Study on Non-holonomic Cartesian Path Planning of a Free-Floating Space Robotic System

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 inertial pose (the position and orientation with respect to the inertial frame) of the end-effector attain the desired values. First, the kinematic equations of a free-floating space robot are simplified and the system state variables are transformed to another form composed of base attitude and joint angles. Then, the joint trajectories are parameterized using sinusoidal functions, whose arguments are seven-order polynomials. Third, the planning problem is transformed to an optimization problem; the cost function, defined according to the accuracy requirements of system variables, is the function of the parameters to be determined. Finally, the Particle Swarm Optimization (PSO) algorithm is used to search the solutions of the parameters that determine the joint trajectories. The presented method meets three typical applications: (i) point-to-point maneuver of the end-effector without changing the base attitude, (ii) attitude maneuver of the base without changing the end-effector's pose and (iii) point-to-point maneuver of the end-effector with adjusting the base attitude synchronously. The simulation results of a spacecraft with a 6-d.o.f. manipulator verify the performance and the validity of the proposed method.     

漂浮基双臂空间机器人系统的模糊神经网络自学习控制

讨论了载体位置、姿态均不受控制的情况下自由漂浮双臂空间机器人系统的高斯基模糊神经网络自 学习控制问题．此类空间机器人系统严格遵守动量守恒和角动量守恒,所以其动力学方程表现出强烈的非线性性 质．将神经网络与模糊控制相结合,即利用神经网络进行模糊推理, 可使模糊控制具有自学习能力．在此基础上, 设计了双臂空间机器人系统关节空间的高斯基模糊神经网络自学习控制方案．系统的数值仿真证实了该方法的有 效性．     

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 normal form augmentation approach to adaptive control of space robot systems

In this paper, we model a free-floating space robot system as anextended robot which is composed of a pseudo-arm representing the base motion resulting from six hyperthetic passive joints, and a real robot arm. The model allows us to categorize the space robot as an under-actuated system, and reveal fundamental properties of the system. Through input-output linearization of the model, we demonstrate a non-trivial internal dynamics, and propose an adaptive control scheme based on a normal form augmentation approach. This approach overcomes two fundamental difficulties in adaptive control design of space robot systems, i.e., nonlinear parameterization of the dynamic equation, and uncertainty of kinematic mapping from Cartesian space to joint space.     

Nonlinear control of planar multibody systems in shape space

Modeling, reduction, and nonlinear control of planar multibody systems motivated by the classicalcat-fall problem and the practical problem of reorientation of free-floating multibody satellites with rotational joints using angular-momentum-preserving controls is studied. The system model considered is reduced by the first integral (the system angular momentum) resulting in a Hamiltonian system with a configuration space of relative joint angles (shape space). Reconstruction of dynamics is applied to modify the shape-space model and track the phase shift of the absolute angles. An important reachability result is then proved in the unreduced configuration space. Control synthesis can then be found in a feedback form, solving the reorientation problem completely. Surprisingly, the reachability result breaks down in the case of the planar coupled two-body system with zero angular momentum, proving that the cat-fall phenomenon is definitely nonplanar.     

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．     

空间机器人目标捕获的零扰动方向分析

空间机器人在执行捕获任务时目标与机械臂的碰撞给基座带来的姿态扰动是致命的针对目标捕获时基座姿态扰动最小化问题,在建立了自由飘浮空间机器人捕获目标动力学模型的基础上,提出了自由飘浮状态下基座零扰动冲击方向的概念,给出了捕获过程中基座姿态无扰的条件是碰撞冲击力方向与基座零扰动冲击方向一致,并用角动量的分布与传递解释了零扰动...     

On point-to-point motion planning for underactuated space manipulator systems

In free-floating mode, space manipulator systems have their actuators turned off, and exhibit nonholonomic behavior due to angular momentum conservation. The system is underactuated and a challenging problem is to control both the location of the end effector and the attitude of the base, using manipulator actuators only. Here a path planning methodology satisfying this requirement is developed. The method uses high order polynomials, as arguments in cosine functions, to specify the desired path directly in joint-space. In this way, the accessibility of final configurations is extended drastically, and the free parameters are determined by optimization techniques. It was found that this approach leads always to a path, provided that the desired change in configuration lies between physically permissible limits. Physical limitations, imposed by system’s dynamic parameters, are examined. Lower and upper bounds for base rotation, due to manipulator motions, are estimated and shown in the implementation section. The presented method avoids the need for many small cyclical motions, and uses smooth functions in the planning scheme, leading to smooth configuration changes in finite and prescribed time.     

Differentially Flat Designs of Underactuated Open-Chain Planar Robots

A fully actuated system can execute any joint trajectory. However, if the system is underactuated, not all joint trajectories are attainable. For such systems, it is difficult to characterize attainable joint trajectories analytically. Numerical methods are generally used to characterize these. This paper investigates the property of differential flatness for underactuated planar open-chain robots and studies dependence on inertia distribution within the system. It is shown that certain choices of inertia distributions make an underactuated open-chain planar robot with revolute joints feedback linearizable, i.e., also differentially flat. Once this property is established, trajectory between any two points in the state space can be planned, and a controller can be developed to correct for errors. To demonstrate the proposed methodology in hardware, experiments with an underactuated 3-DOF planar robot are also presented.      

Final-state control of a two-link cat robot

In this study, we deal with the twisting motion of a falling cat robot by means of two torque inputs around her waist. The cat robot consists of two rigid columns and has two internal actuators at the joint to generate torque inputs around normal coordinates. This system is a nonholonomic system whose angular momentum is conserved. We formulate the state equation that has torque inputs to the joint by using the nonholonomic constraint and the Lagrange-d'Alembert principle. Then, we transform the system into a linear parameter varying system. In order to improve error learning of a final-state control method, we provide the initial inputs in order to determine the appropriate rotation direction in the early stage of the twisting motion. Next, we introduce the method of the artificial potential function to the final-state control in order to make the maximum bending angle small. The feedforward torque inputs can be obtained by the final-state control in order to bring the system from the initial state to the final state in the desired time. In simulations, we also demonstrate that the twolink cat robot can land on her feet by using the 2-d.o.f. control system even when her waist damping coefficient varies.     

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.     

Nonlinear Control of a Robot Manipulator with a Nonholonomic Jerk Constraint

We study the control of a prismatic‐prismatic‐revolute (PPR) robot manipulator subject to a nonholonomic jerk constraint, i.e., a third‐order nonintegrable design constraint. The mathematical model is obtained using the method of Lagrange multipliers. The control inputs are two forces and a torque applied to the prismatic joints and the revolute joint, respectively. The control objective is to control the robot end‐effector movement while keeping the transverse jerk component as zero. The main result of the paper is the construction of a feedback control algorithm that transfers the manipulator from any initial equilibrium configuration to the zero equilibrium configuration in finite time. The effectiveness of the algorithm is illustrated through a simulation example.     

Trajectory generation for the N-trailer problem using Goursatnormal form

Develops the machinery of exterior differential forms, more particularly the Goursat normal form for a Pfaffian system, for solving nonholonomic motion planning problems, i.e., motion planning for systems with nonintegrable velocity constraints. The authors use this technique to solve the problem of steering a mobile robot with n trailers. The authors present an algorithm for finding a family of transformations which will convert the system of rolling constraints on the wheels of the robot with n trailers into the Goursat canonical form. Two of these transformations are studied in detail. The Goursat normal form for exterior differential systems is dual to the so-called chained-form for vector fields that has been studied previously. Consequently, the authors are able to give the state feedback law and change of coordinates to convert the N-trailer system into chained-form. Three methods for planning trajectories for chained-form systems using sinusoids, piecewise constants, and polynomials as inputs are presented. The motion planning strategy is therefore to first convert the N-trailer system into Goursat form, use this to find the chained-form coordinates, plan a path for the corresponding chained-form system, and then transform the resulting trajectory back into the original coordinates. Simulations and frames of movie animations of the N-trailer system for parallel parking and backing into a loading dock using this strategy are included     

空间机器人目标捕获的自适应规划

与地面固定基座机器人不同的是,空间机器人的运动学方程中含有动力学参数。在执行目标捕获任务时,目标动力学参数的不精确会给空间机器人的规划带来致命的影响。针对目标捕获后动力学参数不精确情况下的关节空间规划问题,在建立了自由飘浮空间机器人运动学模型的基础上,给出了雅可比矩阵及其动量守恒方程中的惯性参数以及惯性参数的组合参数线性化的具体形式,提出了一种关节空间的自适应规划方法。以平面二连杆空间机器人为研究对象进行仿真验证。结果表明,所提出的自适应规划方法可以有效降低惯性参数不精确给运动规划带来的影响,为空间机器人执行目标捕获等任务时提供了任务空间内精确轨迹跟踪的能力。     

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.     

Arm path planning of a space robot with angular momentum

Arm path planning of a space robot with angular momentum is considered in this paper. A space robot changes its attitude by the arm motion and angular momentum of the space robot has the possibility to reduce the attitude change. A path planning method of the arm where the final satellite attitude becomes the same as the initial one is proposed. The method derives an approximate path first based on the attitude change when the arm moves along an infinitely small closed curve and then modifies the path by the Newton method. The amplitude of the arm motion decreases with the magnitude of the angular momentum, which shows that the proposed method utilizes the angular momentum effectively.     

欠驱动刚体航天器姿态运动规划的遗传算法

研究欠驱动刚体航天器姿态的非完整运动规划问题．航天器利用3个动量飞轮可以控制其姿态和任意定位,当其中一轮失效,航天器姿态通常表现为不可控．在系统角动量为零的情况下,系统的姿态控制问题可转化为无漂移系统的运动规划问题．基于优化控制理论,提出了求解欠驱动刚体航天器的姿态运动控制遗传算法,并且数值仿真表明：该方法对欠驱动航天器姿态运动的控制是有效的．     

Neural network learning from demonstration and epipolar geometry for visual control of a nonholonomic mobile robot

The control of a robot system using camera information is a challenging task regarding unpredictable conditions, such as feature point mismatch and changing scene illumination. This paper presents a solution for the visual control of a nonholonomic mobile robot in demanding real world circumstances based on machine learning techniques. A novel intelligent approach for mobile robots using neural networks (NNs), learning from demonstration (LfD) framework, and epipolar geometry between two views is proposed and evaluated in a series of experiments. A direct mapping from the image space to the actuator command is conducted using two phases. In an offline phase, NN–LfD approach is employed in order to relate the feature position in the image plane with the angular velocity for lateral motion correction. An online phase refers to a switching vision based scheme between the epipole based linear velocity controller and NN–LfD based angular velocity controller, which selection depends on the feature distance from the pre-defined interest area in the image. In total, 18 architectures and 6 learning algorithms are tested in order to find optimal solution for robot control. The best training outcomes for each learning algorithms are then employed in real time so as to discover optimal NN configuration for robot orientation correction. Experiments conducted on a nonholonomic mobile robot in a structured indoor environment confirm an excellent performance with respect to the system robustness and positioning accuracy in the desired location.     

Control of biomimetic robots based on analysis of human arm trajectories in 3D movements

In this study, a biomimetic robot arm with joint redundancy movable in a three-dimensional space is taken into consideration. The basic trajectories for controlling all joints are formulated under the minimum angular jerk criterion. Then, a time adjustment of the joint motion of the elbow relative to the shoulder is provided for representing specific properties of joint angular trajectories during a movement. Here, a systematical scheme for formulating the human-like trajectory has been developed by use of a direct kinematics. As the angular trajectories of all joints can be formulated in the proposed manner, the hand trajectory can be uniquely produced once the initial and final postures of the arm and a movement duration are given. The trajectories under the proposed scheme are produced by utilizing the same movement conditions observed by experiments. Then, performance for reproducing human-like trajectories has been evaluated under the comparative analysis between the observed and the produced trajectories.     

载体姿态可控的空间机器人系统关节角轨迹的自适应算法

考虑载体姿态可控的空间机器人系统的逆运动学问题，首先推导了空间机器人系统的运动学方程，得到了系统的广义雅可比阵，并证明了该雅可比阵可以表示为一组适当选择的惯性参数的线性函数．当这些惯性参数未知时，分别给出了由期望的手端轨迹产生期望角速度和角加速度的自适应算法．最后对二杆平面空间机器人系统应用文中算法进行了数字仿真，证明了算法的有效性。