基于最优控制的仿人机器人行走振动抑制

针对仿人机器人行走过程中由腿部非刚性特性引起的振动,提出了一种基于最优控制的行走振动抑制方法．首先对振动进行建模,并将这一模型加入到原有机器人动力学模型中去．然后基于拓展的动力学模型,使用预观控制方法求取一条符合质心加速度约束的控制轨迹,作为求解最优控制问题的初始解．进而由此初始解出发,迭代求解此带约束的最优控制问题,利用得到的最优控制轨迹即能以前馈方式抑制行走过程中的振动．最后,使用预观控制方法和本文方法在仿人机器人“空”上进行行走对比实验．实验结果表明提出的方法显著减小了机器人行走过程中零力矩点（ZMP）的振荡和躯干的晃动．该方法对行走振动抑制的有效性得到了验证．     

基于Shannon小波的报幕机器人轨迹控制

针对报幕机器人提出了基于小波采样理论的轨迹控制方法.首先,建立了轮式报幕机器人运动学模型,并给出了运动学约束.然后,基于Shannon小波采样理论,构建了小波抽样函数.并根据机器人报幕时的行走轨迹,给出了二次样条曲线轨迹控制方法.通过实验证明该方法简单、可靠,成功实现了轨迹控制.     

Higher Order Real-Time Approximations in Optimal Control of Multibody-Systems for Industrial Robots

The multibody system of an industrial robot leads to a mathematical model described by ordinary differential equations. Control functions have to be determined to calculate robot trajectories which are optimal due to a given performance index subject to additional constraints. In order to solve such optimal control problems, computationally expensive methods exist. These methods have no real-time capability, since perturbations during the motion of the robot require a recalculation of the optimal trajectory within a time frame much smaller than the operating-time of the robot. Hence, a robust numerical method based on the parametric sensitivity analysis of nonlinear optimization problems is suggested. Optimal control approximations of perturbed optimal solutions can be obtained in real-time by evaluating a first order Taylor expansion of the perturbed solution. Successive improvements to the constraints in the direction of the optimal perturbed solution lead to an admissible solution with a higher order approximation of the objective. The proposed numerical method is illustrated by the optimal control of an industrial robot with three degrees of freedom subject to deviations in the payload and initial values.     

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.     

A Technique to Analytically Formulate and to Solve the 2-Dimensional Constrained Trajectory Planning Problem for a Mobile Robot

A new technique for trajectory planning of a mobile robot in a two-dimensional space is presented in this paper. The main concept is to use a special representation of the robot trajectory, namely a parametric curve consisting in a sum of harmonics (sine and cosine functions), and to apply an optimization method to solve the trajectory planning problem for the parameters (i.e., the coefficients) appearing in the sum of harmonics. This type of curve has very nice features with respect to smoothness and continuity of derivatives, of whatever order. Moreover, its analytical expression is available in closed form and is very suitable for both symbolic and numerical computation. This enables one to easily take into account kinematic and dynamic constraints set on the robot motion. Namely, non-holonomic constraints on the robot kinematics as well as requirements on the trajectory curvature can be expressed in closed form, and act as input data for the trajectory planning algorithm. Moreover, obstacle avoidance can be performed by expressing the obstacle boundaries by means of parametric curves as well. Once the expressions of the trajectory and of the constraints have been set, the trajectory planning problem can be formulated as a standard mathematical problem of constrained optimization, which can be solved by any adequate numerical method. The results of several simulations are also reported in the paper to show the effectiveness of the proposed technique to generate trajectories which meet all requirements relative to kinematic and dynamic constraints, as well as to obstacle avoidance.     

Predictive reference shaping for constrained robotic systems using evolutionary algorithms

This paper proposes a method for reducing the trajectory tracking errors of robotic systems in presence of input saturation and state constraints. Basing on a finite horizon prediction of the future evolution of the robot dynamics, the proposed device online preshapes the reference trajectory, minimizing a multi-objective cost function. The shaped reference is updated at discrete time intervals and is generated taking into account the full nonlinear robot dynamics, input and state constraints. A specialized Evolutionary Algorithm is employed as search tool for the online computation of a sub-optimal reference trajectory in the discretized space of the control alternatives. The effectiveness of the proposed method and the online computational burden are analyzed numerically in two significant robotic control problems; furthermore a comparison of the performance provided by this method and an iterative gradient-based algorithms are discussed.     

An efficient motion generation method for redundant humanoid robot arms based on motion continuity

This paper proposes a novel method of motion generation for redundant humanoid robot arms, which can efficiently generate continuous collision-free arm motion for the preplanned hand trajectory. The proposed method generates the whole arm motion first and then computes the actuators’ motion, which is different from IK (inverse kinematics)-based motion generation methods. Based on the geometric constraints of the preplanned trajectory and the geometric structure of humanoid robot arms, the wrist trajectory and elbow trajectory can be got first without solving inverse kinematics and forward kinematics. Meanwhile, the constraints restrict all feasible arm configurations to an elbow-circle and reduce the arm configuration space to a two-dimension space. By combining the configuration space and collision distribution of arm motion, collision-free arm configurations can be identified and be used to generate collision-free arm motion, which can avoid unnecessary forward and inverse kinematics. The experiments show that the proposed method can generate continuous and collision-free arm motion for preplanned hand trajectories.     

Smooth control of an articulated mobile robot with switching constraints

The paper describes a smooth controller of an articulated mobile robot with switching constraints. The use of switching constraints associated with grounded/lifted wheels is an effective method of controlling various motions; e.g. the avoidance of a moving obstacle. A model of an articulated mobile robot that has active and passive wheels and active joints with switching constraints is derived. A controller that accomplishes the trajectory tracking of the robot’s head and subtasks using smooth joint input is proposed on the basis of the model. Simulations and experiments are presented to show the effectiveness of the proposed controller.     

Path-constrained control of a redundant manipulator in a task space

This study addresses the problem of controlling a redundant manipulator with both state and control dependent constraints. The task of the robot is to follow by the end-effector a prescribed geometric path given in the task space. The control constraints resulting from the physical abilities of robot actuators are also taken into account during the robot movement. Provided that a solution to the aforementioned robot task exists, the Lyapunov stability theory is used to derive the control scheme. The numerical simulation results, carried out for a planar manipulator whose end-effector follows a prescribed geometric path given in a task space, illustrate the trajectory performance of the proposed control scheme.     

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.     

Dual-edge robotic gear chamfering with registration error compensation

This paper describes a novel method for robotic gear chamfering called dual-edge chamfering which can facilitate simultaneous chamfering of the two edges of adjacent gear teeth and overcome typical registration errors arising due to the placement of the workpiece in the robot workspace. Deviations of the robot end-effector trajectory when compared to the nominal trajectory due to registration errors are discussed first; such trajectory deviations caused by typical registration errors due to gear center translation and rotation are quantified. Dual-edge chamfering process is described and an efficient trajectory design strategy is developed by considering the kinematic constraints imposed by the profiles of the gear edge and the abrasive tool. The dual-edge chamfering robot trajectory is facilitated by a simple procedure for identifying the gear and gear root centers by employing the robot. To execute the dual-edge chamfering trajectory, an efficient motion/force control strategy that includes active compliance from the tool mounted on the robot is proposed. A number of real-time experiments are conducted to evaluate the proposed method by employing a commercial six degree-of-freedom robot. Two types of large cylindrical metal gears are utilized for testing, an external gear with teeth on the outside and an internal gear with teeth on the inside. In addition to these, two different robotic compliant tools with axial and radial compliance are tested. A representative sample of the experimental results are presented and discussed.     

工业机器人时间最优轨迹规划及轨迹控制的理论与实验研究

提出了一种用于工业机器人时间最优轨迹规划及轨迹控制的新方法, 它可以确保在关节位移、速度、加速度以及二阶加速度边界值的约束下, 机器人手部沿笛卡尔空间中规定路径运动的时间最短. 在这种方法中, 所规划的关节轨迹都采用二次多项式加余弦函数的形式, 不仅可以保证各关节运动的位移、速度、加速度连续而且还可以保证各关节运动的二阶加速度连续. 采用这种方法, 既可以提高机器人的工作效率又可以延长机器人的工作寿命. 以PUMA 5 6 0机器人为对象进行了计算机仿真和机器人实验, 结果表明这种方法是正确和有效的. 它为工业机器人在非线性运动学约束条件下的时间最优轨迹规划及控制问题提供了一种较好的解决方案.     

基于眼到手视觉伺服的移动机器人模型预测控制

针对具有速度约束的移动机器人视觉轨迹跟踪问题,提出了一种基于LOQO内点法的模型预测控制方法;在眼到手框架下,首先建立了移动机器人误差模型,并对该误差模型进行离散化,给出了移动机器人视觉伺服跟踪的代价函数;同时考虑到实际中移动机器人存在速度约束问题,将代价函数的最小化问题转换为带输入约束的模型预测控制问题;然后采用障碍函数法将移动机器人的速度约束转化为等式约束并采用拉格朗日乘子法引入到代价函数中;进而,利用LOQO内点法求解具有速度约束的最小化问题,得到基于视觉的轨迹跟踪控制器;最后,通过仿真验证了所提算法的有效性和优越性.     

A Sequential Bi-criteria Search Algorithm for Robot Path Planning in the Box Pushing Problem

The collision-free trajectory planning method subject to control constraints for mobile manipulators is presented. The robot task is to move from the current configuration to a given final position in the workspace. The motions are planned in order to maximise an instantaneous manipulability measure to avoid manipulator singularities. Inequality constraints on state variables i.e. collision avoidance conditions and mechanical constraints are taken into consideration. The collision avoidance is accomplished by local perturbation of the mobile manipulator motion in the obstacles neighbourhood. The fulfilment of mechanical constraints is ensured by using a penalty function approach. The proposed method guarantees satisfying control limitations resulting from capabilities of robot actuators by applying the trajectory scaling approach. Nonholonomic constraints in a Pfaffian form are explicitly incorporated into the control algorithm. A computer example involving a mobile manipulator consisting of nonholonomic platform (2,0) class and 3DOF RPR type holonomic manipulator operating in a three-dimensional task space is also presented.     

Path following by the end-effector of a redundant manipulator operating in a dynamic environment

This paper addresses the problem of generating at the control-loop level a collision-free trajectory for a redundant manipulator operating in dynamic environments which include moving obstacles. The task of the robot is to follow, by the end-effector, a prescribed geometric path given in the work space. The control constraints resulting from the physical abilities of robot actuators are also taken into account during the robot movement. Provided that a solution to the aforementioned robot task exists, the Lyapunov stability theory is used to derive the control scheme. The numerical simulation results for a planar manipulator whose end-effector follows a prescribed geometric path, given in both an obstacle-free work space and a work space including the moving obstacles, illustrate the trajectory performance of the proposed control scheme.     

Global Optimal Feedback‐Linearizing Control of Robot Manipulators

The present paper offers a new optimal feedback‐linearizing control scheme for robot manipulators. The method presented aims at solving a special form of the unconstrained optimal control problem (OCP) of robot manipulators globally using the results of the Lyaponov method and feedback‐linearizing strategy and without using the calculus of variations (indirect method), direct methods, or the dynamic programming approach. Most of these methods and their sub‐branches yield a local optimal solution for the considered OCP by satisfying some necessary conditions to find the stationary point of the considered cost functional. In addition, the proposed method can be used for both set‐point regulating (point‐to‐point) tasks (e.g. pick‐and‐place operation or spot welding tasks) and trajectory tracking tasks such as painting or welding tasks. However, the proposed method can not support the physical constraints on robot manipulators and requires precise dynamics of the robot, as well. Instead, it can be used as an on‐line optimal control algorithm which produces the optimal solution without performing any kind of optimization algorithms which require time to find the optimal solution.     

State Space Constrained Iterative Learning Control for Robotic Manipulators

Real‐life work operations of industrial robotic manipulators are performed within a constrained state space. Such operations most often require accurate planning and tracking a desired trajectory, where all the characteristics of the dynamic model are taken into consideration. This paper presents a general method and an efficient computational procedure for path planning with respect to state space constraints. Given a dynamic model of a robotic manipulator, the proposed solution takes into consideration the influence of all imprecisely measured model parameters, making use of iterative learning control (ILC). A major advantage of this solution is that it resolves the well‐known problem of interrupting the learning procedure due to a high transient tracking error or when the desired trajectory is planned closely to the state space boundaries. The numerical procedure elaborated here computes the robot arm motion to accurately track a desired trajectory in a constrained state space taking into consideration all the dynamic characteristics that influence the motion. Simulation results with a typical industrial robot arm demonstrate the robustness of the numerical procedure. In particular, the results extend the applicability of ILC in robot motion control and provide a means for improving the overall trajectory tracking performance of most robotic systems.     

Robust Adaptive Terminal Sliding Mode Control of an Omnidirectional Mobile Robot for Aircraft Skin Inspection

In this paper, an adaptive terminal sliding mode control scheme for an omnidirectional mobile robot is proposed as a robust solution to the trajectory tracking control problem. The omnidirectional mobile robot has a double-frame structure, which adsorbes on the aircraft surface by suction cups. The major difficulties lie in the existence of nonholonomic constraints, system uncertainty and external disturbance. To overcome these difficulties, the kinematic model is established, the dynamic model is derived by using Lagrange method. Then, a robust adaptive terminal sliding mode (RATSM) control scheme is proposed to solve the problem of state stabilization and trajectory tracking. In order to enhance the robustness of the system, an adaptive online estimation law is designed to overcome the total uncertainty. Subsequently, the asymptotic stability of the system without total uncertainty is proved with basis on Lyapunov theory, and the system considering total uncertainty can converge to the domain containing the origin. Simulation results are given to show the verification and validation of the proposed control scheme.

     

Optimal trajectory planning for industrial robots

An analysis of the results of an algorithm for optimal trajectory planning of robot manipulators is described in this paper. The objective function to be minimized is a weighted sum of the integral squared jerk and the execution time. Two possible primitives for building the trajectory are considered: cubic splines or fifth-order B-splines. The proposed technique allows to set constraints on the robot motion, expressed as upper bounds on the absolute values of velocity, acceleration and jerk. The described method is then applied to a 6-d.o.f. robot (a Cartesian gantry manipulator with a spherical wrist); the results obtained using the two different primitives are presented and discussed.     

Simultaneous dynamic optimization: A trajectory planning method for nonholonomic car-like robots

Trajectory planning in robotics refers to the process of finding a motion law that enables a robot to reach its terminal configuration, with some predefined requirements considered at the same time. This study focuses on planning the time-optimal trajectories for car-like robots. We formulate a dynamic optimization problem, where the kinematic principles are accurately described through differential equations and the constraints are strictly expressed using algebraic inequalities. The formulated dynamic optimization problem is then solved by an interior-point-method-based simultaneous approach. Compared with the prevailing methods in the field of trajectory planning, our proposed method can handle various user-specified requirements and different optimization objectives in a unified manner. Simulation results indicate that our proposal efficiently deals with different kinds of physical constraints, terminal conditions and collision-avoidance requirements that are imposed on the trajectory planning mission. Moreover, we utilize a Hamiltonian-based optimality index to evaluate how close an obtained solution is to being optimal.