Non-holonomic Path Planning of a Free-Floating Space Robotic System Using Genetic Algorithms

In this paper, the non-holonomic characteristic of a free-floating space robotic system is used to plan the path of the manipulator joints, by whose motion the base attitude and the manipulator joints attain the desired states. Here, we parameterize the joint trajectory using sinusoidal functions, whose arguments are high-order polynomials. Then, we define the cost function for optimization according to the constraint conditions and the accuracy of the space robot. Finally, genetic algorithms (GAs) are used to search for the solutions of the parameters. Compared with others, our approach has advantages as follows. (i) The motion of the manipulator and the disturbance on the base are practically constrained. (ii) The dynamic singularities cannot affect the algorithm since only the direct kinematic equations are utilized. (iii) The planned path is smooth and more applicable for the control of the manipulator. (iv) The convergence of the algorithm is not affected by the attitude singularity since the orientation error is represented by quaternion, which is globally singularity-free. The simulation results of the spacecraft with a 6-d.o.f. manipulator verify the performance and the validity of the proposed method.     

Kinematic control of redundant free-floating robotic systems

This paper is aimed at presenting solution algorithms to the inverse kinematics of a space manipulator mounted on a free-floating spacecraft. The reaction effects of the manipulator's motion on the spacecraft are taken into account by means of the so-called generalized Jacobian. Redundancy of the system with respect to the number of task variables for spacecraft attitude and manipulator end-effector pose is considered. Also, the problem of both spacecraft attitude and end-effector orientation representation is tackled by means of a non-minimal singularity-free representation: the unit quaternion. Depending on the nature of the task for the spacecraft/manipulator system, a number of closed-loop inverse kinematics algorithms are proposed. Case studies are developed for a system of a spacecraft with a six-joint manipulator attached.     

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.     

A Differentially Flat Open-Chain Space Robot with Arbitrarily Oriented Joint Axes and Two Momentum Wheels at the Base

The motion of a free-floating space robot is characterized by the principle of conservation of angular momentum. It is well known that these angular momentum equations are nonholonomic, i.e., are nonintegrable rate equations. If the base of the free-floating robot is partially actuated, it is difficult to determine joint trajectories that will result in point-to-point motion of the entire robot system in its configuration space. However, if the drift-less system associated with the angular momentum conservation equations is differentially flat, point-to-point maneuvers of the free-floating robot in its configuration space can be constructed by properly choosing trajectories in the differentially flat space. The primary advantages of this approach is that it avoids the use of nonlinear programming (NLP) to solve the nonintegrable rate equations, which at best can provide only approximate solutions. A currently open research problem is how to design a differentially flat space robot with under-actuated base. The contributions of this technical note are as follows: i) study systematically the structure of the nonholonomic rate constraint equations of a free-floating open-chain space robot with two momentum wheels at the base and arbitrarily oriented joint axes; ii) identify a set of sufficient conditions on the inertia distribution under which the system exhibits differential flatness; iii) exploit these design conditions for point-to-point trajectory planning and control of the space robot.     

自由飘浮空间机器人系统基座姿态调整

规划机械臂的运动以调整作为其基座的卫星的姿态，既节约姿控燃料，又可作为常规姿控系统的备份手段．首先，建立自由飘浮空间机器人系统的状态方程，其状态变量为关节角和卫星姿态角，输入变量为关节角速度．基于系统能控性理论，规划连接系统初始状态和期望状态的路径，实现了仅通过机械臂关节的运动同时控制基座姿态和机械臂关节角的目的．从理论上分析了机械臂的能量消耗，给出了使能量指标最小的近似最优算法．仿真结果表明了该方法的有效性．     

自由漂浮空间机器人的笛卡尔连续路径规划

对于自由漂浮空间机器人,位置级逆运动学方程不适合于笛卡尔连续路径的规划,而且机械臂的运动会对基座产生扰动.为此提出了基于速度级逆运动学方程的方法,可实现5个目标:1)惯性空间连续位姿跟踪;2)基座姿态无扰动的连续位置跟踪;3)基座姿态无扰动的连续姿态跟踪;4)基座姿态调整的连续位置跟踪;5)基座姿态调整的连续姿态跟踪.采用阻尼最小方差法回避动力学奇异,所规划的路径连续平滑.仿真结果表明了该方法的有效性.     

On the connectivity of manipulator free workspace

This article presents a new topological characterization of the free workspace of manipulators moving among obstacles. The free workspace is the set of positions and orientations that the end-effector of the manipulator can reach, according to the joint limits of each of its links, and taking into account the obstacles of the environment. A classification of new connectivity properties of the free workspace is proposed, corresponding to different types of motions (point-to-point motions, following of continuous trajectories) that the manipulator can perform in the Cartesian space. For each property, a necessary and sufficient condition is given, which permits verification of the connectivity of the whole free workspace and leads to all the connected subspaces in it. These properties have been implemented in a Robotics C.A.D. system using octree representation of spaces. Some applications are presented, which show that this work is of primary interest for preparing off-line tasks, and is a new contribution to the problem of robotic cell layout design.     

Singularity robust path planning for real time base attitude adjustment of free-floating space robot

This paper presents a singularity robust path planning for space manipulator to achieve base (satellite) attitude adjustment and end-effector task. The base attitude adjustment by the movement of manipulator will save propellant compared with conventional attitude control system. A task-priority reaction null-space control method is applied to achieve the primary task of adjusting attitude and secondary task of accomplishing end-effector task. Furthermore, the algorithm singularity is eliminated in the proposed algorithm compared with conventional reaction null-space algorithm. And the singular value filtering decomposition is introduced to dispose the dynamic singularity, the unit quaternion is also introduced to overcome representation singularity. Hence, a singularity robust path planning algorithm of space robot for base attitude adjustment is derived. A real time simulation system of the space robot under Linux/RTAI (realtime application interface) is developed to verify and test the feasibility and reliability of the method. The experimental results demonstrate the feasibility of online base attitude adjustment of space robot by the proposed algorithm.     

Sliding mode force,motion control,and stabilization of elastic manipulator in the presence of uncertainties

This article considers the question of position and force control of three-link elastic robotic systems on a constraint surface in the presence of robot parameter and environmental constraint geometry uncertainties. The approach of this article is applicable to any multi-link elastic robot. A sliding mode control law is derived for the position and force trajectory control of manipulator. Unlike the rigid robots, sliding mode control of an end point gives rise to unstable zero dynamics. Instability of the zero dynamics is avoided by Controlling a point that lies in the neighborhood of the actual end point position. The sliding mode controller accomplishes tracking of the end-effector and force trajectories on the constrained surface; however, the maneuver of the arm causes elastic mode excitation. For point-to-point control on the constraint surface, a stabilizer is designed for the final capture of the terminal state and vibration suppression. Numerical results are presented to show that in the closed-loop system position and force control is accomplished in spite of payload and constraint surface geometry uncertainty. © 1995 John Wiley & Sons, Inc.     

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.     

Unified multi-domain modelling and simulation of space robot for capturing a moving target

Space robotic systems are expected to play an increasingly important role in the future on-orbit service. The applications include repairing, refueling or de-orbiting of a satellite, or removal of the space debris. The dynamical performances of space robotic system result from the multi-physics interactions between mechanical, electrical, electronic, control, etc. In this paper, we developed a unified multi-domain modelling and simulation system. The system is composed of the following modules: the path planner, joint controllers, motor and its driver, gearing mechanism of the space manipulators, the Guidance, Navigation, and Control (GNC) system, the actuators of the base, and the orbital environment, orbital dynamic and the multi-body dynamic of the whole system, etc. Based on this system, the operation during different stages, including far range rendezvous, close range rendezvous (is usually divided into two sub-phases: closing and final approach) and target capturing can be studied from the view of multi-physics domains. The key algorithms, such as pose (position and attitude) measurement, GNC of the base, path planning and control of the space manipulator, and so on, can be validated using the system. As examples, the capturing processes of a moving target under free-floating and attitude-controlled modes are simulated and the simulation results are given.     

Whole-body Control of a Mobile Manipulator Using Feedback Linearization and Dual Quaternion Algebra

This paper presents the whole-body control of a nonholonomic mobile manipulator using feedback linearization and dual quaternion algebra. The controller, whose reference is a unit dual quaternion representing the desired end-effector pose, acts as a dynamic trajectory generator for the end-effector, and input signals for both nonholonomic mobile base and manipulator arm are generated by using the pseudoinverse of the whole-body Jacobian matrix. In order to deal with the nonholonomic constraints, the input signal to the mobile base generated by the whole-body motion control is properly remapped to ensure feasibility. The Lyapunov stability for the proposed controller is presented and experimental results on a real platform are performed in order to compare the proposed scheme to a traditional classic whole-body linear kinematic controller. The results show that, for similar convergence rate, the nonlinear controller is capable of generating smoother movements while having lower control effort than the linear controller.     

Adaptive end-effector pose control for tomato harvesting robots

This paper investigates the development of a tomato-harvesting robot operating on a plant factory and primarily studies the reachable pose of tomatoes in the nondexterous workspace of manipulator. The end-effector can only reach the tomatoes with reachable poses when the tomatoes are within the nondexterous workspace. If the grasping pose is not reachable, it will lead to grasping failure. An adaptive end-effector pose control method based on a genetic algorithm (GA) is proposed to find a reachable pose. The inverse kinematic solution based on analysis method of the manipulator is analyzed and the objective function of whether the manipulator has a solution or not is obtained. The grasping pose is set as an individual owing to the position of the tomatoes is fixed and the grasping pose is variable. The GA is used to solve until a pose that can make the inverse kinematics have a solution is generated. This pose is the reachable grasping pose of the tomato at this position. The quintic interpolation polynomial is used to plan the trajectory to avoid damage to tomatoes owing to fast approaching speed and a distance based background filtering method is proposed. Experiments were performed to verify the effectiveness of the proposed method. The radius of the workspace of the UR3e manipulator with the end-effector increased from 550 to 800 mm and the grasping range expanded by 208%. The harvesting success rate using the adaptive end-effector pose control method and trajectory planning method was 88%. The cycle of harvesting a tomato was 20 s. The experimental results indicated that the proposed tomato-recognition and end-effector pose control method are feasible and effective.     

双臂四自由度空间机器人捕捉未知目标的参数辨识

给出了双臂四自由度空间机器人捕捉未知目标的参数辨识方法．该方法基于线动量和角动量守恒定律,推出了机械臂负载未知目标的新的末端效应器的质量、质心和转动惯量的方程组. 在线测量当机械臂运动时的本体的线速度和角速度,以求得方程组中这些未知的惯性参数．数值试验显示了该方法的有效性．     

Canonical parameterization of excess motor degrees of freedom withself-organizing maps

The problem of sensorimotor control is underdetermined due to excess (or "redundant") degrees of freedom when there are more joint variables than the minimum needed for positioning an end-effector. A method is presented for solving the nonlinear inverse kinematics problem for a redundant manipulator by learning a natural parameterization of the inverse solution manifolds with self-organizing maps. The parameterization approximates the topological structure of the joint space, which is that of a fiber bundle. The fibers represent the "self-motion manifolds" along which the manipulator can change configuration while keeping the end-effector at a fixed location. The method is demonstrated for the case of the redundant planar manipulator. Data samples along the self-motion manifolds are selected from a large set of measured input-output data. This is done by taking points in the joint space corresponding to end-effector locations near "query points", which define small neighborhoods in the end-effector work space. Self-organizing maps are used to construct an approximate parameterization of each manifold which is consistent for all of the query points. The resulting parameterization is used to augment the overall kinematics map so that it is locally invertible. Joint-angle and end-effector position data, along with the learned parameterizations, are used to train neural networks to approximate direct inverse functions.     

Control of a three-link manipulator with inequality constraints on the trajectories of its joints

This work deals with the control of a three-link planar manipulator whose motion is subjected to inequality constraints on the trajectories of its joints, and to other constraints on the trajectory of its end-effector.     

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。     

Motion Planning for Redundant Manipulators Using a Floating Point Genetic Algorithm

This paper deals with the trajectory planning problem for redundant manipulators. A genetic algorithm (GA) using a floating point representation is proposed to search for the optimal end-effector trajectory for a redundant manipulator. An evaluation function is defined based on multiple criteria, including the total displacement of the end-effector, the total angular displacement of all the joints, as well as the uniformity of Cartesian and joint space velocities. These criteria result in minimized, smooth end-effector motions. Simulations are carried out for path planning in free space and in a workspace with obstacles. Results demonstrate the effectiveness and capability of the proposed method in generating optimized collision-free trajectories.     

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。     

Adaptive control of free-floating space manipulators using dynamically equivalent manipulator model

In this paper, adaptive control of free-floating space manipulators is considered. The dynamics based on the momentum conservation law for the free-floating space manipulator has non-linear parameterization properties. Therefore, the adaptive control based on a linear parameterization model cannot be used in this dynamics. In this paper, the dynamics of the free-floating space manipulator system are derived using the Dynamically Equivalent Model (DEM) approach. The DEM is a fixed-base manipulator system and allows us to linearly parameterize the dynamic equations. Using this linearly parameterized dynamic equation, an adaptive control method is developed to control the system in joint space. Parameter identification and torque calculations are done using the DEM dynamics. Simulations show that the tracking errors of the manipulator joints to a given desired trajectory become zero when the calculated torques act on the joints of the space manipulator system.