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.     

Motion control for a wheeled robot following a curvilinear path

A control synthesis problem for planar motion of a wheeled robot with regard to the steering gear dynamics is considered. The control goal is to bring the robot to a given curvilinear path and to stabilize its motion along the path. The trajectory is assumed to be an arbitrary parameterized smooth curve satisfying some additional curvature constraints. 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 control law is synthesized for an arbitrary target path with regard to phase and control constraints. The form of the boundary manifold and the phase portrait of the system for the case of the straight target trajectory are studied. Results of numerical experiments are presented.     

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.     

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.     

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.     

Optimization of layout and path planning of surgical robotic system

Positioning a surgical robot for optimal operation in a crowded operating room is a challenging task. In the robotic-assisted surgical procedures, the surgical robot’s end-effector must reach the patient’s anatomical targets because repositioning of the patient or surgical robot requires additional time and labor. This paper proposes an optimization algorithm to determine the best layout of the operating room, combined with kinematics criteria and optical constraints applied to the surgical assistant robot system. A new method is also developed for trajectory of robot’s end-effector for path planning of the robot motion. The average deviations obtained from repeatability tests for surgical robot’s layout optimization were 1.4 and 4.2 mm for x and y coordinates, respectively. The results of this study show that the proposed optimization method successfully solves the placement problem and path planning of surgical robotic system in operating room.

     

Nonsingular path following control of a unicycle in the presence of parametric modelling uncertainties

A new type of control law is derived to steer the dynamic model of a wheeled robot of unicycle type along a desired path. The methodology adopted for path following control deals explicitly with vehicle dynamics and plant parameter uncertainty. Furthermore, it overcomes stringent initial condition constraints that are present in a number of path following control strategies described in the literature. This is done by controlling explicitly the rate of progression of a ‘virtual target’ to be tracked along the path, thus bypassing the problems that arise when the position of the virtual target is simply defined by the projection of the actual vehicle on that path. In the paper, a nonlinear adaptive control law is derived that yields convergence of the (closed‐loop system) path following error trajectories to zero. Controller design relies on Lyapunov theory and backstepping techniques. Simulation results illustrate the performance of the control system proposed. Copyright © 2006 John Wiley & Sons, Ltd.     

基于滑模变结构控制的路径跟踪研究

为解决锅炉水冷壁磨损检测机器人的路径跟踪问题,提出了一种基于指数趋近律的滑模变结构控制的机器人路径跟踪方法。在水冷壁磨损检测机器人运动模型的基础上,进行路径跟踪误差分析,设计一种基于指数趋近律的滑模变结构控制器,再利用Lyapunov定理验证其收敛性,最后通过MATLAB软件模拟仿真,仿真结果表明该控制器可以克服误差,使位姿误差收敛至零。     

一种球形滚动机器人的路径跟踪控制器设计

对一种球形滚动机器人的路径跟踪问题进行研究,设计一种基于自适应滑模控制策略的路径跟踪控制器。所设计的路径跟踪控制器采用鲁棒滑模自适应增益控制律,能够有效实现带有扰动和不确定性的实际球形滚动机器人的路径跟踪。推导球壳纯滚动和无自转非完整约束下球形滚动机器人的运动方程,并在此基础上设计自适应滑模路径跟踪控制器。对于给定的参考几何路径,所设计的路径跟踪控制器能够确保路径跟踪误差在有限时间内收敛至很小的零邻域内。基于Lyapunov稳定性理论证明了闭环控制系统的稳定性,数值仿真与样机实验结果进一步验证了所设计的路径跟踪控制器的有效性。     

无线传感器网络环境下基于粒子滤波的移动机器人SLAM算法

定位问题是移动机器人研究领域中最基本的问题,在Bayes的框架下研究了机器人与无线传感器网络(WSN)组成系统中的同时建图与定位问题(SLAM).针对该系统中只存在距离测量信息可用的情况提出了一种基于粒子滤波的SLAM算法.该方法将机器人状态和节点位置估计设置为一组全局估计粒子,通过对粒子及其权重的更新来计算整个系统的状态.算法将WSN节点的位置估计在机器人的路径上分解为相互独立的估计,从而将全局粒子的计算转化为使用一个机器人状态滤波器和对应于每个机器人粒子的节点位置滤波器进行计算.针对观测信息低维的特点,设计了处理低维观测信息的方法,使得观测信息可以在滤波阶段得到合理利用.并且详细介绍了提出的SLAM算法原理和计算过程,并通过仿真实验证明了算法的有效性和实用性.     

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.     

Optimal Navigation for a Differential Drive Disc Robot: A Game Against the Polygonal Environment

This paper considers the problem of globally optimal navigation with respect to minimizing Euclidean distance traveled by a disc-shaped, differential-drive robot (DDR) to reach a landmark. The robot is equipped with a gap sensor, which indicates depth discontinuities and allows the robot to move toward them. In this work we assume that a topological representation of the environment called GNT has already been built, and that the landmark has been encoded in the GNT. A motion strategy is presented that optimally navigates the robot to any landmark in the environment, without the need of using a previously known geometric map of the environment. To our knowledge this is the first time that the shortest path for a DDR (underactuated system) is found in the presence of obstacle constraints without knowing the complete geometric representation of the environment. The robot’s planner or navigation strategy is modeled as a Moore Finite State Machine (FSM). This FSM includes a sensor-feedback motion policy. The motion policy is based on the paradigm of avoiding the state estimation to carry out two consecutive mappings, that is, from observation to state and then from state to control, but instead of that, there is a direct mapping from observation to control. Optimality is proved and the method is illustrated in simulation.     

Methodology of Concept Control Synthesis to Avoid Unmoving and Moving Obstacles (II)

Dynamic path generation problem of robot in environment with other unmoving and moving objects is considered. Generally, the problem is known in literature as find path or robot motion planning. In this paper we apply the behavioral cloning approach to design the robot controller. In behavioral cloning, the system learns from control traces of a human operator. The task for the given problem is to find a controller not only in the form of the explicit mathematical expression. So RBF neural network is used also. The goal is to apply controller for the mobile robot motion planning in situation with infinite number of obstacles. The advantage of this approach lies in the fact that a complete path can be defined off-line, without using sophisticated symbolical models of obstacles.     

水冷壁爬壁机器人路径跟踪研究

摘要：准确的直线运动是水冷壁爬壁机器人完成磨损检测工作的前提,为了保证其做直线运动,设计了一种水冷壁爬壁机器人路径跟踪控制律。本文通过建立爬壁机器人的运动学模型,用摄像机采集水冷壁图像,对图像处理并提取直线路径,实现对其位姿的反馈,再根据Backstepping跟踪算法设计路径跟踪控制律对机器人位姿进行控制,同时采用Lyapunov稳定理论对控制律的收敛性进行验证,最后通过MATLAB软件进行仿真实验,仿真结果验证了控制律的有效性。     

Interaction rule learning with a human partner based on an imitation faculty with a simple visuo-motor mapping

Imitation has been receiving increasing attention from the viewpoint of not simply generating new motions but also the emergence of communication. This paper proposes a system for a humanoid who obtains new motions through learning the interaction rules with a human partner based on the assumption of the mirror system. First, a humanoid learns the correspondence between its own posture and the partner’s one on the ISOMAPs supposing that a human partner imitates the robot motions. Based on this correspondence, the robot can easily transfer the observed partner’s gestures to its own motion. Then, this correspondence enables a robot to acquire the new motion primitive for the interaction. Furthermore, through this process, the humanoid learns an interaction rule that control gesture turn-taking. The preliminary results and future issues are given.     

A Smooth Path Tracking Algorithm for Wheeled Mobile Robots with Dynamic Constraints

In order to avoid wheel slippage or mechanical damage during the mobile robot navigation, it is necessary tosmoothly change driving velocity or direction of the mobile robot. This means that dynamic constraints of the mobile robotshould be considered in the design of path tracking algorithm. In the study, a path tracking problem is formulated asfollowing a virtual target vehicle which is assumed to move exactly along the path with specified velocity. The drivingvelocity control law is designed basing on bang-bang control considering the acceleration bounds of driving wheels. Thesteering control law is designed by combining the bang-bang control with an intermediate path called the landing curve whichguides the robot to smoothly land on the virtual target's tangential line. The curvature and convergence analyses providesufficient stability conditions for the proposed path tracking controller. A series of path tracking simulations and experimentsconducted for a two-wheel driven mobile robot show the validity of the proposed algorithm.     

Homing a robot with range-only measurements under unknown drifts

The problem of homing a mobile robot to a given reference location under unknown relative and absolute positions is addressed in this paper. This problem is easy to solve when all the positions and kinematic variables are known or are observable, but remains a challenge when only range is measured. Its complexity further increases when variable and unknown drifts are added to the motion, which is typical for marine vehicles. Based on the range measurements, it is possible to drive the robot arbitrarily close to the reference. This paper presents a complete solution and demonstrates the validity of the approach based on the Lyapunov theory. The use of models, which are often affected by uncertainties and/or unmodeled terms, is intended to be minimal and only some constraints are imposed on the speed of the robot. We derive a control law that makes the robot converge asymptotically to the reference and prove its stability theoretically. Nevertheless, as it is well known, practical limitations on the actuation can weaken some properties of convergence, namely when the system dynamics require increasing actuation along the approach trajectory. We will demonstrate that the robot reaches a positively invariant set around the reference whose upper bound is determined. Finally, we conclude our work by presenting simulation and experimental data and by demonstrating the validity and the robustness of the method.     

动态环境中基于改进粒子群的机器人路径规划

提出一种模糊隶属度函数对动态环境中机器人的运动状况进行建模,该建模方法不会无谓地牺牲机器人的可运动空间,可尽量减少机器人路径规划的约束强度;同时提出通过调整位置加权趋向无约束最优解的算子改进粒子群算法,提高算法的寻优速度。仿真结果表明,通过两者结合,可快速获得动态环境中的优化路径。     

Control of wheel system under uncertainty

Consideration was given to the nonholonomic mechanical systems with rolling or the wheel systems such as mobile robot, car, or wheeled tractor. Analysis was confined to the kinematic models with regard for the dynamics of the controlling drives. Control of system motion along a given trajectory (planar smooth curve) was studied. The designed control law stabilizes this motion in large in the basic variables. The main result lies in solution of the problem of control under uncertainty when only sufficiently general dynamic characteristics of the wheel system drive are known.     

Stabilizing manipulator motion along a given surface

We consider mechanical systems like a manipulating robot, an excavator, and other similar devices. Known solutions for the general problem of manipulator motion stability have been obtained under rather strong assumptions. A special but important case of the stability problem under natural assumptions is solved in this work. We have constructed a control law that stabilizes the motions of a system lying inside a given surface. One example of such surface might be the surface along which a welding seam goes in the problem of automated welding with a manipulator.