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.     

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 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.     

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.     

Adaptive robust fuzzy control for path tracking of a wheeled mobile robot

This paper proposes an adaptive robust fuzzy control scheme for path tracking of a wheeled mobile robot with uncertainties. The robot dynamics including the actuator dynamics is considered in this work. The presented controller is composed of a fuzzy basis function network (FBFN) to approximate an unknown nonlinear function of the robot complete dynamics, an adaptive robust input to overcome the uncertainties, and a stabilizing control input. The stability and the convergence of the tracking errors are guaranteed using the Lyapunov stability theory. When the controller is designed, the different parameters for two actuator models in the dynamic equation are taken into account. The proposed control scheme does not require the accurate parameter values for the actuator parameters as well as the robot parameters. The validity and robustness of the proposed control scheme are demonstrated through computer simulations. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

Time optimal path planning for a wheeled mobile robot

This paper investigates time optimal path planning under kinematic and dynamic constraints for a 2‐DOF wheeled mobile robot (WMR). The dynamic model of a WMR is derived using the Newton–Euler method and the constraints are analyzed. Kinematic constraints are imposed by WMR's nonholonomy and structural limits, while dynamic constraints are due to motor saturation. The path planning is formulated as a two‐stage planning. First, path planning under kinematic constraints is transformed into a pure geometric problem. The shortest path composed of circular arcs and straight lines is obtained. Then, a time optimal velocity profile is generated under dynamic constraints. Since constraints of a WMR are fully exploited, the proposed method is simple and effective. Simulation results are demonstrated. © 2000 John Wiley & Sons, Inc.     

基于观测器的轮式移动机器人路径跟踪控制

研究基于状态观测器的轮式移动机器人的路径跟踪控制问题.首先简要回顾了基于状态反馈的移动机器人的路径跟踪控制问题;进而通过适当的状态变换将移动机器人模型转换为合适的形式,并在移动机器人的位置可以测量的情况下设计了一种可保证状态观测误差指数收敛的状态观测器;最后结合状态反馈路径跟踪控制器和所设计的观测器得到了一种基于观测器的路径跟踪控制器,该控制器可以保证移动机器人的运动轨迹指数收敛到期望路径上.仿真结果证实了所提出的基于观测器的路径跟踪控制器的有效性.     

Variable structure control for a wheeled mobile robot

This paper is concerned with a robust control for wheeled mobile robots. Mobile robots equipped with undeformable wheels are referred to as 'wheeled mobile robots' and constitute a typical example of non-holonomic systems, where the standard control algorithms developed for robotic manipulators without constraints are no longer applicable. It is shown using the formulation of a dynamic feedback linearization (DFL) methodology that a robust sliding mode controller is an efficient design tool to take into account stabilization and tracking control problems. Compared with previous studies based on DFL, the proposed method shows improvement of the trajectory tracking and stabilization process. The robustness is guaranteed in the presence of parameter uncertainty or unmodeled dynamics by the robust sliding mode control technique. Simulation results along with the conclusions drawn are discussed.     

基于滚动时域优化的轮式移动机器人路径跟踪问题研究

轮式移动机器人是典型的非完整约束系统. 本文基于滚动时域控制策略研究轮式移动机器人的路径跟踪问题. 为了既能够保证移动机器人渐近收敛到期望轨迹, 又能够保证在线求解的优化问题的滚动可行性, 参考轨迹 被选为优化问题中的终端等式约束. 仿真结果验证了所提出的控制策略的有效性.     

Ellipsoidal approximations of the attraction domain in the path following problem for a wheeled robot with constrained resource

The path following problem for a wheeled robot with constrained resource moving along a given curvilinear path is studied. With the help of an earlier introduced change of variables, the path following problem is reduced to that of stability of the zero solution, and a control law linearizing the system in the case of the unconstrained control resource is synthesized. For the closed-loop system, the problem of finding the best ellipsoidal approximation of the attraction domain of the target path is set. To take into account the control constraint, an approach based on absolute stability theory is used. In the framework of this approach, construction of an approximating ellipse reduces to solving a parameterized system of linear matrix inequalities. The LMI system in the considered case can be solved analytically. Owing to this, construction of the best ellipsoidal approximation is reduced to solving a standard constrained optimization problem for a function of two variables. The proposed method is further extended to finding the best ellipsoidal approximation with an additional constraint on the maximum deviation from the target path. The discussion is illustrated by numerical examples.     

带拖车移动机器人全局路径跟踪控制

研究带拖车移动机器人的前向路径跟踪控制和倒车路径跟踪控制问题.首先建立系统的运动学模型,并进行系统的运动特性分析;然后基于Lyapunov方法提出一种新的单体移动机器人全局路径跟踪控制器,并将其引入带拖车移动机器人的前向路径跟踪控制;再后通过运动学变换,实现了拖挂任意节拖车的系统的倒车路径跟踪控制;最后针对三车体系统的两种路径跟踪控制进行仿真,结果表明了该方法的有效性.     

离轴式拖车移动机器人的任意路径跟踪控制

离轴式拖车移动机器人属于非完整系统,当车头线速度随时间变化且过零变号时,难以用一个控制器实现系统对期望路径的跟踪.本文研究离轴式拖车移动机器人系统的任意路径跟踪问题.首先由系统和虚拟小车的运动学方程得到误差状态模型,线性化后用坐标变换将其化为标准型,然后基于Lyapunov方法构造出一种跟踪控制律.只要车头的运动线速度有界且不趋于零,其导数有界,则所设计的控制律就可以保证系统跟踪任意的期望路径,且跟踪误差最终一致有界,最终界的大小与期望路径的曲率变化率成比例.当期望路径的曲率变化率为零或趋于零时,所设计的控制律可以保证拖车移动机器人指数收敛到期望路径.仿真结果证实了控制律的有效性.     

基于行为的轮式移动机器人导航控制

介绍了一种轮式移动机器人CASIA-I及其运动机构,针对该运动机构给出了机器人的运动方程和基于行为的导航控制算法,并根据该算法进行了软件仿真和实物实验．实验结果表明,该导航控制算法是一种有效的导航算法．     

Canonical representation of the path following problem for wheeled robots

For the problem of stabilizing motion of an n-dimensional nonholonomic wheeled system along a prescribed path, the concept of a canonical representation of the equations of motion is introduced. The latter is defined to be a representation that can easily be reduced to a linear system in stabilizable variables by means of an appropriate nonlinear feedback. In the canonical representation, the path following problem is formulated as that of stabilizing the zero solution of an (n?1)-dimensional subsystem of the canonical system. It is shown that, by changing the independent variable, the construction of the canonical representation reduces to finding the normal form of a stationary affine system. The canonical representation is shown to be not unique and is determined by the choice of the independent variable. Three changes of variables known from the literature, which were earlier used for synthesis of stabilizing controls for wheeled robot models described by the third- and fourth-order systems of equations, are shown to be canonical ones and can be generalized to the n-dimensional case. Advantages and disadvantages of the linearizing control laws obtained by means of these changes of variables are discussed.     

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.     

Path guidance and control of a guided wheeled mobile robot

A practical mobile-robot-based automatic transport service system is presented and discussed in this paper. A wheeled mobile robot, capable of two-directional movement, is developed to transport and feed materials to an industrial production line. For path guidance, an electromagnetic approach is investigated in detail. A conductor line laid on or under the ground defines the path, through which runs a square-wave current signal of a certain frequency, to produce an alternating magnetic field. Specific sensors are designed to measure this field and provide a path guidance signal for the robot. For path control, the proportional plus derivative (PD) algorithm is adopted to control the robot's movement along the path line. Multi-mode control strategies are developed to cover different path cases. The active turn control scheme is used for turning path modes. Finally, some practical testing results are presented.     

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.     

Estimation of attraction domains in wheeled robot control

Considered is the control design problem for planar motion of a wheeled robot. The mathematical model of the robot accounts for kinematic relationships between the velocity of a given point of chassis referred to as the reference point, orientation of the chassis, and control. Among the kinematic relations is the requirement that each of the four wheels perform a slip-free motion. The rear wheels are assumed to be driving while the front wheels are responsible for the rotation of the chassis. The control objective is to place the reference point in the prespecified trajectory and to stabilize the motion of the reference point along the prespecified trajectory. The trajectory consists of line segments and circular arcs. In the mathematical model under consideration, the current curvature of the trajectory of the reference point is taken as control; it is related to the steering angle of the front wheels by a simple algebraic expression. The control is subject to two-sided constraints due to limitations on the steering angle of the front wheels. For the control law proposed, the attraction domain in the space “distance to the trajectory—orientation” is analyzed. For the initial conditions from this domain, the system is guaranteed to hit a trajectory with given index of exponential stability.     

基于T-S模型的轮式移动机器人轨迹跟踪控制

针对带有执行机构饱和约束与外部干扰的轮式移动机器人,提出了一种基于T-S模糊模型的轨迹跟踪方法.利用机器人运动特性和参考轨迹建立轨迹跟踪的误差系统并将其作T-S模型描述.通过求解具有LMI约束的半定规划问题,对每个线性子系统单独设计满足控制约束与H∞性能约束的状态反馈控制器,并在PDC(动态平行分配补偿)设计框架下构建全局控制器,最后证明闭环系统的李雅普诺夫稳定性.仿真结果验证了该方法的有效性和可行性.     

Simplified motion control of a two-axle compliant framed wheeled mobile robot

Kinematic models and motion control algorithms for a two-axle compliant frame mobile robot are examined. General kinematics describing the compliantly coupled nonholonomic kinematics are derived using velocity constraints that minimize traction forces and consider foreshortening of the frame. Given the complexity of these equations, the steering ratio a is defined to describe the relative heading angles of the front and rear axles. Simplified kinematic models are developed based upon a (Types I, II, and III) and the reference point used to guide the robot. Physical limitations and performance metrics (lateral mobility and maneuverability per unit of traction force) are derived to evaluate the models. Six groups of simulations and 24 experimental tests consisting of 120 trials evaluate the performance of the algorithms on carpet, sand, and sand with rocks. Results indicate that Type I (curvature-based steering) provides superior maneuverability and regulation accuracy, whereas Type II provides excellent lateral mobility at the cost of high traction forces, reduced accuracy, and potential singularities. Both models offer significant reductions in complexity for simplified control using standard curvature-based unicycle control algorithms. These results support expectations derived from performance metrics and physical limitations. Experimental results also demonstrate the efficacy of the robot to adapt to and maneuver over extremely rugged rocky terrain.