW), and its force capabilities are improved by employing base mobility and redundancy. An efficient numerical algorithm based on 2ⁿ‐tree decomposition of Cartesian space is designed to generate FW. Based on the FW generation algorithm, a planning method is presented resulting in proper base positioning relative to large‐force quasistatic tasks. Additionally, the case of tasks requiring application of a wrench along a given path is considered. Task workspace, the set of Cartesian space locations that are feasible starting positions for such tasks, is shown to be a subset of FW. This workspace is used for identifying proper base or task positions guaranteeing task execution along desired paths. Finally, to plan redundant manipulator postures during large‐force‐tasks, a new method based on a min–max optimization scheme is developed. Unlike norm‐based methods, this method guarantees no actuator capabilities are exceeded, and force or torque of the most loaded joint is minimized. Illustrative examples are given demonstrating validity and usefulness of the proposed framework. ©1999 John Wiley & Sons, Inc.     

冗余机器人的双向自运动路径规划

冗余机器人的自运动路径规划是在保持手端任务向量不变的情况下,在关节空间内寻找一条连接机器人初始关节构形和期望关节构型的几何路径.本文给出一种双向自运动路径规划算法,其基本思想是使位于初始关节构形的真实机器人和位于期望关节构形的虚拟机器人在自运动流形上运动并收敛到同一关节构形,从而得到一条连接初始和期望关节构形的自运动几何路径.该算法克服了以往算法容易陷入局部极小构形的缺陷.仿真结果证实了算法的有效性.     

基于免疫遗传算法的冗余空间机械臂设计

空间机械臂的工作任务特殊,工作环境极其恶劣,因而提高空间机械臂的可靠性显得尤为重要。冗余是提高机械臂可靠性的重要方法,寻求实用的故障容错冗余机械臂设计方法是论文研究的核心内容。冗余机械臂设计是多参数、多模态、非线性设计问题,用传统的优化方法难以解决。论文模拟抗体搜索机制,结合免疫网络理论,用抗体表示函数优化解的可能模式,通过克隆算子完成全局搜索,利用B细胞网络保持抗体的多样性。通过实际设计表明,算法是可行有效的。     

Determining the initial configuration of uninterrupted redundant manipulator trajectories in a manufacturing environment

In a manufacturing environment where a redundant manipulator is programmed to follow a specific trajectory such as welding, painting, and soldering, it is often the case that the manipulator reaches a singular configuration where the program is stopped, the manipulator has to be switched to a new configuration, and the motion continued. This paper presents a method of determining the initial configuration of robotic manipulators to traverse a path trajectory without halting the motion. The method consists of: (1) identifying singular curves/surfaces using the Jacobian rank deficiency method; (2) determining non-crossable curves/surfaces using acceleration-based crossability criteria; (3) finding if the path intersects any non-crossable singular curve/surface. If there is not any intersection, the manipulator does not interrupt with any initial configuration on the trajectory. Otherwise, the intersection is determined, and the non-crossable singular configuration at the intersection point is determined; (4) solving the differential algebraic system of equations (DAE) of index 2 using the Runge–Kutta method; and (5) solving the optimization problem. The method is illustrated through examples.     

Trajectory planning for a manipulator with nonlinear Coulomb friction using a dynamically incremental genetic algorithm

Global warming and environmental destruction are caused in part by the mass consumption of energy by industries that use robotic manipulators. Hence, there is a need to minimize the energy used for manipulator control systems. It is relatively easy to analytically obtain an optimal solution for a linear system. However, a multi-link manipulator is governed by a nonlinear dynamical equation that is difficult to solve as a two-point boundary value problem. Here, the manipulator angles are approximated by Taylor and Fourier series, whose coefficients are sought by a genetic algorithm (GA) to optimize the objective function subject to the boundary conditions. A search method is proposed for planning the trajectory of a manipulator with nonlinear friction and geometrical constraints.