scholarly journals Tracking an omnidirectional evader with a differential drive robot at a bounded variable distance

2014 ◽  
Vol 24 (2) ◽  
pp. 371-385 ◽  
Author(s):  
Ubaldo Ruiz ◽  
Jose Luis Marroquin ◽  
Rafael Murrieta-Cid
Keyword(s):  
Euclidean Plane ◽  
Nonholonomic Constraints ◽  
Motion Direction ◽  
Specific Strategy ◽  
Dynamic Constraints ◽  
Differential Drive ◽  
Pursuit Evasion ◽  
Variable Distance ◽  
Evasion Problem ◽  
Differential Drive Robot

Abstract In this paper, we address the pursuit-evasion problem of tracking an Omnidirectional Agent (OA) at a bounded variable distance using a Differential Drive Robot (DDR), in an Euclidean plane without obstacles. We assume that both players have bounded speeds, and that the DDR is faster than the evader, but due to its nonholonomic constraints it cannot change its motion direction instantaneously. Only a purely kinematic problem is considered, and any effect due to dynamic constraints (e.g., acceleration bounds) is neglected. We provide a criterion for partitioning the configuration space of the problem into two regions, so that in one of them the DDR is able to control the system, in the sense that, by applying a specific strategy (also provided), the DDR can achieve any inter-agent distance (within an error bound), regardless of the actions taken by the OA. Particular applications of these results include the capture of the OA by the DDR and maintaining surveillance of the OA at a bounded variable distance.

Approximation of Capture Sets in Visibility-Based Target-Tracking Games for Non-Holonomic Players

2017 ◽  
Author(s):  
Rui Zou ◽  
Sourabh Bhattacharya
Keyword(s):  
Target Tracking ◽  
Computing Time ◽  
Line Of Sight ◽  
Differential Drive ◽  
Pursuit Evasion ◽  
Optimal Paths ◽  
Evasion Game ◽  
Time Optimal ◽  
Differential Drive Robot ◽  
Arbitrary Line

In this work, we analyze approximations of capture sets [1] for a visibility based pursuit-evasion game. In contrast to the capture problem, the pursuer tries to maintain a line-of-sight with the evader in free space in our problem. We extend the concept of U set initially proposed in [2] for holonomic players to the scenario in which the pursuer is holonomic. The problem of computing the U set is reduced to that of computing time-optimal paths for the non-holonomic vehicles to an arbitrary line. We characterize the primitives for time-optimal paths for the Dubin’s vehicle, Reed-shepps car and a Differential Drive robot. Based on these primitives, we construct the optimal paths and provide an algorithm to compute the U set.

An Autonomously Guided Differential Drive Robot Base Using Asus® Xtion Pro Live

2020 ◽  
Author(s):  
S. I. A. P. Diddeniya ◽  
J. Liyanage ◽  
W. K. I. L. Wanniarachchi ◽  
C. Premachandra ◽  
H. N. Gunasinghe
Keyword(s):  
Differential Drive ◽  
Differential Drive Robot

scholarly journals A VISIBILITY-BASED PURSUIT-EVASION PROBLEM

1999 ◽  
Vol 09 (04n05) ◽  
pp. 471-493 ◽  
Author(s):  
LEONIDAS J. GUIBAS ◽  
JEAN-CLAUDE LATOMBE ◽  
STEVEN M. LAVALLE ◽  
DAVID LIN ◽  
RAJEEV MOTWANI
Keyword(s):  
Finite Graph ◽  
Initial Position ◽  
Moving Target ◽  
Multiply Connected ◽  
Pursuit Evasion ◽  
Minimum Number ◽  
Evasion Problem ◽  
Free Spaces ◽  
Simply Connected ◽  
Motion Strategy

This paper addresses the problem of planning the motion of one or more pursuers in a polygonal environment to eventually "see" an evader that is unpredictable, has unknown initial position, and is capable of moving arbitrarily fast. This problem was first introduced by Suzuki and Yamashita. Our study of this problem is motivated in part by robotics applications, such as surveillance with a mobile robot equipped with a camera that must find a moving target in a cluttered workspace. A few bounds are introduced, and a complete algorithm is presented for computing a successful motion strategy for a single pursuer. For simply-connected free spaces, it is shown that the minimum number of pursuers required is Θ( lg  n). For multiply-connected free spaces, the bound is [Formula: see text] pursuers for a polygon that has n edges and h holes. A set of problems that are solvable by a single pursuer and require a linear number of recontaminations is shown. The complete algorithm searches a finite graph that is constructed on the basis of critical information changes. It has been implemented and computed examples are shown.

Minimum Energy Control of a Unicycle Model Robot

2021 ◽  
Author(s):  
Youngjin Kim ◽  
Tarunraj Singh
Keyword(s):  
Optimal Control ◽  
Minimum Energy ◽  
Kinematic Model ◽  
Elliptic Functions ◽  
Terminal Point ◽  
Jacobi Elliptic Functions ◽  
Differential Drive ◽  
Terminal Constraints ◽  
Differential Drive Robot ◽  
Point To Point

Abstract Point-to-point path planning for a kinematic model of a differential-drive wheeled mobile robot (WMR) with the goal of minimizing input energy is the focus of this work. An optimal control problem is formulated to determine the necessary conditions for optimality and the resulting two point boundary value problem is solved in closed form using Jacobi elliptic functions. The resulting nonlinear programming problem is solved for two variables and the results are compared to the traditional shooting method to illustrate that the Jacobi elliptic functions parameterize the exact profile of the optimal trajectory. A set of terminal constraints which lie on a circle in the first quadrant are used to generate a set of optimal solutions. It is noted that for maneuvers where the angle of the vector connecting the initial and terminal point is greater than a threshold, which is a function of the radius of the terminal constraint circle, the robot initially moves into the third quadrant before terminating in the first quadrant. The minimum energy solution is compared to two other optimal control formulations: (1) an extension of the Dubins vehicle model where the constant linear velocity of the robot is optimized for and (2) a simple turn and move solution, both of whose optimal paths lie entirely in the first quadrant. Experimental results are used to validate the optimal trajectories of the differential-drive robot.

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