Synthesis of a stabilizing control for a wheeled robot following a curvilinear path

The synthesis control problem for the plane motion of a wheeled robot with constrained control resource is studied. The goal of the control is to bring the robot to an assigned curvilinear trajectory and to stabilize its motion along it. A new change of variable is suggested that reduces the problem of stabilizing robot’s motion to that of stabilizing the zero solution in the form that admits feedback linearization. A control law stabilizing robot’s motion along an arbitrary curvilinear target trajectory is synthesized. For a straight target path, the closed-loop system is shown to be asymptotically stable for any initial conditions except for the case where the initial direction of motion is perpendicular to the target path.     

Construction of invariant ellipsoids in the stabilization problem for a wheeled robot following a curvilinear path

The synthesis control problem for the plane motion of a wheeled robot is studied. The goal of the control is to bring the robot to an assigned curvilinear trajectory and to stabilize its motion along it in the presence of phase and control constraints. For a synthesized control law, invariant ellipsoids—quadratic approximations of the attraction domains of the target trajectory—are constructed, which allow one to check in the course of the robot motion whether the control law can stabilize motion along the current trajectory segment. To take into account constraints on the control, methods of absolute stability theory are applied. The construction of the invariant ellipsoids reduces to solving a system of linear matrix inequalities.     

在线考虑运动学限制的最小加速度的轨迹规划

提出了一种基于简化运动规划的机器人轨迹规划新方法,可用于多自由度的机器人操作臂系统。关键问题是找到最小加速度的轨迹规划,来优化操作臂的运动以减少抖动。此外,给出了轨迹规划的解存在的充分必要条件,并考虑了所有的关节位置、角速度、加速度、加加速度等运动学限制。而且这种方法能够在线应用,适合任意非零的关节初始状态和目标状态,以便使机器人能够在运动过程中进行实时路径修正。最后提出的方法应用于一个七自由度的仿人机器人手臂来验证方法的有效性。     

Construction of the best ellipsoidal approximation of the attraction domain in stabilization problem for a wheeled robot

The synthesis control problem for the plane motion of a wheeled robot with constrained control resource is studied. The goal of the control is to bring the robot to an assigned curvilinear trajectory and to stabilize its motion along it. For a synthesized control law, the problem of finding the best in the sense of volume ellipsoidal approximation of the attraction domain of the target path is posed. To take into account constraints on the control, an approach based on methods of absolute stability theory is used, in the framework of which construction of an approximating ellipsoid reduces to solving a system of linear matrix inequalities. It is shown that the desired maximum-volume approximating ellipsoid can be found by solving a standard constrained optimization problem for a function of two variables.     

A linearizing feedback for stabilizing a car-like robot following a curvilinear path

The path following problem for a car-like robot is considered. The control goal is to bring the robot to a pre-assigned curvilinear path and to stabilize its motion along the path. A new canonical change of variables is suggested. It reduces the problem of stabilizing robot’s motion to that of stability of the zero solution of the transformed system in the form that admits feedback linearization. A new control law is synthesized that ensures linearity of the closed-loop system and stabilizes robot’s motion along a given target path if the initial conditions belong to a known region. Comparison of the new control law with two earlier obtained linearizing feedbacks known from the literature demonstrates its unquestionable advantages.     

Synthesis of a stabilizing feedback for a wheeled robot with constrained control resource

Stabilization of motion of a wheeled robot with constrained control resource by means of a continuous feedback linearizing the closed-loop system in a neighborhood of the target path is considered. We pose the problem of finding the feedback coefficients such that the phase portrait of the nonlinear closed-loop system is topologically equivalent to that of a linear system with a stable node, with the asymptotic rate of decrease of the deviation from the target path being as high as possible. On this family, we pose the problem of minimization of “overshooting” for arbitrary initial conditions. The solution of this optimization problem is proved to be a limit discontinuous control law. A hybrid control law is proposed that, on the one hand, ensures the desired properties of the phase portrait and minimal overshooting and, on the other hand, does not result in a chattering inherent in systems with discontinuous feedbacks.     

Safe proactive plans and their execution

We present in this paper a methodology for computing the maximum velocity profile over a trajectory planned for a mobile robot. Environment and robot dynamics as well as the constraints of the robot sensors determine the profile. The planned profile is indicative of maximum speeds that can be possessed by the robot along its path without colliding with any of the mobile objects that could intercept its future trajectory. The mobile objects could be arbitrary in number and the only information available regarding them is their maximum possible velocity. The velocity profile also enables one to deform planned trajectories for better trajectory time. The methodology has been adopted for holonomic and non-holonomic motion planners. An extension of the approach to an online real-time scheme that modifies and adapts the path as well as velocities to changes in the environment such that both safety and execution time are not compromised is also presented for the holonomic case. Simulation and experimental results demonstrate the efficacy of this methodology.     

基于PLC技术的焊接机器人主从协调运动控制系统研究

焊接机器人运动控制系统的控制功能直接决定了焊接工作质量,利用PLC技术优化设计焊接机器人主从协调运动控制系统。在系统硬件设计方面,装设位置、速度、旋转电弧等传感器设备,利用传感数据检测焊接机器人实时位姿。在考虑焊接机器人组成结构、工作原理以及动力驱动方式的情况下,构建焊接机器人的数学模型。结合当前位姿和控制目标之间的位置关系,规划焊接机器人主从协调运动轨迹,在约束条件的作用下,利用PLC控制器生成控制指令,作用在改装的焊接机器人驱动器上,实现系统的焊接机器人主从协调运动控制功能。通过系统测试实验得出结论：与传统控制系统相比,优化设计系统的速度控制误差、姿态角控制误差分别降低了0.075mm/s和0.38°,在优化系统控制下,主从焊接机器人的运动轨迹与规划轨迹之间无明显差异。     

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.     

Algorithm to construct invariant ellipsoids in the problem of stabilization of wheeled robot motion

Design of the control law for planar motion of the wheeled robot was studied. The aim of control lies in driving the robot to the desired smooth curvilinear trajectory and stabilizing its motion. At that, the control resource and the domain of variations of the phase variables are bounded. It was previously suggested to construct the criterion for control law stabilizability as invariant ellipsoids, that is, quadratic approximations of the attraction domains of the target trajectory. Then construction of the invariant ellipsoids came to solving a system of linear matrix inequalities and testing a scalar inequality. The paper was devoted to practical application of the previous results. Choice of the parameters of the system of linear matrix inequalities was discussed. An algorithm to construct an invariant ellipsoid in at most three iterations was developed. It also determines the maximal ellipsoid for a given maximal permissible deviation of the robot from the target trajectory.     

Reactive navigation of underwater mobile robot using ANFIS approach in a manifold manner

Learning and self-adaptation ability is highly required to be integrated in path planning algorithm for underwater robot during navigation through an unspecified underwater environment. High frequency oscillations during underwater motion are responsible for nonlinearities in dynamic behavior of underwater robot as well as uncertainties in hydrodynamic coefficients. Reactive behaviors of underwater robot are designed considering the position and orientation of both target and nearest obstacle from robot’s current position. Human like reasoning power and approximation based learning skill of neural based adaptive fuzzy inference system (ANFIS) has been found to be effective for underwater multivariable motion control. More than one ANFIS models are used here for achieving goal and obstacle avoidance while avoiding local minima situation in both horizontal and vertical plane of three dimensional workspace. An error gradient approach based on input-output training patterns for learning purpose has been promoted to spawn trajectory of underwater robot optimizing path length as well as time taken. The simulation and experimental results endorse sturdiness and viability of the proposed method in comparison with other navigational methodologies to negotiate with hectic conditions during motion of underwater mobile robot.     

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.     

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     

Navigation system including associative memory

A new adaptive linear robot control system for a robot work cell that can visually track and intercept stationary and moving objects undergoing arbitrary motion anywhere along its predicted trajectory within the robot's workspace is presented in this paper. The proposed system was designed by integrating a stationary monocular CCD camera with off-the-shelf frame grabber and an industrial robot operation into a single application on the MATLAB platform. A combination of the model based object recognition technique and a learning vector quantization network is used for classifying stationary objects without overlapping. The optical flow technique and the MADALINE network are used for determining the target trajectory and generating the predicted robot trajectory based on visual servoing, respectively. The necessity of determining a model of the robot, camera, all the stationary and moving objects, and environment is eliminated. The location and image features of these objects need not be preprogrammed, marked and known before, and any change in a task is possible without changing the robot program. After the learning process on the robot, it is shown that the KUKA robot is capable of tracking and intercepting both stationary and moving objects at an optimal rendezvous point on the conveyor accurately in real-time.     

Homography-based visual servo tracking control of a wheeled mobile robot

A visual servo tracking controller is developed in this paper for a monocular camera system mounted on an underactuated wheeled mobile robot (WMR) subject to nonholonomic motion constraints (i.e., the camera-in-hand problem). A prerecorded image sequence (e.g., a video) of three target points is used to define a desired trajectory for the WMR. By comparing the target points from a stationary reference image with the corresponding target points in the live image and the prerecorded sequence of images, projective geometric relationships are exploited to construct Euclidean homographies. The information obtained by decomposing the Euclidean homography is used to develop a kinematic controller. A Lyapunov-based analysis is used to develop an adaptive update law to actively compensate for the lack of depth information required for the translation error system. Experimental results are provided to demonstrate the control design.     

Waypoint Following for Differentially Driven Wheeled Robots with Limited Velocity Perturbations

In this paper a unified motion control strategy dedicated for the waypoint following task realized by a differentially driven robot is presented. It is assumed that the vehicle moves with limited velocities and accelerations in order to reduce excessive slip and skid effects. In order to include operational constraints, a motion planner is combined with a universal stabilizer taking advantage of transverse functions. To improve tracking precision translated transverse functions are deployed and a new adaptive technique for the controller tuning is proposed. During the motion planning stage an auxiliary trajectory connecting points in the configuration space and satisfying assumed phase constraints is generated. The resulting motion execution system has been implemented on a laboratory-scale skid-steering mobile robot, which served as platform for experimental validation of presented algorithms.     

Stabilization problem for a wheeled robot following a curvilinear path on uneven terrain

A control synthesis problem for a wheeled robot moving on uneven terrain is studied. The terrain is assumed to be described by a sufficiently smooth function that does not vary too much at distances of the order of the platform size, which makes it possible to employ a planar robot model. The terrain model is not a priori known, and the information on the local terrain configuration is made available for the robot through measuring its pitch and roll angles. The control goal is to bring the robot to a given curvilinear path and to stabilize robot’s motion along it. A change of variables is found by means of which the system of differential equations governing controlled motion of the robot reduces to the form that admits feedback linearization. A numerical example presented demonstrates advantages of the synthesized control compared to that derived without regard to the terrain unevenness. It is shown that the latter is generally not capable of stabilizing robot’s motion with a desired accuracy.     

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.     

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.     

A geometric approach to target convergence and obstacle avoidance of a nonstandard tractor‐trailer robot

In this article, a solution to target convergence and obstacle avoidance problem of an underactuated nonstandard n‐trailer robot is proposed. With a new geometric approach, we propose autonomous velocity and steering angle controllers for the car‐like tractor robot such that the tractor‐trailer system moves from an initial position to a designated target. The proposed method simultaneously takes into account the dynamics constraints of the system and also ensures that the robot avoids any fixed obstacles on its way to the target. We also generalize the results to control the motion of the nonstandard n‐trailer system with an arbitrary number of passive trailers, a mathematically challenging nonlinear underactuated system, given that the angular velocity of a trailer is dependent on the angular velocity of the preceding trailer. The effectiveness of the new geometric approach and the stabilizing control inputs is verified using computer simulations.