Numerical methods for estimation of the attraction domain in the problem of control of the wheeled robot

The problem of controlling the wheeled robot was considered. In the robot model used, the current curvature of the trajectory of the objective point which is related by simple algebraic expressions with the angle of rotation of the front wheels was taken as the control parameter. Boundedness of the angle of rotation of the robot front wheels imposes bilateral constraints on the control. The control constraints influence strongly the transients of the robot entering the desired trajectory. Additionally, the nature of the transients depends on the initial conditions. The aim of the paper was to construct the attraction domain guaranteeing the given rate of the transients. The quadratic Lyapunov function was used to approximate this domain. The problem of determining the quadratic Lyapunov functions was reduced to the standard mathematical verification for solvability of the system of linear matrix inequalities. For the case where the aim of control is to drive the robot objective point to the straight segment of the trajectory, the results of calculations of the stability domains were presented for various formulations of the problem.     

Cycab bi-steerable cars: a new family of differentially flat systems

The Cycab robots are a family of new mobile platforms already used in several research laboratories and meant for different applications such as public transportation in airport terminals or self-service cars in pedestrian zones. From a kinematic point of view, the Cycab specificity is the turning of its rear wheels as a function of the steering angle of the front wheels which makes it a bi-steerable non-holonomic vehicle. This feature enhances the maneuverability of the Cycab in cluttered environments. However, the associated kinematic model is new and different from those commonly treated in the robotics literature (such as the car-like robot, tractor-trailer, etc). To our knowledge such a system has not yet been studied and, in particular, there is no existing motion planner for it. In this paper, we tackle the study of this non-holonomic system, by establishing its kinematic model and analyzing its differential flatness property. We give a necessary and sufficient condition on the front/rear steering angle relation to guarantee the flatness of the system. This opens the way to the application of many motion planning and control methods. From this study we deduce a first motion planner for the system.     

Dynamic path tracking control of a vehicle on slippery terrain

This paper deals with accuracy and reliability for the path tracking control of a four wheel mobile robot with a double-steering system when moving at high dynamics on a slippery surface. An extended kinematic model of the robot is developed considering the effects of wheel–ground skidding. This bicycle type model is augmented to form a dynamic model that considers an actuation of the four wheels. Based on the extended kinematic model, an adaptive and predictive controller for the path tracking is developed to drive the wheels front and rear steering angles. The resulting control law is combined with a stabilization algorithm of the yaw motion which modulates the actuation torque of each four wheels, on the basis of the robot dynamic model. The global control architecture is experimentally evaluated on a wet grass slippery terrain, with speeds up to 7 m/s. Experimental results demonstrate enhancement of tracking performances in terms of stability and accuracy relative to the kinematic control.     

四轮转向车辆转向解耦的双点跟踪控制

针对四轮转向(4WS)无人车辆路径跟踪中的过约束问题, 本文提出一种前后轮转向解耦的双点跟踪控制策略. 建立4WS车辆单轨运动学模型, 约束前后轮转向角速度, 规划曲率连续的回旋曲线参考位姿序列, 将其解耦为前后轴中心的双点参考轨迹; 以前后轮中心点为控制点, 采用非线性反馈控制的预瞄方法分别获得转向控制率, 双点跟踪误差指数收敛于0. 仿真和实车验证结果表明, 所提出的双点跟踪控制策略横向误差标准差减少0.2 m, 横摆角误差标准差减小3.0?, 具有更大的前后轮转角控制域和较高的跟踪精度     

Dynamic control model of a cobot with three omni-wheels

In this paper, a new collaborative robot with omni-wheels has been proposed and its dynamic control has been developed and validated. Collaborative robots (Cobots) have been introduced to guide and assist human operators to move heavy objects in a given trajectory. Most of the existing cobots use steering wheels; typical drawbacks of using steering wheels include the difficulties to (i) follow a trajectory with a curvature larger than that of the base platform, (ii) mount encoders on steering wheels due to self-spinning of the wheels, and (iii) quarantine dynamic control performance since it is purely kinematic control. The new collaborative robot is proposed to overcome the above-mentioned shortcomings. The methodologies for its dynamic control are focused and the simulation has been conducted to validate the control performance of the system.     

Estimating the attraction domain of the invariant set in the problem of wheeled robot control

Consideration was given to the problem of controlling the planar motion of a wheeled robot with the driving rear wheels and forewheels intended for chassis rotation. The aim of control is to drive the goal point to the prescribed trajectory and stabilize the motion along it. The trajectory consists of segments of straight lines and circles. The forewheel rotation mechanism has inertiality due to its dynamic characteristics. Disregard for the dynamic properties of the forewheel drive at designing the control law leads in the course of motion to transients in the closed-loop system at passing from one trajectory segment to another. It was assumed that the drive dynamics obeys a first-order differential equation whose right-hand side satisfies the “sector condition.” To estimate these transients, in the system state space an invariant set is defined and estimated together with the estimate of the attraction domain.     

Introducing Climax: A novel strategy to a tri-wheel spiral robot

This paper describes a prototype and analytical studies of a tri-wheel spiral mobile robot. The robot can reach any desired point with a sequence of rotational movements. The robot has a simple actuation mechanism, consisting of three wheels mounted on a platform with axes fixed in 120° and a motor connected to each. Our approach introduces several new features such as simple repeated sequence of commands for steering and spiral motion, versus direct movement to target. The mathematical model of the robot is discussed, and a steering method is developed to achieve full motion capabilities. For a number of missions, it is shown experimentally that the proposed motion planning agrees well with the results.     

Study of the internal dynamics of an autonomous mobile robot

The requirement of ideal rolling without sideways slipping for wheels imposes nonholonomic (non-integrable) constraints on the motion of the wheels and consequently on the motion of wheeled mobile robots. From the control point of view, the dynamics of nonholonomic systems can be divided in two parts: external and internal dynamics. The dimension of the external dynamics of nonholonomic systems depends on the number of inputs to the system and the dimension of the internal dynamics depends on the number of independent nonholonomic constraints. For different motion control problems of nonholonomic systems, a smooth (model based) state feedback control law only deals with the system external dynamics; therefore, the system internal dynamics must be examined separately and its stability has to be analyzed and proved.In this paper, the internal dynamics of a three-wheel mobile robot with front wheel steering and driving is investigated. In particular, its internal dynamics stability is analyzed for two different situations, when the mobile robot is moving and when it is stationary.     

Motion planning algorithms of an omni-directional mobile robot with active caster wheels

This work deals with motion planning algorithms of an omni-directional mobile robot with active caster wheels. A typical problem occurred in the motion control of such omni-directional mobile robot, which has been identified through experimental experiences, is skidding of the mobile wheel. It sometimes results in uncertain rotation of the steering wheel. To cope with this problem, a motion planning algorithm which resolves the skidding problem and uncertain motions of the steering wheel is mainly investigated. For navigation of the mobile robot, the posture of the omni-directional mobile robot is initially calculated using the odometry information. Then, the accuracy of the mobile robot’s odometry is measured through comparison of the odometry information and the external sensor measurement. Finally, for successful navigation of the mobile robot, a motion planning algorithm that employs kinematic redundancy resolution method is proposed. Through simulations and experimentation, the feasibility of proposed algorithms was verified.     

轮式移动机器人在圆形管道中的运动学建模与分析

为解决圆形管道中轮式移动机器人的运动控制问题,分析了轮式移动机器人在圆形管道中的运动学特性．借助接触点的切平面,单个轮子在平面上的位置和运动描述方法被应用在圆管的柱面上．推导了单个轮子在柱面上纯滚动时轮心的轨迹和速度．运用刚体运动瞬时螺旋理论,对由两个固定轮和一个舵轮组成的(1,1)型三轮机器人在圆形管道中的运动进行了建模分析,并对此运动学模型进行了仿真．     

Modeling and Control of Head Raising Snake Robots by Using Kinematic Redundancy

In this paper, we consider trajectory tracking control of a head raising snake robot on a flat plane by using kinematic redundancy. We discuss the motion control requirements to accomplish trajectory tracking and other tasks, such as singular configuration avoidance and obstacle avoidance, for the snake robot. The features of the internal motion caused by kinematic redundancy are considered, and a kinematic model and a dynamic model of the snake robot are derived by introducing two types of shape controllable point. The first is the head shape controllable point, and the other is the base shape controllable point. We analyzed the features of the two kinds of shape controllable point and proposed a controller to accomplish the trajectory tracking of the robot’s head as its main task along with several sub-tasks by using redundancy. The proposed method to accomplish several sub-tasks is useful for both the kinematic model and the dynamic model. Experimental results using a head raising snake robot which can control the angular velocity of its joints show the effectiveness of the proposed controller.     

非同轴两轮机器人自平衡与转向闭环控制

针对车速、车身侧倾角和前轮转角变化较大工况下的非同轴两轮机器人在基于前轮转角的自平衡控制中,因动力学模型准确性对自平衡控制带来的影响,设计了基于RBF神经网络模糊滑模控制的自平衡控制器,利用RBF神经网络的逼近特性,对动力学模型中非线性时变的不确定部分进行自适应逼近,从而提高动力学模型的准确性,并借助模糊规则削弱滑模控制中产生的系统抖振;以及因前轮转角用于自平衡控制中难以实现转向闭环控制,建立了基于纯跟踪法的轨迹跟踪控制器,并设计利用车身平衡时车身侧倾角与前轮转角的耦合关系,将转向闭环控制中的目标前轮转角替换为目标车身侧倾角,从而将自平衡控制器与轨迹跟踪控制器相结合,在保证车身平衡行驶的前提下,实现带有轨迹跟踪的转向闭环控制。实验结果表明,凭借动力学模型的较高准确性,RBF神经网络模糊滑模自平衡控制器具有鲁棒性好、超调量低和响应迅速的优点,并且利用车身平衡后车身侧倾角与前轮转角耦合关系,实现转向闭环控制是可行的,具有良好的轨迹跟踪效果。     

三轮驱动移动机器人轨迹跟踪控制

针对三轮驱动移动机器人在轨迹跟踪控制过程中运动不平滑的问题,建立了移动机器人在一定运动约束条件下的运动学模型。根据移动机器人位姿误差微分方程的描述,设计了基于后退时变状态反馈方法的移动机器人轨迹跟踪控制器。基于李雅普诺夫方法,对轨迹跟踪控制器的稳定性进行了分析,证明了该控制器能够保证闭环系统全局一致渐进稳定。仿真结果验证了运动学模型的正确性,以及轨迹跟踪控制器的有效性。     

基于视觉图像的全向移动机器人轨迹跟踪控制研究

机器人轨迹节点跟踪比较难,导致机器人实际轨迹偏离期望轨迹,所以设计基于视觉图像的全向移动机器人轨迹跟踪控制方法;构建全向移动机器人的运动学数学模型,以此确定机器人移动轨迹数学模型;以移动轨迹数学模型为基础,按照视觉图像划分标准对全向移动机器人运动图像的分割,通过分离目标节点的方式提取运动学特征参量,完成机器人轨迹节点跟踪处理;结合节点跟踪处理结果,将运动学不等式与误差向量作为机器人轨迹跟踪控制的约束条件,利用滑模变结构搭建轨迹跟踪控制模型,实现全向移动机器人轨迹跟踪控制;对比实验结果表明,所设计的方法应用后,全向移动机器人角速度曲线、线速度曲线与期望运动轨迹曲线之间的贴合程度均超过90%,满足全向移动机器人轨迹跟踪控制要求。     

Kinematics of automatic guided vehicles with an inclined steering column and an offset distance: criterion for existence of inverse kinematic solution

This article presents the kinematic model of an automatic guided vehicle (AGV) with an inclined steering column and an offset distance. The vehicle configuration considered here employs the front wheel as the driving and steering wheel. From the kinematic model, a criterion is derived to test the existence of inverse kinematic solution. The criterion is a function of the geometric parameters of the AGV and the steering angle of the wheel. From the criterion defined, conditions for the existence of inverse kinematic solution for steering column configurations with and without inclination and offset distance are obtained. The criterion also presents the range of steering angles for which the inverse kinematic solution exists. The criterion signifies the presence of a unique solution for the motion parameters of the wheel, i.e., the wheel speed, steering angle, and steering rate for desired values of the motion parameters of the AGV, i.e., the linear and angular velocities of the AGV. This information is needed for the guidance control of AGVs based upon a kinematic control scheme (dead-reckoning control) without using the absolute position referencing system to follow a predefined path at prescribed linear and angular velocities. © 1992 John Wiley & Sons, Inc.     

Motion Control of a Nonholonomic Mobile Manipulator in Task Space

In this paper, the motion control of a mobile manipulator subjected to nonholonomic constraints is investigated. The control objective is to design a computed‐torque controller based on the coupled dynamics of the mobile manipulator. The proposed controller achieves the capability of simultaneous tracking of a reference velocity for the mobile base and a reference trajectory for the end‐effector. The aforementioned reference velocity and trajectory are defined in the task space, such task setting imitates the actual working conditions of a mobile manipulator and thus makes the control problem practical. To solve this tracking problem, a steering velocity is firstly designed based on the first‐order kinematic model of the nonholonomic mobile base via dynamic feedback linearization. The main merit of the proposed steering velocity design is that it directly utilizes the reference velocity set in the task space without requiring the knowledge of a reference orientation. A torque controller is subsequently developed based on a proposed Lyapunov function which explicitly considers the coupled dynamics of the mobile manipulator to ensure the mobile base and end‐effector track the reference velocity and trajectory respectively. This proposed computed‐torque controller is able to realize asymptotic stability of both the base velocity tracking error and the end‐effector motion tracking error. Simulations are conducted to demonstrate the effectiveness of the proposed controller.     

Kinematic modeling,mobility analysis and design of wheeled mobile robots

Wheeled mobile robots (WMRs) consist of interconnections of many electromechanical systems. Their mechanical subsystem comprises primarily the platform and the wheel units. To formulate the kinematic model of this class of robots, we model the individual subsystems separately. The composite kinematic model of a WMR is then a coupling of the various kinematic submodels. We study WMRs with different wheels, i.e. offset wheels, centered wheels and dual-wheels. The study focuses on system mobility, which is derived using the functional matrix. We also identified the kinematic equivalence between the dual-wheel and the centered wheels, and some advantages of the dual-wheels over the centered wheels and offset wheels. Results suggest that WMRs with mobility less than 3 cannot track a trajectory with a discontinuous heading without incorporating a time delay, during which the wheel orientation should be changed. Moreover, the steering angles of WMRs equipped with steered wheels require proper coordination to avoid jamming of the drive subsystem. For design purposes, we aim at a kinetostatically robust WMR. The concept of kinetostatic isotropy is applied to find the location of the wheels with respect to the platform and their type in order to achieve isotropy. It is shown that WMRs with three conventional wheels can be made isotropic if the offset either vanishes or equals the radius of the wheel, and if the three wheels are mounted at the vertices of an equilateral triangle.     

Redundant Control of a Planar Snake Robot with Prismatic Joints

This paper presents a control method of a planar snake robot with prismatic joints. The kinematic model is derived considering velocity constraints caused by passive wheels. The proposed control method based on the model allows the robot to track a target trajectory by appropriately changing its link length using prismatic joints. The degrees of freedom of prismatic joints are represented as kinematic redundancy in the model and are used in realizing subtasks such as singularity avoidance and obstacle avoidance. In addition, the link length is below its limit when introducing a sigmoid function into the kinematic model. Simulations are carried out to demonstrate the effectiveness of the proposed method and show a novel motion that avoids singular configurations through changes in link lengths.

     

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。     

Design and Control of a Four‐Wheeled Omnidirectional Mobile Robot with Steerable Omnidirectional Wheels

Omnidirectional mobile robots are capable of arbitrary motion in an arbitrary direction without changing the direction of wheels, because they can perform 3 degree‐of‐freedom (DOF) motion on a two‐dimensional plane. In this research, a new class of omnidirectional mobile robot is proposed. Since it has synchronously steerable omnidirectional wheels, it is called an omnidirectional mobile robot with steerable omnidirectional wheels (OMR‐SOW). It has 3 DOFs in motion and one DOF in steering. One steering DOF can function as a continuously variable transmission (CVT). CVT of the OMR‐SOW increases the range of velocity ratio from the wheel velocities to robot velocity, which may improve performance of the mobile robot. The OMR‐SOW with four omnidirectional wheels has been developed in this research. Kinematics and dynamics of this robot will be analyzed in detail. Various tests have been conducted to demonstrate the validity and feasibility of the proposed mechanism and control algorithm. © 2004 Wiley Periodicals, Inc.