基于Lyapunov方法和快速终端滑模的轨迹跟踪控制

针对移动机器人的运动学模型,提出一种具有全局渐近稳定性的跟踪控制器。该跟踪控制器的设计分为两部分：第一部分是采用全局快速终端滑动模态的思想设计了角速度的控制律,用来渐近镇定移动机器人跟踪的前向角误差;第二部分是采用Lyapunov方法设计了线速度的控制律,用来渐近镇定移动机器人跟踪的平面坐标误差。采用Lyapunov稳定性定理,证明了移动机器人在满足这些控制律条件下,实现了对参考轨迹的全局渐近跟踪。实验结果表明移动机器人能够有效地跟踪期望轨迹,有利于在实际应用中推广。     

非完整移动机器人全局路径跟踪控制

根据制导路径跟踪理论,提出了一种非完整移动机器人全局路径跟踪控制方法.这一方法首先在路径坐标系上计算实际位置与期望位置的误差,利用制导的路径跟踪理论,导出消除该误差所需的姿态角和路径参数更新律,然后据此求解角速度及实际控制.文中还给出了初始路径参考点的计算方法,分析了路径跟踪方向和反转方法.稳定性分析证明该方法没有控制奇异点,受控闭环系统全局一致渐近稳定.最后通过移动机器人典型路径跟踪实验验证了所提出方法的可行性.     

轮式移动机器人的位置量测输出反馈轨迹跟踪控制

针对机器人的姿态角难以精确测量的困难,本文研究基于位置测量的轮式移动机器人的轨迹跟踪问题.首先提出一种利用机器人的位置信息估计其姿态角的降维状态观测器,当机器人的线速度严格大于零时,可保证姿态角观测误差的指数收敛.然后给出一种新的状态反馈轨迹跟踪控制律,当参考轨迹满足一定的激励条件时,可以保证机器人的线速度严格大于零且跟踪误差全局渐近收敛.进一步结合姿态角观测器和状态反馈控制律,得到一种输出反馈轨迹跟踪控制算法.理论分析表明,当参考轨迹满足一定的激励条件时,所提出的输出反馈控制算法可以保证跟踪误差的全局渐近收敛.最后对所提出的姿态角观测器、状态反馈和输出反馈轨迹跟踪控制算法进行了仿真验证,证实了算法的有效性,并且当存在位置测量误差时,所提出的输出反馈轨迹跟踪控制算法仍可以保证机器人对参考轨迹的实际跟踪.     

基于模型预测—中枢模式发生器的六足机器人轨迹跟踪控制

为了模仿动物卓越的运动能力和环境适应能力,提出了六足仿生机器人的轨迹跟踪控制方法。首先建立了机器人的运动学模型,接着通过转向参数将机器人的速度和角速度与中枢模式发生器（CPG）参数结合起来,设计了转换函数。然后通过转换函数将模型预测控制器和CPG网络结合起来,提出了基于CPG的模型预测控制器（MPC-CPG）,并证明了其稳定性。最后对机器人跟踪圆周轨迹和直线轨迹进行了仿真和实验。实验表明,在有初始误差的条件下,机器人在MPC-CPG控制器的作用下能够快速地消除位置误差和航向角误差,跟踪上参考轨迹。轨迹跟踪的位置误差始终保持在-0.1～0.1 m,航向角误差保持在-27?～20?。在MPC-CPG控制器的作用下,机器人不仅具有较高的轨迹跟踪精度,同时还表现出良好的运动平滑性和协调性,进一步验证了所提出的MPC-CPG控制器的有效性。     

VFO Path following Control with Guarantees of Positionally Constrained Transients for Unicycle-Like Robots with Constrained Control Input

The Vector-Field-Orientation (VFO) method is a control design concept which was originally introduced for the unicycle kinematics to solve two classical control tasks corresponding to the trajectory tracking and set-point control problems. A unified solution to both the tasks was possible by appropriate definitions of the so-called convergence vector field. So far, there has not been a version of the VFO control law for the third classical control task concerning the path following problem, which is particularly meaningful in the context of practical applications. The paper fills this gap by presenting a novel VFO path following controller devised for robots of unicycle-like kinematics with the amplitude-limited control input. Opposite to most path following controllers proposed in the literature, the new control law utilizes the recently introduced level curve approach which does not employ any parametrization of a reference path. In this way, the proposed solution is free of main limitations resulting from the need of unique determination of the shortest distance from a robot to the path. In contrast to other solutions, a formal analysis of the closed-loop dynamics presented in this paper provides sufficient conditions which guarantee constrained transients of robot motion with the position confined to a prescribed subset around a reference path. Theoretical results have been validated by numerical examples and experimentally verified with utilization of a laboratory-scale differentially driven robot.     

Iterative Path Tracking of an Omni-Directional Mobile Robot

We propose a path-tracking algorithm that is developed using an iterative learning control (ILC) technique and use the algorithm to control an omni-directional mobile robot. The proposed algorithm can be categorized as an open–closed PD-type ILC; it generates robot velocity commands by a PD-type ILC update rule using both previous and current information. When applied to the omni-directional mobile robot, it can decrease position errors and track the desired trajectory. Under the general problem setting that includes a mobile robot, we show that the proposed algorithm guarantees that the system states, outputs and control inputs converge to within small error bounds around the desired ones even under state disturbances, measurement noises and initial state errors. By using simulation and experimental tests, we demonstrate that the proposed algorithm converges fast to the desired path, and results in small root-mean-square (r.m.s.) position error under various surface conditions. The proposed algorithm shows better path-tracking performance than the conventional PID algorithm and achieves faster convergence and lower r.m.s. error than the existing two ILC algorithms.     

Tracking Control for a Cushion Robot Based on Fuzzy Path Planning With Safe Angular Velocity

This study proposes a new nonlinear tracking control method with safe angular velocity constraints for a cushion robot. A fuzzy path planning algorithm is investigated and a realtime desired motion path of obstacle avoidance is obtained. The angular velocity is constrained by the controller, so the planned path guarantees the safety of users. According to Lyapunov theory, the controller is designed to maintain stability in terms of solutions of linear matrix inequalities and the controller's performance with safe angular velocity constraints is derived. The simulation and experiment results confirm the effectiveness of the proposed method and verify that the angular velocity of the cushion robot provided safe motion with obstacle avoidance.      

基于hp自适应伪谱法的空间机器人路径规划

针对空间机器人运动过程中基座姿态产生较大扰动的问题,基于hp自适应高斯伪谱法提出了一种以基座所受反作用力矩最小为目标函数的空间机器人路径规划方法.首先,综合考虑空间机器人运动过程中存在的关节角度约束、关节角速度约束、控制力矩约束及初始状态和终端状态约束等约束条件,将空间机器人路径规划问题看成满足一系列约束条件和边界条件并实现特定性能指标最优的最优控制问题.其次,结合hp自适应高斯伪谱法（hp-AGPM）与非线性规划技术,求解带有边界约束和路径约束的优化控制问题,得到满足约束且性能指标最优的空间机器人运动轨迹.最后,以平面2自由度空间机械臂为例对所设计方法进行仿真验证,并与其他伪谱法进行对比分析.仿真结果表明：本文算法能在10.6 s的时间内规划出满足各约束条件且容许偏差低于10^-6的最优运动轨迹,并且在计算速度和配点数量上都优于其他伪谱法.     

An online reference governor for mobile robot to reduce the occurrence of control input saturation

This study proposed an online reference governor for a mobile robot to reduce the occurrence of control input saturation. For following the trajectory by a mobile robot, it is one of the practical subjects to provide appropriate control reference even if any disturbances occur. We proposed a methodology to regulate the control reference iteratively based on time-scaling approach. The time-scaling approach is a method to realize to regulate time development characteristic on the given trajectory. It is difficult to model the effect of the interaction with the road surface and the trajectory tracking error is appeared as the amount of accumulated such factors. Therefore, it is a practical approach to reduce the occurrence of control input saturation based on the evaluation of the trajectory tracking error. Proposed reference governor realizes online time scaling based on the trajectory tracking error index and a smooth transition dynamics. By introducing the proposed method, the occurrence of control input saturation can be reduced in case of that the disturbances occur. For verification of our proposed method, computer simulations utilizing a stable velocity controller were conducted and the results were discussed.     

A novel cartesian trajectory planning method by using triple NURBS curves for industrial robots

This article presents a novel method of robot pose trajectory synchronization planning. First of all, based on triple NURBS curves, a method of describing the position and orientation synchronization of the robot is proposed. Then, through considering geometric and kinematic constraints, especially angular velocity constraint, and employing bidirectional interpolation algorithm, a robot pose trajectory planning approach is developed, which has limited linear jerk, continuous bounded angular velocity and approximate optimal time, and does not need an optimization program. Ultimately, two robot pose paths, blade-shaped curve and fan-shaped curve, are utilized for simulations, and the results indicate that the proposed trajectory planning method can satisfy the given constraint conditions, i.e. the linear jerk is limited and the angular velocity is continuous bounded. The trajectory tracking experiments are further carried out on a 6-DOF industrial robot, and the results show that the proposed planning method can generate smooth trajectories to ensure the stability of the robot motion without impact in practical situations.     

CPG modulation for navigation and omnidirectional quadruped locomotion

Navigation in biological mechanisms represents a set of skills needed for the survival of individuals, including target acquisition and obstacle avoidance.In this article, we focus on the development of a quadruped locomotion controller able to generate omnidirectional locomotion and a path planning controller for heading direction. The heading direction controller is able to adapt to sensory-motor visual feedback, and online adapt its trajectory according to visual information that modifies the control parameters. This allows for integration of sensory-motor feedback and closed-loop control. This issue is crucial for autonomous and adaptive control, and has received little attention so far. This modeling is based on the concept of dynamical systems.We present experiments performed on a real AIBO platform. The obtained results demonstrate both the adequacy of the proposed locomotor controller to generate the required trajectories and to generate the desired movement in terms of the walking velocity, orientation and angular velocity. Further, the controller is demonstrated on a simulated quadruped robot which walks towards a visually acquired target while avoiding online-visually detected obstacles in its path.     

Iterative path-accurate trajectory generation for fast sensor-based motion of robot arms

Sensor-based trajectory generation of industrial robots can be seen as the task of, first, adaptation of a given robot program according to the actually sensed world, and second, its modification that complies with robot constraints regarding its velocity, acceleration, and jerk. The second task is investigated in this paper. Whenever the sensed trajectory violates a constraint, a transient trajectory is computed that, both, keeps the sensed path, and reaches the sensed trajectory as fast as possible while satisfying the constraints. This is done by an iteration of forward scaling and backtracking. In contrast to previous papers, a new backtracking algorithm and an adaptation of the prediction length are presented that are favorable for high-speed trajectories. Arc Length Interpolation is used in order to improve the path accuracy. This is completed by provisions against cutting short corners or omitting of loops in the given path. The refined trajectory is computed within a single sampling step of 4 ms using a standard KUKA industrial robot.     

Optimal Robot Speed Trajectory by Minimization of the Actuator Motor Electromechanical Losses

This paper considers the control problem of a robotic manipulator with separately excited dc motor drives as actuators. An innovative method is proposed which achieves robot speed-control requirements, with simultaneous minimization of total electromechanical losses, while the drives follow the desired speed profiles of the robot joints under various loads and random load disturbances. If there is no demand for a specific speed profile, the optimal speed trajectory is determined by minimizing an electromechanical losses criterion. Controllable energy losses, such as armature copper losses, armature iron losses, field copper losses, stray load losses, brush load losses, friction and windage losses, can be expressed proportionally to the squares of the armature and the field (exciting) currents, the angular velocity and the magnetic field flux. The controllable energy loss term is also included in the optimal control integral quadratic performance index, defined for the whole operation period. Thus the appropriate control signals required for following the desired trajectory by simultaneous energy loss minimization for the whole operation interval are achieved. Two case studies of optimal robot control with and without minimization of actuator energy losses are presented and compared, showing the energy savings that can be achieved by the proposed methodology.     

A Case Study of the Collision-Avoidance Problem Based on Bernstein–Bézier Path Tracking for Multiple Robots with Known Constraints

In this paper a case study of a new, cooperative, collision-avoidance method for multiple, nonholonomic robots based on Bernstein–Bézier curves is given. In the presented examples the velocities and accelerations of the mobile robots are constrained and the start and the goal velocity are defined for each robot. This means that the proposed method can be used as a subroutine in a huge path-planning problem in real time, in a way to split the whole path into smaller partial paths. The reference path of each robot, from the start pose to the goal pose, is obtained by minimizing the penalty function, which takes into account the sum of all the path lengths subjected to the distances between the robots, which should be bigger than the minimum distance defined as the safety distance, and subjected to the velocities and accelerations which should be lower than the maximum allowed for each robot. When the reference paths are defined the model-predictive trajectory tracking is used to define the control. The prediction model derived from the linearized tracking-error dynamics is used to predict future system behavior. The control law is derived from a quadratic cost function consisting of the system tracking error and the control effort. The proposed method was tested with a simulation and with a real-time experiment in which four robots were used.     

Global exponential tracking control of a mobile robot system via aPE condition

This paper presents the design of a differentiable, kinematic control law that achieves global asymptotic tracking. In addition, we also illustrate how the proposed kinematic controller provides global exponential tracking provided the reference trajectory satisfies a mild persistency of excitation (PE) condition. We also illustrate how the proposed kinematic controller can be slightly modified to provide for global asymptotic regulation of both the position and orientation of the mobile robot. Finally, we embed the differentiable kinematic controller inside of an adaptive controller that fosters global asymptotic tracking despite parametric uncertainty associated with the dynamic model. Experimental results are also provided to illustrate the performance of the proposed adaptive tracking controller.     

Adaptive unified motion control of mobile manipulators

This paper presents a unified motion controller for mobile manipulators which not only solves the problems of point stabilization and trajectory tracking but also the path following problem. The control problem is solved based on the kinematic model of the robot. Then, a dynamic compensation is considered based on a dynamic model with inputs being the reference velocities to the mobile platform and the manipulator joints. An adaptive controller for on-line updating the robot dynamics is also proposed. Stability and robustness of the complete control system are proved through the Lyapunov method. The performance of the proposed controller is shown through real experiments.     

An Analytical Method for Decoupled Local Smoothing of Linear Paths in Industrial Robots

The linear-format path is widely adopted to approximate the continuous contour in robot controllers. The tangential discontinuity of the linear paths usually causes the discontinuity of the joint velocity. To comply with the joint kinematics limits, the robots have to stop at each corner point, resulting in a great loss of efficiency. To achieve a smooth motion, this paper presents an analytical decoupled C³ continuous local path smoothing method for industrial robots. The tool position path is smoothed in the reference frame while the tool orientation is smoothed in the rotation parametric space based on the exponential coordinates of rotations. The quintic B-splines are inserted at the corners of the linear segments to achieve the G³ continuity of the tool position path and tool orientation path. The orientation smoothing error is constrained analytically. By reparameterization of the remaining linear segments using specially constructed B-splines, the C³ continuity of the tool position path and tool orientation path is achieved. Then, the synchronization of the tool orientation path and tool position path can be guaranteed by sharing the same curve parameter. Besides, to improve the smoothness of the angular motion on the remaining linear segments during parameter synchronization, the transition lengths of the inserted B-splines are optimized. The proposed local smoothing method guarantees that the generated smooth orientation path in the rotation space is invariant with the selection of the reference frame and the orientation of the tool frame, and ensures the jerk-continuous motion with a smoother angular motion on the remaining linear segments, which could improve the motion smoothness of the tool path and tracking accuracy. The effectiveness of the proposed method is validated through simulation and experiments.     

挠性卫星姿态机动三段式轨迹规划与滚动跟踪控制

以新颖成像模式对挠性敏捷卫星姿态的快速机动控制为需求,本文针对金字塔构型控制力矩陀螺(CMG)群为执行机构的挠性卫星,提出基于三段式正弦角加速度的姿态路径规划方法及具有滚动优化思想的跟踪算法。在姿态路径规划方法设计中,融合谱分析及非线性优化方法,设计了兼顾卫星姿态机动快速性及抑制挠性附件振动性能的姿态轨迹;为实现对规划姿态轨迹的高精度跟踪,综合加权优化指标及奇异性、执行机构能力等约束,设计了金字塔构型CMG群框架角速度的非线性模型预测(NMPC)跟踪控制律。在转动惯量存在测量误差及空间干扰情况下,多种姿态机动仿真表明,本文提出的控制方法是有效的,且表现出较强的鲁棒性。     

Rolling Contact Motion Generation and Control of Robotic Fingers

Dexterity in human hand is connected with the fingertip rolling ability. In this work we consider rolling motion of spherical robotic fingertips as one of the control objectives together with the set point position control and force trajectory tracking. The generation of a rolling motion trajectory is proposed and a control solution is designed which achieves prescribed transient and steady state tracking behavior. The proposed control law is structurally and computationally simple and does not utilize the dynamics of the robot model or its approximation. A simulation of a five degrees of freedom robot show excellent contact rolling performance even at cases of adverse friction conditions while alternative controllers lead to contact sliding. Experiments with a KUKA LWR4 + are performed to validate the proposed method.     

基于视觉的移动机器人地面轨线跟踪导航研究

地面轨线跟踪是机器人视觉导航控制基本技术之一．文中针对曲率变化较大的地面轨线跟踪提出了一种新的状态控制方法．该方法从图像中提取参考轨线的方向和幅度参数作为状态控制的输入，调整速度和转速实现跟踪控制．为改善控制性能，当由于摄像机倾角较大而引起的图像畸变较大时，利用射影变换把参考轨线参数从图像坐标系映射到机器人坐标系，而无须提供位置、曲率等参数．实验表明该方法控制效果良好．