A Direct Algorithm to Compute the Switching Curve for Time-Optimal Motion of Cooperative Multi-Manipulators Moving on a Specified Path

For more than two decades it has been known that the solution to the time-optimal problem for a manipulator along a specified path is bang–bang in terms of acceleration along the path and the switching points can be found by phase plane analysis. Despite great advances, no direct method is available for finding the switching points and constructing a switching curve specially for cooperative multi-manipulator systems (CMMSs). So far, all proposed methods are based on search algorithms in which one has to: (i) search the whole phase plane to establish the boundary of the non-feasible area in which the end-effector cannot follow the path and (ii) find the critical points by numerical calculation of the slope of the non-feasible boundary. Although this search algorithm can give the solution, it is very tedious and time consuming, and the problem gets worse for CMMSs. This paper is concerned with developing a direct method to find the critical points and construction of the switching curve for non-redundant CMMSs. To this end, a rigorous study of the characteristics of the critical points and the switching curve is presented, and based on that a direct algorithm is introduced.     

Modified Transpose Effective Jacobian Law for Control of Underactuated Manipulators

Underactuated manipulators consist of active and passive joints, and developing a control technique that can manage such systems is an attractive, challenging problem. Most works in this area present model-based control laws that require a full dynamics model, and are consequently affected from uncertainties and time delays due to massive computations. Non-model-based control approaches provide an efficient alternative for practical implementation. The Modified Transpose Jacobian (MTJ) algorithm is one of these controllers that has been recently proposed for fully actuated manipulators with a square matrix Jacobian. Based on an approximated feedback linearization approach, the MTJ does not need a priori knowledge of the plant dynamics. In this paper, this scheme is extended to the complicated control problem of underactuated robots in Cartesian space. To this end, the notion of the Transpose Effective Jacobian (TEJ) is presented and so the proposed algorithm is called the Modified TEJ (MTEJ) algorithm. The MTEJ control law employs stored data of the control command in the previous time step, as a learning tool to yield an improved performance. Therefore, the proposed law needs just to a portion of mass matrix that corresponds to passive joint(s), and it is much less affected by inaccuracies in system properties. The gains of the proposed MTEJ can be selected more systematically and do not need to be large; hence, the noise rejection characteristics of the algorithm are improved. Also, no need for the pseudo-inversion of the Jacobian matrix in the proposed controller makes further convenience in the underactuated cases. In addition, the relationship between kinematic and dynamic manipulability measures is discussed for underactuated manipulators. Obtained results show its superior performance even compared to that of the model-based algorithms that need full dynamics models, while the proposed MTEJ requires much lower computation effort.     

Path-following control of a mobile robot in the presence of actuator constraints

In this paper, we present a control law for a non-holonomic mobile robot that achieves path following. In the path-following problem, the objective is to control the angular velocity of the robot so that the robot tracks a given reference trajectory. In this paper, we propose a control law that achieves path following in the presence of a constraint on the angular velocity. By applying the proposed control law, the robot can track the reference trajectory even if the distance from the initial position of the robot and the reference trajectory is arbitrary large. Further, we extend the control law so that the linear velocity of the robot becomes small when the robot passes through corners. By using the control algorithm, we can prevent the angular velocity of the robot becoming extremely large when the robot passes through corners. Numerical examples are provided to illustrate the effectiveness of the proposed methods.     

Mechanical Design of a Trunk with Redundant and Viscoelastic Joints for Rhythmic Quadruped Locomotion

Passive mechanisms, such as free joints and viscoelastic components, enable natural oscillation of the robot body, which allows rhythmic locomotion with low energy and computational costs. In particular, joint viscoelasticity can be a powerful candidate for changing natural oscillation and so influence the operation performance of locomotion. The present study considers the passive mechanism of a trunk, and investigates the contributions of a trunk mechanism with redundant joints and tunable viscoelasticity to quadruped locomotion. A physical quadruped robot with a trunk mechanism is developed, and the walking performance of this robot for various gait patterns and joint viscoelasticities is investigated. A simulation model is also constructed based on the physical robot, and the contribution of the viscoelasticity to trunk oscillation and the appropriate joint viscoelasticity and number of trunk joints are discussed. Experimental results obtained using the physical robot indicate that the proposed trunk mechanism contributes to successful locomotion as compared to a robot with a rigid trunk and that the velocity is influenced by not only the gait pattern, but also the joint viscoelasticity (i.e., there are appropriate couplings of the joint viscoelasticity and gait pattern). The simulation results indicate that the trunk mechanism requires joint viscoelasticity in order to achieve oscillation and that a greater number of joints having a smaller joint viscoelasticity enables higher velocity. These results suggest that, in addition to the leg mechanism and the controller design, the design of the trunk mechanism is also important.     

Theoretical Investigation of Time Suboptimal Control of Industrial Manipulators Along Specified Paths

A method for the time suboptimal control of an industrial manipulator from an initial position and orientation to a final position and orientation as it moves along a specified path is proposed. Nonlinear system equations that describe the manipulator motion are linearized at each time step along the path. A method which gives the control inputs (joint angular velocities) for time suboptimal control of the manipulator is developed. In the formulation, joint angular velocity and acceleration limitations are also taken into consideration. A six degree of freedom elbow type manipulator is used in numerical examples to verify the method developed.     

用阻尼伪逆法控制冗余度机器人的一种新方案

提出一种带次级性能指标优化的阻尼伪逆控制方案,它是通常的阻尼伪逆解的扩展形式.使用文中给出的方案和阻尼因子、优化因子选择法,冗余度机器人的灵活性有望得到更为有效地利用.基于奇异值分解(SVD)方法,还提供一种高效并行算法,以利于在实际的机器人控制系统中实施.仿真结果表明了所提方法比其它相关方法所具有的优点.     

Compilation of Constraint Programs with Noncyclic and Cyclic Dependencies to Procedural Parallel Programs

This paper reports on a compiler for translation of constraint specifications into procedural parallel programs. A constraint program in our system consists of a set of constraints and an input set containing a subset of the variables appearing in the constraints. The compiler described in this paper successfully compiles a substantially larger class of constraint specifications to efficient programs than did its predecessors. In particular the compiler has been extended to generate processor and memory efficient programs for cyclic constraints which can be resolved by computational relaxation methods. The paper first details the basic compilation process for noncyclic constraints. It then describes the additional steps in the compilation process which enable resolution of cyclic constraints to iterative computational processes and illustrates the process using derivation of a parallel program for solution of the Laplace equation as the example.     

Time-Optimal Control of a Hovering Quad-Rotor Helicopter

The time-optimal control problem of a hovering quad-rotor helicopter is addressed in this paper. Instead of utilizing the Pontryagin's Minimum Principle (PMP), in which one needs to solve a set of highly nonlinear differential equations, a nonlinear programming (NLP) method is proposed. In this novel method, the count of control steps is fixed initially and the sampling period is treated as a variable in the optimization process. The optimization object is to minimize the sampling period such that it will be below a specific minimum value, which is set in advance considering the accuracy of discretization. To generate initial feasible solutions of the formulated NLP problem, genetic algorithms (GAs) are adopted. With the proposed method, one can find a time-optimal movement of the helicopter between two configurations. To show the feasibility of the proposed method, simulation results are included for illustration.     

基于RFID及其路径约束的生产检查流程控制

针对生产检测流程控制中,产品可能会沿着多种工位流动,且工位的执行顺序是复杂的问题,文中提出了一种基于RFID及其路径约束的生产检测流程控制方法。该方法在产品上贴有RFID标签,在产品经过的生产检测工位上安装有阅读器;产品按固定的工位操作顺序进行生产检测,当贴有标签的产品经过每一个工位时就能被阅读器识别,从而判定产品经过的生产检测流程是否按照规定的顺序执行,将这一顺序称之为路径约束。使用NFA构造贴有RFID标签的产品在生产检测流程中所需要遵守的工位执行顺序(路径约束)。利用构造好的路径,按照设计好的算法先过滤RFID数据流,使用清洗后的数据流进行生产检测流程的控制。实验结果表明该算法能有效地控制生产检测的流程。     

基于变结构动态逆控制的平流层飞艇时间最优航迹设计

解决平流层飞艇自主航行的首要问题就是航迹规划。飞艇模型具有高度非线性,因此利用动态逆控制理论,通过非线性反馈和动态补偿实现飞艇非线性系统精确线性化,以方便使用庞特里亚金极小值原理设计飞艇时间最优航迹。同时以动态逆控制作为控制内环,以滑模变结构控制作为控制外环,设计双层结构的变结构动态逆航迹跟踪控制系统,实现对飞艇理想航迹的跟踪。该方法将动态逆控制的非线性解耦能力、变结构控制的鲁棒性能与庞特里亚金极小值原理有机结合,可以用来解决平流层飞艇定点悬停控制、悬停点间机动控制等问题,具有很好的工程实用价值。     

基于数据驱动的冗余机器人末端执行器位姿控制方案

模型未知的冗余机器人执行任务的过程中会产生较大的控制误差, 其末端执行器的位置与姿态也需要针对不同任务进行修正. 为解决该问题, 提出一种基于数据驱动的冗余机器人末端执行器位置与姿态控制方案. 该方案使用在线学习技术, 能够应用于模型未知的冗余机器人控制. 同时引入四元数表示法将控制机器人末端执行器姿态问题转化为基于四元数表示的控制方法. 随后, 设计一种神经动力学求解器对所提方案进行求解. 相关的理论分析、仿真及对比体现了所提方案的可行性、有效性与新颖性.     

Adaptive Chattering Free Neural Network Based Sliding Mode Control for Trajectory Tracking of Redundant Parallel Manipulators

In this paper, an adaptive chattering free neural network‐based sliding mode control (ACFN‐SMC) method is proposed for tracking trajectories of redundant parallel manipulators. ACFN‐SMC combines adaptive chattering free radial basis function neural networks (RBFN), sliding mode control with online updating the robust term parameters, and a nonlinear compensation item for reducing tracking errors. The stability of the closed‐loop system with modeling uncertainties, frictional uncertainties, and external disturbances is ensured by using the Lyapunov method. The proposed controller has a simple structure and little computation time while securing dynamic performance with expected quality in tracking trajectories of redundant parallel manipulators. In addition, the ACFN‐SMC strategy does not need to know the upper bound of any uncertainties. From the simulation results, it is evident that the proposed control strategy not only has significantly higher robustness capability for uncertainties but also can achieve better chattering elimination when compared with those using existing intelligent control schemes.     

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.     

Redundant Control of a Planar Snake Robot with Prismatic Joints

This paper presents a control method of a planar snake robot with prismatic joints. The kinematic model is derived considering velocity constraints caused by passive wheels. The proposed control method based on the model allows the robot to track a target trajectory by appropriately changing its link length using prismatic joints. The degrees of freedom of prismatic joints are represented as kinematic redundancy in the model and are used in realizing subtasks such as singularity avoidance and obstacle avoidance. In addition, the link length is below its limit when introducing a sigmoid function into the kinematic model. Simulations are carried out to demonstrate the effectiveness of the proposed method and show a novel motion that avoids singular configurations through changes in link lengths.

     

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.     

Three-Dimensional Path Planning of a Climbing Robot Using Mixed Integer Linear Programming

The City-Climber robot is a novel wall-climbing robot developed at The City College of New York that has the capability to move on floors, climb walls, walk on ceilings and transit between them. In this paper, we first develop the dynamic model of the City-Climber robot when it travel on different surfaces, i.e., floors, walls and ceilings, respectively. Then, we present a path planning method for the City-Climber robot using mixed integer linear programming (MILP) in three-dimensional (3-D) building environments that consist of objects with primitive geometrical shapes. MILP provides an optimization framework that can directly incorporate dynamic constraints with logical constraints such as obstacle avoidance and waypoint selection. In order to use MILP to solve the obstacle avoidance problem, we simplify and decouple the robot dynamic model into a linear system by introducing a restricting admissible controller. The decoupled model and obstacle can be rewritten as a linear program with mixed-integer linear constraints that account for the collision avoidance. A key benefit of this approach is that the path optimization can be readily solved using the AMPL and CPLEX optimization software with a MATLAB interface. Simulation results show that the framework of MILP is well suited for path planning and obstacle avoidance problems for the wall-climbing robot in 3-D environments.     

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.     

Global PID Control of Robot Manipulators Equipped with PMSMs

This paper is concerned with PID position regulation of robot manipulators actuated by permanent magnet synchronous motors (PMSMs). We present a global asymptotic stability proof when the electric dynamics of these actuators is taken into account. Our controller is so simple that it differs from standard field oriented control (SFOC) of PMSMs in only three simple nonlinear terms that have to be added and a nonlinear PID controller which is used instead of a classical PID controller. Thus, our proposal represents the closest result to SFOC of PMSMs provided with a formal global asymptotic stability proof. We present an advancement, if modest, towards presenting a global stability proof for SFOC when used in robotics.     

不确定机器人的神经网络轨迹控制

针对不确定机器人的轨迹跟踪问题,提出了一种基于自适应神经网络的控制方案.对于系统中的各种未知非线性,通过RBF神经网络和变结构光滑集成的控制器来自适应学习并且补偿,这种控制器克服了局部泛化网络的不足,提高了控制精度及其收敛速度.而且在考虑神经网络失效的情况下,仍能保证系统具有良好的鲁棒性.网络权重的自适应修正规则基于Lyapunov函数方法得到,它保证了跟踪误差的全局渐进稳定性.试验结果证明了这种控制算法的有效性.     

柔性臂漂浮基空间机器人建模与轨迹跟踪控制

利用拉格朗日法和假设模态方法建立了末端柔性的两臂漂浮基空间机器人的非线性动力学方程．通过坐标变换,推导出一种新的以可测关节角为变量的全局动态模型,并在此基础上运用基于模型的非线性解耦反馈控制方法得到关节相对转角与柔性臂的弹性变形部分解耦形式控制方程．最后,讨论了柔性臂漂浮基空间机器人的轨迹跟踪问题,并通过仿真实例计算,表明该模型转换及控制方法对于柔性臂漂浮基空间机器人末端轨迹跟踪控制的有效性．