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.     

A constrained assumed modes method for dynamics of a flexible planar serial robot with prismatic joints

In the present study, for the first time, flexible multibody dynamics for a three-link serial robot with two flexible links having active prismatic joints is presented using an approximate analytical method. Transverse vibrations of flexible links/beams with prismatic joints have complicated differential equations. This complexity is mostly due to axial motion of the links. In this study, first, vibration analysis of a flexible link sliding through an active prismatic joint having translational motion is considered. A rigid-body coordinate system is used, which aids in obtaining a new and rather simple form of the kinematic differential equation without the loss of generality. Next, the analysis is extended to include dynamic forces for a three-link planar serial robot called PPP (Prismatic, Prismatic, Prismatic), in which all joints are prismatic and active. The robot has a rigid first link but flexible second and third links. To model the prismatic joint, time-variant constraints are written, and a motion equation in a form of virtual displacement and virtual work of forces/moments is obtained. Finally, an approximate analytical method called the “constrained assumed modes method” is presented for solving the motion equations. For a numerical case study, approximate analytical results are compared with finite element results, which show that the two solutions closely follow each other.     

Single and multi-purpose optimization of vibrating Timoshenko shafts

Optimization of transversely vibrating shafts with respect to eigenfrequencies, with constraints on the design variables, has been almost fully investigated in recent years - as far as the Bernoulli-Euler equation of motion is concerned. In the present paper, Timoshenko's equations are applied, i.e. the effects of shear and rotational energy are taken into account in the calculation of the transverse vibration modes and frequencies of the shaft. This is done via a finite element formulation. The sensitivity analysis of the transverse vibration frequencies is based on analytical differentation of the stiffness- and mass matrices. The computer program developed provides the user with an option to suppress the Timoshenko effects, such that the analysis can be carried out within the Bernoulli-Euler theory as well and then comparisons can be made. Torsional vibrations of shafts are also considered, computing the vibration modes and natural frequencies by means of a finite difference approach. Again, the sensitivity analysis is carried out analytically. Objective functions and behavioral constraints are selected from fundamental frequencies, higher order frequencies and differences between adjacent frequencies of the vibrational types considered. The cross-sectional area function of the shaft is used as the design variable and the total volume of structural material is assumed to be given, along with some sizing constraints. The shafts considered may be equipped with non-structural disks and flexible supports. Several examples are presented and some notable differences between optimized Timoshenko and Bernoulli-Euler shafts derived.     

Higher Order Real-Time Approximations in Optimal Control of Multibody-Systems for Industrial Robots

The multibody system of an industrial robot leads to a mathematical model described by ordinary differential equations. Control functions have to be determined to calculate robot trajectories which are optimal due to a given performance index subject to additional constraints. In order to solve such optimal control problems, computationally expensive methods exist. These methods have no real-time capability, since perturbations during the motion of the robot require a recalculation of the optimal trajectory within a time frame much smaller than the operating-time of the robot. Hence, a robust numerical method based on the parametric sensitivity analysis of nonlinear optimization problems is suggested. Optimal control approximations of perturbed optimal solutions can be obtained in real-time by evaluating a first order Taylor expansion of the perturbed solution. Successive improvements to the constraints in the direction of the optimal perturbed solution lead to an admissible solution with a higher order approximation of the objective. The proposed numerical method is illustrated by the optimal control of an industrial robot with three degrees of freedom subject to deviations in the payload and initial values.     

约束条件下的巡线机器人逆运动学求解

高压输电线路巡检机器人是一种多关节悬挂运动机构,要实现其运动控制就需要根据机器人的本身机构特点和悬挂系统的运动约束条件进行运动学分析.本文利用微分扭转法对巡线机器人的正向运动学进行了求解,并通过对机器人悬挂系统的力学分析,得到了机器人运动学的约束条件,并在这种约束条件下,采用了一种可用来进行实时控制的迭代循环坐标下降(CCD)算法,来进行机器人的逆运动学求解.这种迭代算法对于有运动约束系统的逆运动学求解具有较强的适用性,而且它具有较好的收敛性和有效性,适合于在线计算,便于巡线机器人的实时运动控制.     

仿人机器人复杂动作设计中人体运动数据提取及分析方法

提出了仿人机器人复杂动作设计中人体运动数据提取及分析方法. 首先, 通过运动捕捉系统获取人体运动数据, 并采用运动重定向技术, 输出人--机简化模型的数据; 然后, 对运动数据进行分析和运动学解算, 给出基于人体运动数据的仿人机器人逆运动学求解方法, 得到仿人机器人模型的关节角数据; 再经过运动学约束和稳定性调节后, 生成能够应用于仿人机器人的运动轨迹. 最终, 通过在仿人机器人BHR-2上进行刀术实验验证了该方法的有效性.     

非完整约束下的机器人运动规划算法

由非完整约束定义提出一种改进RRT(快速搜索随机树)算法,解决受动力学约束的移动机器人运动规划问题.该算法将移动机器人的非完整约束条件与RRT搜索算法相结合.针对RRT算法在全局状态空间均匀随机搜索导致算法无谓耗费代价大的缺陷,引入目标偏向思想,并选择计算复杂度低的距离参数提高求解速度.通过几类典型的非完整约束下的机器...     

A Technique to Analytically Formulate and to Solve the 2-Dimensional Constrained Trajectory Planning Problem for a Mobile Robot

A new technique for trajectory planning of a mobile robot in a two-dimensional space is presented in this paper. The main concept is to use a special representation of the robot trajectory, namely a parametric curve consisting in a sum of harmonics (sine and cosine functions), and to apply an optimization method to solve the trajectory planning problem for the parameters (i.e., the coefficients) appearing in the sum of harmonics. This type of curve has very nice features with respect to smoothness and continuity of derivatives, of whatever order. Moreover, its analytical expression is available in closed form and is very suitable for both symbolic and numerical computation. This enables one to easily take into account kinematic and dynamic constraints set on the robot motion. Namely, non-holonomic constraints on the robot kinematics as well as requirements on the trajectory curvature can be expressed in closed form, and act as input data for the trajectory planning algorithm. Moreover, obstacle avoidance can be performed by expressing the obstacle boundaries by means of parametric curves as well. Once the expressions of the trajectory and of the constraints have been set, the trajectory planning problem can be formulated as a standard mathematical problem of constrained optimization, which can be solved by any adequate numerical method. The results of several simulations are also reported in the paper to show the effectiveness of the proposed technique to generate trajectories which meet all requirements relative to kinematic and dynamic constraints, as well as to obstacle avoidance.     

Function from motion

In order for a robot to operate autonomously in its environment, it must be able to perceive its environment and take actions based on these perceptions. Recognizing the functionalities of objects is an important component of this ability. In this paper, we look into a new area of functionality recognition: determining the function of an object from its motion. Given a sequence of images of a known object performing some function, we attempt to determine what that function is. We show that the motion of an object, when combined with information about the object and its normal uses, provides us with strong constraints on possible functions that the object might be performing     

A Sequential Bi-criteria Search Algorithm for Robot Path Planning in the Box Pushing Problem

The collision-free trajectory planning method subject to control constraints for mobile manipulators is presented. The robot task is to move from the current configuration to a given final position in the workspace. The motions are planned in order to maximise an instantaneous manipulability measure to avoid manipulator singularities. Inequality constraints on state variables i.e. collision avoidance conditions and mechanical constraints are taken into consideration. The collision avoidance is accomplished by local perturbation of the mobile manipulator motion in the obstacles neighbourhood. The fulfilment of mechanical constraints is ensured by using a penalty function approach. The proposed method guarantees satisfying control limitations resulting from capabilities of robot actuators by applying the trajectory scaling approach. Nonholonomic constraints in a Pfaffian form are explicitly incorporated into the control algorithm. A computer example involving a mobile manipulator consisting of nonholonomic platform (2,0) class and 3DOF RPR type holonomic manipulator operating in a three-dimensional task space is also 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.     

Collision-Free Cartesian Trajectory Generation Using Raster Scanning and Genetic Algorithms

An algorithm for Cartesian trajectory generation by redundant robots in environments with obstacles is presented. The algorithm combines a raster scanning technique, genetic algorithms and functions for interpolation in the joint coordinates space in order to approximate a desired Cartesian curve by the robot's hand tip under maximum allowed position deviation. A raster scanning technique determines a minimal set of knot points on the desired curve in order to generate a Cartesian trajectory with bounded position approximation error. Genetic algorithms are used to determine an acceptable robot configuration under obstacle avoidance constraints corresponding to a knot point. Robot motion between two successive knot points is finally achieved using well known interpolation techniques in the joint coordinates space. The proposed algorithm is analyzed and its performance is demonstrated through simulated experiments carried out on planar redundant robots.     

Optimal Motion Planning of Robotic Manipulators Removing Mobile Objects Grasped in Motion

The following study deals with motion optimization of robot arms having to transfer mobile objects grasped when moving. This approach is aimed at performing repetitive transfer tasks at a rapid rate without interrupting the dynamics of both the manipulator and the moving object. The junction location of the robot gripper with the object, together with grasp conditions, are partly defined by a set of local constraints. Thus, optimizing the robot motion in the approach phase of the transfer task leads to the statement of an optimal junction problem between the robot and the moving object. This optimal control problem is characterized by constrained final state and unknown traveling time. In such a case, Pontryagin"s maximum principle is a powerful mathematical tool for solving this optimization problem. Three simulated results of removing a mobile object on a conveyor belt are presented; the object is grasped in motion by a planar three-link manipulator.     

A neural network-based approach for an assembly cell control

In several robotics applications, the robot must interact with the workspace, and thus its motion is constrained by the task. In this case, pure position control will be ineffective since forces appearing during the contacts must also be controlled. However, simultaneous position and force control called hybrid control is then required. Moreover, the nonlinear plant dynamics, the complexity of the dynamic parameters determination and computation constraints makes more difficult the synthesis of control laws. In order to satisfy all these constraints, an effective hybrid force/position approach based on artificial neural networks for multi-inputs/multi-outputs systems is proposed. This approach realizes, simultaneously, an identification and control of systems, and it is implemented according to two phases: At first, a neural observer is trained off-line on the basis of the data acquired during contact motion, in order to realize a smooth transition from free to contact motion. Then, an online learning of the neural controller is implemented using neural observer parameters so that the closed-loop system maintains a good performance and compensates for uncertain/unknown dynamics of the robot and the environment. A typical example on which we shall focus is an assembly task. Experimental results on a C5 links parallel robot demonstrate that the robot's skill improves effectively and the force control performances are satisfactory, even if the dynamics of the robot and the environment change.     

Motion coordination for industrial robotic systems with redundant degrees of freedom

This work investigates how to distribute in an optimum fashion the desired movement of the end-effector of an industrial robot with respect to the workpiece, when there are redundant degrees of freedom, such as a positioning table. The desired motion is given as a series of acceleration functions in respective time intervals. The constraints of the optimisation are the available acceleration limit of axes, such as the table axes, the upper bounds to velocity and displacement of each axis and the avoidance of singular point areas of the robot, as defined by its manufacturer. The optimisation criterion is minimum total work for the motion. A genetic algorithm was used to solve the problem. The fitness function of the genetic algorithm calls a kinematics and dynamics simulation model of the robotic installation constructed in Matlab™, in order to compute the work consumed and to check possible violation of constraints. Examples of straight line and circular movement are given to prove the concept. Results are encouraging, yet demand on computing power is high.     

The VFO-Driven Motion Planning and Feedback Control in Polygonal Worlds for a Unicycle with Bounded Curvature of Motion

Integrated motion planning and control for the purposes of maneuvering mobile robots under state- and input constraints is a problem of vital practical importance in applications of mobile robots such as autonomous transportation. Those constraints arise naturally in practice due to specifics of robot mechanical construction and the presence of obstacles in motion environment. In contrast to approaches focusing on feedback control design under the assumption of given reference motion or motion planning with neglection of subsequent feedback motion execution, we adopt a controller-driven motion planning paradigm, which has recently gained attention of many researchers. It postulates design of motion planning algorithms dedicated to specific feedback control policies, which compute a sequence of feedback control subtasks instead of classically planned open-loop controls or parametric paths. In this spirit, we propose a motion planning algorithm driven by the VFO (Vector Field Orientation) control law for the waypoint-following task. Presented analysis of the VFO control law reveals its beneficial properties, which are subsequently utilized to solve a generally nonlinear and non-convex optimal motion planning problem by formulating it as a mixed-integer linear program (MILP). The solution proposed in this paper yields a waypoint sequence, which is designed for execution by application of the VFO control law to drive a robot to a prescribed final configuration under an input constraint imposed by bounded curvature of robot motion and state constraints resulting from a convex decomposition of task space. Satisfaction of these constraints is guaranteed analytically and exactly, i.e., without utilization of numerical approximations. Moreover, for a given discrete set of possible waypoint orientations, the proposed algorithm computes plans optimal w.r.t. given cost functional, which can be any convex linear combination of quantities such as robot path length, curvature of robot motion, distance to imposed state constraints, etc. Furthermore, the planning algorithm exploits the possibility of both forward or backward movement of the robot to allow maneuvering in demanding environments. Generated waypoint sequences are a compact representation of a motion plan, which can be immediately executed with the VFO controller without any additional post-processing. Validity of the proposed approach has been confirmed by simulation studies and experimental motion execution with a laboratory-scale mobile robot.     

Handling uncertainties of robot manipulators and active vision by constraint propagation

Joint errors are inevitable in robot manipulation. These uncertainties propagate to give rise to translational and orientational errors in the position and orientation of the robot end‐effector. The displacement of the active vision head mounted on the robot end‐effector produces distortion of the projected object on the image. Upon active visual inspection, the observed dimension of a mechanical part is given dimension by the measurement on the projected edge segment on the image. The difference between the observed dimension and the actual dimension is the displacement error in active vision. For different motion of the active vision head, the resulting displacement errors are different. Given the uncertainties of the robot manipulator's joint errors, constraint propagation can be employed to assign the motion of the active sensor in order to satisfy the tolerance of the displacement errors for inspection. In this article, we define the constraint consistency and network satisfaction in the constraint network for the problem of displacement errors in active vision. A constraint network is a network where the nodes represent variables, or constraints, and the arcs represent the relationships between the output variables and the input variables of the constraints. In the displacement errors problem, the tolerance of the displacement errors and the translational and orientational errors of robot manipulators have interval values while the sensor motion has real values. Constraint propagation is developed to propagate the tolerance of displacement errors in the hierarchical interval constraint network in order to find the feasible robot motion. © 2002 Wiley Periodicals, Inc.     

Stepping over obstacles with humanoid robots

The wide potential applications of humanoid robots require that the robots can walk in complex environments and overcome various obstacles. To this end, we address the problem of humanoid robots stepping over obstacles in this paper. We focus on two aspects, which are feasibility analysis and motion planning. The former determines whether a robot can step over a given obstacle, and the latter discusses how to step over, if feasible, by planning appropriate motions for the robot. We systematically examine both of these aspects. In the feasibility analysis, using an optimization technique, we cast the problem into global optimization models with nonlinear constraints, including collision-free and balance constraints. The solutions to the optimization models yield answers to the possibility of stepping over obstacles under some assumptions. The presented approach for feasibility provides not only a priori knowledge and a database to implement stepping over obstacles, but also a tool to evaluate and compare the mobility of humanoid robots. In motion planning, we present an algorithm to generate suitable trajectories of the feet and the waist of the robot using heuristic methodology, based on the results of the feasibility analysis. We decompose the body motion of the robot into two parts, corresponding to the lower body and upper body of the robot, to meet the collision-free and balance constraints. This novel planning method is adaptive to obstacle sizes, and is, hence, oriented to autonomous stepping over by humanoid robots guided by vision or other range finders. Its effectiveness is verified by simulations and experiments on our humanoid platform HRP-2.     

Dynamic Modeling and Analysis of a Robot Manipulator Intercepting and Capturing a Moving Object,with the Consideration of Structural Flexibility

In this paper we investigate the dynamics of robotic interception and capture of a moving object. This problem, i.e., the interception and capture of a moving object by a robot, is called dynamic mass capture. The effects of structural flexibility of the robot is taken into consideration. In terms of time, the analysis is divided into three phases: before capture (finite motion), at the vicinity of interception and capture (impulsive motion), and after capture (finite motion). Special attention is paid to the modeling of the second phase when the robot captures the target and it becomes part of the end effector, thus, the system's degrees of freedom suddenly change. To decribe this event, a novel approach is proposed. This is based on the use of a class of impulsive constraints, the so-called inert constraints. Jourdain's principle is employed to derive the dynamic equations for both finite and impulsive motions. Simulation results are presented for two examples: a single flexible link and a two-link manipulator capturing moving objects. In the example of the single link, the results are compared with the observations of an experiment, and good agreement is found between experimental and simulation results.     

An approach to software organization for control of industrial robots

This article describes a philosophy and practical application of software organization for control of industrial robots. In order to apply an industrial robot to a work cell as a component or device, not only is a language to command the robot motion necessary, powerful functions of the robot to realize a robot work cell with a hierarchical structure are also required. First, we discuss an outline of industrial robot control and select required functions. Second, we discuss software organizations and significant points to realize them. Finally, as a practical application we introduce a robot system using a personal computer that is widely available in Japan.