基于阿克曼原理的车式移动机器人运动学建模

基于阿克曼原理的轮式移动机器人运动学模型对于无人驾驶车辆的研究有着重要的意义.对轮式移动机器人的运动学特性进行了分析,建立了不考虑滑行、刹车等的轮式移动机器人的运动学模型.对该运动学模型引入了阿克曼约束,给出了描述机器人运动状态的转向角、航向角和转弯半径等物理量的数学公式.最后对该运动学模型进行仿真实验,验证了所建立的运动学模型的正确性,为进一步研究轮式移动机器人提供了理论分析的基础.     

A generic kinematic formulation for wheeled mobile robots

This article presents a generic kinematic formulation and a procedure developed to deduce the kinematics of wheeled mobile robots (WMRs), also known in the literature as driverless ground vehicles, automated guided vehicles (AGVs), and autonomous transit vehicles (ATVs). The generic formulation to deduce the kinematics of WMRs with various combinations of driving and steering wheels is obtained by making use of the transformation approach and modifying the kinematic formulations developed for WMRs with inclined steering columns. A general expression for the angular velocity of wheel slip is derived to extend the suitability of the formulations for WMRs with various combinations of driving and steering wheels. It is illustrated that the procedure developed provides the final form of the kinematic equations by providing only the kinematic parameters of the WMR, including the type of wheels employed for the generic model. This approach is useful to automate the modeling procedure to obtain either symbolic expressions or numerical values for WMR kinematics. Several case studies are presented to illustrate the simplicity of the developed approach. © 1997 John Wiley & Sons, Inc.     

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.     

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.     

A generalized kinematic modeling method for modular robots

Modular robots can be defined as reconfigurable mechanical arms which can be automatically controlled using suitable motion control software. In this article, a generalized kinematic modeling method is presented for such modular robots. This method can be used to derive the individual kinematic models of all the mechanical elements that make up the inventory of modular units, independently of their geometry and sequence of assembly into a robot. A general procedure is also presented to derive a global kinematic model of any robot configured using these modular units. The kinematic modeling technique of the units is based on Denavit-Hartenberg (D-H) parameter notation. A provision is also presented for converting “non D-H” parameter transformations, obtained in assembling the kinematic chain, into D-H transformations. This D-H conversion feature allows the modeling technique to preserve its generality when a kinematic model is obtained for the specific robot configuration at hand. The conceptual design of modular robot units that is under development in the Computer Integrated Manufacturing Laboratory (CIML) is also presented to show the feasibility of a modular approach to robot design and to clarify some of the mathematical for mulations developed in the article.     

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.     

Characterizing geometric patterns formable by oblivious anonymous mobile robots

In a system in which anonymous mobile robots repeatedly execute a “Look–Compute–Move” cycle, a robot is said to be oblivious if it has no memory to store its observations in the past, and hence its move depends only on the current observation. This paper considers the pattern formation problem in such a system, and shows that oblivious robots can form any pattern that non-oblivious robots can form, except that two oblivious robots cannot form a point while two non-oblivious robots can. Therefore, memory does not help in forming a pattern, except for the case in which two robots attempt to form a point. Related results on the pattern convergence problem are also presented.     

A new method for the geometric modeling of lower pairs and its application to the kinematic spaces of spatial robots

A new notation is developed to model and analyze spatial robots. This method is formulated based on the homogeneous cylindrical coordinates and Bryant angles transformation matrices and thus termed “C-B notation.” At first, shape matrix for a binary link is derived. Then, the characteristic matrices for the five most commonly used kinematic lower pairs—revolute (R), prismatic (P), cylindrical (C), helical (H), and spherical (S)—are formulated. The “exact” joint positions, that is, the actual location of the physical joint center in space, can be defined using this method. The governing kinematic equations for the analysis of spatial robots are derived as well. Finally, the “kinematic spaces” for the open-chain robot are defined as “the group of space of work (displacement) space, velocity space (the velocity envelope in the displacement differential V_x-V_y-V_z coordinates), and acceleration space (the acceleration envelope in the velocity differential A_x-A_y-A_z coordinates).” Numerical examples for parallel projections of kinematic spaces on both sagittal and frontal planes are illustrated by the industrial Unimate 2000 spherical (SP/RRR) robot, Bendix AA/CNC (RRP/RRR) robot, and 6R Cincinnati Milacron T3 robot.     

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.     

Distributed algorithms for formation of geometric patterns with many mobile robots

We discuss a method for controlling a group of mobile robots in a distributed manner. The method is distributed in the sense that all robots, or most of the robots in some cases, plan their motion individually based upon the given goal of the group and the observed positions of other robots. We illustrate the method by showing how a large number of robots can form an approximation of a circle, a simple polygon, or a line segment in the plane. We also show how the robots can distribute themselves nearly uniformly within a circle or a convex polygon in the plane. Finally, we show how the robots can be divided into two or more groups. It turns out that in many cases most robots execute an identical, simple algorithm. The performance of the method is demonstrated by simulation. © 1996 John Wiley & Sons, Inc.     

Matrix modeling of inverse dynamics of spatial and planar parallel robots

Recursive matrix relations for kinematics and dynamics analysis of two known parallel mechanisms: the spatial 3-PRS and the planar 3-RRR are established in this paper. Knowing the motion of the platform, we develop first the inverse kinematical problem and determine the positions, velocities, and accelerations of the robot’s elements. Further, the inverse dynamic problem is solved using an approach based on the principle of virtual work, and the results can be verified in the framework of the Lagrange equations with their multipliers. Finally, compact matrix equations and graphs of simulation for power requirement comparison of each of three actuators in two different actuation schemes are obtained. For the same evolution of the moving platform, the power distribution upon the three actuators depends on the actuating configuration, but the total power absorbed by the set of three actuators is the same, at any instant, for both driving systems. The study of the dynamics of the parallel mechanisms is done mainly to solve successfully the control of the motion of such robotic systems.     

EP-based kinematic control and adaptive fuzzy sliding-mode dynamic control for wheeled mobile robots

This paper proposes a complete control law comprising an evolutionary programming based kinematic control (EPKC) and an adaptive fuzzy sliding-mode dynamic control (AFSMDC) for the trajectory-tracking control of nonholonomic wheeled mobile robots (WMRs). The control gains for kinematic control (KC) are trained by evolutionary programming (EP). The proposed AFSMDC not only eliminates the chattering phenomenon in the sliding-mode control, but also copes with the system uncertainties and external disturbances. Additionally, the convergence of trajectory-tracking errors is proved by the Lyapunov stability theory. Computer simulations are presented to confirm the effectiveness of the proposed complete control law. Finally, real-time experiments are done in the test field to demonstrate the feasibility of real WMR maneuvers.     

Virtual joint method for kinematic modeling of wheeled mobile manipulators

In this paper, we propose a virtual joint method that better utilizes quasi-velocities for the kinematic modeling of wheeled mobile manipulators. By identifying quasi-velocities as motions of imaginary revolute and prismatic kinematic pairs, our method enables one to regard a mobile manipulator as an ordinary articulated manipulator for the purposes of velocity analysis. We also propose an inverse kinematic scheme for the mobile manipulators along the line with the virtual joint based kinematic framework. Details are worked out for mobile manipulators with representative differential-drive and car-like mobile platforms.     

Nonlinear kinematic tolerance analysis of planar mechanical systems

This paper presents a nonlinear kinematic tolerance analysis algorithm for planar mechanical systems comprised of higher kinematic pairs. The part profiles consist of line and circle segments. Each part translates along a planar axis or rotates around an orthogonal axis. The part shapes and motion axes are parameterized by a vector of tolerance parameters with range limits. A system is analyzed in two steps. The first step constructs generalized configuration spaces, called contact zones, that bound the worst-case kinematic variation of the pairs over the tolerance parameter range. The zones specify the variation of the pairs at every contact configuration and reveal failure modes, such as jamming, due to changes in kinematic function. The second step bounds the worst-case system variation at selected configurations by composing the zones. Case studies show that the algorithm is effective, fast, and more accurate than a prior algorithm that constructs and composes linear approximations of contact zones.     

基于视觉显著性的移动机器人动态环境建模

本文采用视觉显著性提出了一种移动机器人动态环境建模方法.该方法利用提出的视觉显著性模型,对连续的2帧图像中匹配的加速稳健特征点(SURF)利用其位置关系并采用多重随机抽样一致(multi-RANSAC)算法实现了环境中动态物体显著性检测.采用投影方法和快速均值漂移算法构建了动态环境的栅格模型,利用得到的动态显著性物体的位置更新环境地图中的栅格占据值以及动态物体的影响区域.动态环境显著图构建实验和动态环境的栅格模型构建实验的结果证明了上述方法是可行的.     

Visual navigation of wheeled mobile robots using direct feedback of a geometric constraint

Many applications of wheeled mobile robots demand a good solution for the autonomous mobility problem, i.e., the navigation with large displacement. A promising approach to solve this problem is the following of a visual path extracted from a visual memory. In this paper, we propose an image-based control scheme for driving wheeled mobile robots along visual paths. Our approach is based on the feedback of information given by geometric constraints: the epipolar geometry or the trifocal tensor. The proposed control law only requires one measurement easily computed from the image data through the geometric constraint. The proposed approach has two main advantages: explicit pose parameters decomposition is not required and the rotational velocity is smooth or eventually piece-wise constant avoiding discontinuities that generally appear in previous works when the target image changes. The translational velocity is adapted as demanded for the path and the resultant motion is independent of this velocity. Furthermore, our approach is valid for all cameras with approximated central projection, including conventional, catadioptric and some fisheye cameras. Simulations and real-world experiments illustrate the validity of the proposal.     

Characterization of zero tracking error references in the kinematic control of wheeled mobile robots

This work establishes the reference signal conditions for zero tracking error when controlling wheeled mobile robots under the kinematic framework, that is, when the low-level dynamics is neglected. The reference characterization is based on the classical decoupled robot control and the inverse kinematics of fixed, centered orientable, castor and Swedish wheels. Procedures to avoid tracking error when a particular condition is not satisfied are also indicated. Simulations are shown to illustrate the reference conditions for each type of mobile robot and their implications. Finally, an industrial forklift is considered in a real situation to validate the previous results and to highlight the limits of the kinematic framework assumption.     

Formation optimization for a fleet of wheeled mobile robots — A geometric approach

Tight formation-based operations are critical in several emerging applications for robot collectives — ranging from cooperative payload transport to synchronized distributed data-collection. In this paper, we investigate the optimal relative layout for members of a team of Differentially-Driven Wheeled Mobile Robots (DD-WMRs) moving in formation for ultimate deployment in cooperative payload transport tasks.Our particular focus is on modeling such formations, developing the motion plans and determining the “best formation” in a differential-geometric setting. Specifically, a preferred team-fixed frame serves as a virtual leader inducing motion plans for the individual DD-WMRs which form the vertices of a virtual structure. The resulting motion plans for the DD-WMRs as well as overall team-performance depend both on the specifiedteam-frame motions as well as their relative-layout within the formation.Emphasis is placed on developing suitable invariant (yet quantitative) measures of formation quality and a systematic optimization-based selection of the formation-layout. The use of relative formation-parameterization with respect to a team-frame serves to decouple the team-level optimal layout selection process. The optimal location of each DD-WMR can now be found with respect to the team-frame individually and the feasibility of distributed implementation facilitates scaling to larger-sized formations. Analytical and numerical results, from case studies of formation optimization of three DD-WMRs maneuvering along certain desired planar paths, are presented to highlight the salient features and benefits.     

Guaranteed interval analysis localization for mobile robots

This paper presents a set membership method (named Interval Analysis Localization (IAL)) to deal with the global localization problem of mobile robots. By using a LIDAR (LIght Detection And Ranging) range sensor, the odometry and a discrete map of an indoor environment, a robot has to determine its pose (position and orientation) in the map without any knowledge of its initial pose. In a bounded error context, the IAL algorithm searches a set of boxes (interval vector), with a cardinality as small as possible that includes the robot’s pose. The localization process is based on constraint propagation and interval analysis tools, such as bisection and relaxed intersection. The proposed method is validated using real data recorded during the CAROTTE challenge, organized by the French ANR (National Research Agency) and the French DGA (General Delegation of Armament). IAL is then compared with the well-known Monte Carlo Localization showing weaknesses and strengths of both algorithms. As it is shown in this paper with the IAL algorithm, interval analysis can be an efficient tool to solve the global localization problem.