Screw-based kinematic modeling and geometric analysis of planar mobile robots

Typical mobile robots can be modeled as parallel mechanisms by employing an interfacing variable between the ground and the wheels. Based on this conception, the screw theory was employed in the following work as an alternative approach in the modeling of such parallel-natured mobile robots. This theory allows for a geometric analysis of mobile mechanisms. As a result, the computational load in the derivation of a Jacobian model can be reduced, the kinematic model for different sets of inputs can be easily obtained, and an equivalent serial-chain model can be analyzed. Two mobile robots were examined as exemplary models. The proposed approach can also be applied to kinematic modeling and the analysis of general types of mobile robots.     

Kinematic modeling of wheeled mobile robots with slip

This work presents a kinematic modeling method for wheeled mobile robots with slip based on physical principles. First, we present the kinematic modeling of a mobile robot with no-slip considering four types of wheels: fixed, centered orientable, off-centered orientable (castor) and Swedish (also called Mecanum, Ilon or universal). Then, the dynamics of a wheeled mobile robot based on Lagrange formulation are derived and discussed. Next, a quasi-static motion is considered to obtain the kinematic conditions that provide the slip modeling equations. Several types of traction models for the slip between the wheel and the floor are indicated. In particular, for a frictional force linearly dependent on the sliding velocity, the no-slip kinematic equation of the wheeled mobile robot is related, through the weighted least-squares algorithm, with the slip modeling equations. To illustrate the applications of the proposed approach a tricycle vehicle is considered in a real situation. The experimental results obtained for the slip kinematic model are compared with the ones obtained for the well-known Kalman filter.     

Kinematic Modeling and Analysis of Skid-Steered Mobile Robots With Applications to Low-Cost Inertial-Measurement-Unit-Based Motion Estimation

Skid-steered mobile robots are widely used because of their simple mechanism and high reliability. Understanding the kinematics and dynamics of such a robotic platform is, however, challenging due to the complex wheel/ground interactions and kinematic constraints. In this paper, we develop a kinematic modeling scheme to analyze the skid-steered mobile robot. Based on the analysis of the kinematics of the skid-steered mobile robot, we reveal the underlying geometric and kinematic relationships between the wheel slips and locations of the instantaneous rotation centers. As an application example, we also present how to utilize the modeling and analysis for robot positioning and wheel slip estimation using only low-cost strapdown inertial measurement units. The robot positioning and wheel slip-estimation scheme is based on an extended Kalman filter (EKF) design that incorporates the kinematic constraints for accuracy enhancement. The performance of the EKF-based positioning and wheel slip-estimation scheme are also presented. The estimation methodology is tested and validated experimentally on a robotic test bed.     

移动机器人滑动参数定界及鲁棒镇定控制

本文针对带运动学参数不确定性的野外轮式移动机器人模型的在线辨识、定界和点镇定控制问题展开了研究.考虑了移动机器人二维平面运动过程中所存在的滑动效应和自身几何参数未知等不确定性,并将其建模为运动学模型中所包含的未知时变参数.通过引入基于有界误差假设的非线性集员滤波方法,对移动机器人运动学模型中存在的不确定性参数进行了辨识和定界.在此基础上结合backstepping控制思想和Lyapunov分析方法解决了移动机器人的鲁棒镇定问题,在存在滑动参数干扰的情况下实现了移动机器人的全局指数收敛点镇定控制,提高了整体控制系统的稳定性和鲁棒性.仿真结果证明了本方法的有效性和鲁棒性.     

野外移动机器人滑动效应的在线建模和跟踪控制

针对野外移动机器人的滑动效益建模和补偿控制问题进行了研究.以履带式移动机器人为研究对象,将履带和地面之间的滑动效应建模为时变的滑动参数,由此建立起带滑动参数的机器人运动学和动力学模型,并采用基于方根无色卡尔曼滤波(SR-uKF)的在线非线性估计方法对机器人的位姿和滑动参数进行联合估计.在此基础上,提出了一种基于动态反馈...     

Optimal design of a stair-climbing mobile robot with flip mechanism

Stairs overcoming is a primary challenge for mobile robots moving in human environments, and the contradiction between the portability and the adaptability of stair climbing robot is not well resolved. In this paper, we present an optimal design of a flip-type mobile robot in order to improve the adaptability as well as stability while climbing stairs. The kinematic constraints on the flip mechanism are derived to prevent undesired interferences among stairs, wheels and main body during climbing stairs. The objective function is proposed according to the traction demand of the robot during stair-climbing motion for the first time and the value of the objective function is calculated though kinetic analysis. The Taguchi method is using as the optimization tool because of its simplicity and cost-effectiveness both in formulating an objective function and in satisfying multiple constraints simultaneously. The performance of the robot under the optimal parameters is verified through simulations and experiments.     

四轮全方位移动机器人各向相异性研究

由于全方位轮的特殊构造，使得全方位移动机器人沿不同方向运动时具有的最大速度不同，以及在不同方向上的加速性能也不同，称之为各向相异性（anisotropy）．为了充分发挥全方位移动机器人的优越性，通过对4轮全方位移动机器人进行运动学、动力学建模，分析了机器人各向相异性，确定了轮系布置与最大速度曲线的相关规律，以及当机器人沿某一方向以一定加速度运动时，不同轮子上驱动电机所需提供的转矩，从而使得机器人加速运动时更好地避免轮子打滑．并且通过Matlab-ADAMS联合仿真以及实际实验，验证了分析结果的正确性．对机器人的各向相异性作了全面系统的研究，从而更清楚地表述了模型特性，为更好地控制全方位移动机器人提供了基础．     

A novel XY-Theta precision table and a geometric procedure for its kinematic calibration

Spatial precision positioning devices are often based on parallel robots, but when it comes to planar positioning, the well-known serial architecture is virtually the only solution available to industry. Problems with parallel robots are that most are coupled, more difficult to control than serial robots, and have a small workspace. In this paper, new parallel robot is proposed, which can deliver accurate movements, is partially decoupled and has a relatively large workspace. The novelty of this parallel robot lies in its ability to achieve the decoupled state by employing legs of a different kinematic structure. The robot repeatability is evaluated using a CMM and so are the actual lead errors of its actuators. A simple geometric method is proposed for directly identifying the actual base and mobile reference frames, two actuator's offsets and one distance parameter, using a measurement arm from FARO Technologies. While this method is certainly not the most efficient one, it yields a satisfactory improvement of the robot accuracy without the need for any background in robot calibration. An experimental validation shows that the position accuracy achieved after calibration is better than 0.339 mm within a workspace of approximately 150 mm×200 mm.     

Kinematic modeling and singularity of wheeled mobile robots

This paper presents a global singularity analysis for wheeled mobile robots (WMRs). First, a kinematic model of a generic wheel is obtained using a recursive kinematics formulation. This novel and efficient approach is valid for all the common types of wheels: fixed, centered orientable, off-centered orientable (caster or castor) and Swedish or Mecanum. Then, a procedure for generating robot kinematic models is presented based on the set of wheel equations and the null space concept. Next, the singularity of kinematic models is discussed: first, the kinematic singularity condition in forward models is obtained, and then the singularity condition in inverse, or even mixed, models. A generic and practical geometric approach is established to characterize the singularity of any kinematic model of any WMR with the mentioned wheels. To illustrate the applications of the proposed approach, the singular configurations for many types of WMRs are depicted. Finally, the singularity characterization is extended to include other specialized wheels: dual-wheel, dual-wheel castor, ball-type and orthogonal.     

Cooperative adaptive consensus tracking for multiple nonholonomic mobile robots

This paper addresses the cooperative adaptive consensus tracking for a group of multiple nonholonomic mobile robots, where the nonholonomic robot model is assumed to be a canonical vehicle having two actuated wheels and one passive wheel. By integrating a kinematic controller and a torque controller for the nonholonomic robotic system, a cooperative adaptive consensus tracking strategy is developed for the uncertain dynamic models using Lyapunov-like analysis in combination with backstepping approach and sliding mode technique. A key feature of the developed adaptive consensus tracking algorithm is the introduction of a directed network topology into the control constraints based on algebraic graph theory to characterise the communication interaction among robots, which plays an important role in realising the cooperative consensus tracking with respect to a specific common reference trajectory. Furthermore, a novel framework is proposed for developing a unified methodology for the convergence analysis of the closed-loop control systems, which can fully ensure the desired adaptive consensus tracking for multiple nonholonomic mobile robots. Subsequently, illustrative examples and numerical simulations are provided to demonstrate and visualise the theoretical results.     

Kinematic analysis and error modeling of TAU parallel robot

The TAU robot presents a new configuration of parallel robots with three degrees of freedom. This robotic configuration is well adapted to perform with a high precision and high stiffness within a large working range compared with a serial robot. It has the advantages of both parallel robots and serial robots. In this paper, the kinematic modeling and error modeling are established with all errors considered using Jacobian matrix method for the robot. Meanwhile, a very effective Jacobian approximation method is introduced to calculate the forward kinematic problem instead of Newton–Raphson method. It denotes that a closed form solution can be obtained instead of a numerical solution. A full size Jacobian matrix is used in carrying out error analysis, error budget, and model parameter estimation and identification. Simulation results indicate that both Jacobian matrix and Jacobian approximation method are correct and with a level of accuracy of micron meters. ADAMS's simulation results are used in verifying the established models.     

The kinematics for redundantly actuated omnidirectional mobile robots

Omnidirectional mobile robots have been popularly employed in several application areas. However, the kinematics and singularity analysis for these systems have not been clearly identified, especially for the redundantly actuated case, which is common in current omnidirectional mobile robots. In light of this fact, this article introduces two different kinematic approaches for a typical omnidirectional mobile robot having three caster wheels, and examines singularity configurations of such systems. Then, a singularity‐free load‐distribution scheme for a redundantly actuated three‐wheeled omnidirectional mobile robot is proposed. Through simulation, several advantages of the redundantly actuated mobile robot (singularity avoidance, input‐load saving, and exploiting several subtasks) are presented. © 2002 Wiley Periodicals, Inc.     

INTELLIGENT MOTION CONTROL FOR OMNIDIRECTIONAL MOBILE ROBOTS USING ANT COLONY OPTIMIZATION

This article presents an intelligent system-on-a-programmable-chip-based (SoPC) ant colony optimization (ACO) motion controller for embedded omnidirectional mobile robots with three independent driving wheels equally spaced at 120 degrees from one another. Both ACO parameter autotuner and kinematic motion controller are integrated in one field-programmable gate array (FPGA) chip to efficiently construct an experimental mobile robot. The optimal parameters of the motion controller are obtained by minimizing the performance index using the proposed SoPC-based ACO computing method. These optimal parameters are then employed in the ACO-based embedded kinematic controller in order to obtain better performance for omnidirectional mobile robots to achieve trajectory tracking and stabilization. Experimental results are conducted to show the effectiveness and merit of the proposed intelligent ACO-based embedded controller for omnidirectional mobile robots. These results indicate that the proposed ACO-based embedded optimal controller outperforms the nonoptimal controllers and the conventional genetic algorithm (GA) optimal controllers.     

Kinematic modeling of wheeled mobile robots

We formulate the kinematic equations of motion of wheeled mobile robots incorporating conventional, omnidirectional, and ball wheels.¹ We extend the kinematic modeling of stationary manipulators to accommodate such special characteristics of wheeled mobile robots as multiple closed-link chains, higher-pair contact points between a wheel and a surface, and unactuated and unsensed wheel degrees of freedom. We apply the Sheth-Uicker convention to assign coordinate axes and develop a matrix coordinate transformation algebra to derive the equations of motion. We introduce a wheel Jacobian matrix to relate the motions of each wheel to the motions of the robot. We then combine the individual wheel equations to obtain the composite robot equation of motion. We interpret the properties of the composite robot equation to characterize the mobility of a wheeled mobile robot according to a mobility characterization tree. Similarly, we apply actuation and sensing characterization trees to delineate the robot motions producible by the wheel actuators and discernible by the wheel sensors, respectively. We calculate the sensed forward and actuated inverse solutions and interpret the physical conditions which guarantee their existence. To illustrate the development, we formulate and interpret the kinematic equations of motion of Uranus, a wheeled mobile robot being constructed in the CMU Mobile Robot Laboratory.     

Dynamics and input–output feedback linearization control of a wheeled mobile cable-driven parallel robot

In comparison to the conventional parallel robots, cable-driven parallel robots (CDPRs) have generally superior features such as simple production technology, low energy consumption, large workspace, high payload to moving weight ratio, and also low cost. On the other hand, a wheeled mobile robot (WMR) which is capable of covering a vast area can be used when no specific space is designated for the stationary accessories of a robot. In this paper, the integration of a CDPR with a WMR is proposed to overcome some of the issues related to each of these robots. The kinematic equations of the robot are presented. To derive the dynamic equations, Gibbs–Appel (G–A) formulation is used, which in contrary to the Lagrange formulation benefits from advantages of quasi-velocities over generalized coordinates as well as not requiring Lagrange multipliers. The dynamic equations of the two parts are coupled, and the interacting effects are observable from the governing equations. By considering non-holonomic wheels for the robot, internal dynamics appears in the equations. However, based on some conditions, the equations are input–output linearizable via a static feedback. The platform trajectory is designed based on the given end-effector trajectory. The effectiveness of the controller is shown through simulations and experimental tests.     

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.

     

Dynamics,control, and simulation of robots with differential drive

The problem of synthesizing trajectories, planning and implementing the motion of a mobile robot is investigated. The statement of the problem is motivated by the need for designing an optimal control of robots with two wheels controlled independently. Mobile robots with this kinematic scheme are called robots with “differential drive.”     

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.     

轮子纵向打滑条件下的移动机器人自适应跟踪控制

针对纵向滑动参数未知的轮式移动机器人的轨迹跟踪问题,提出一种自适应跟踪控制策略.利用两个未知参数来描述移动机器人左右轮的纵向打滑程度,建立了产生纵向滑动的差分驱动轮式移动机器人的运动学模型;设计了补偿纵向滑动的自适应非线性反馈控制律;应用 Lyapunov 稳定性理论与 Barbalat 定理证明了闭环系统的稳定性;同时,提出了一种由极点配置方法在线调整控制器增益的方法.仿真结果验证了所提出控制方法的有效性.     

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.