타원 로봇의 충돌 회피를 위한 속도 기반의 지역 경로 계획 방법

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2017. 2. 이범희.Collision-free motion planning has been hierarchically decomposed into two parts: global and local planners. While the former generates the shortest path to the goal from global environmental information, the latter modifies the path from the global one by considering unexpected dynamic obstacles and motion constraints of mobile robots. In the local navigation problem, robots and obstacles have been approximated by simple geometric objects in order to decrease the computation time. They have been generally enclosed by circles due to its simplicity in collision detection. However, this approximation becomes overly conservative if the objects are elongated, which leads the robots to travel longer paths than necessary to avoid collisions. This dissertation presents a velocity-based approach to address the local navigation problem of anisotropic mobile robots bounded by ellipses. Compared with the other geometries, Löwner ellipse, the minimum area bounding ellipse, provides more compact representation for robots and obstacles in a 2D plane, but the collision detection between them is more complicated. Hence, it is first investigated under what conditions a collision between two ellipses occurs. To this end, the configuration space framework and an algebraic approach are introduced. In the former method, it is found that an elliptic robot can be regarded as a circular robot with radius equal to its minor radius by adequately controlling its orientation. In the latter method, the interior-disjoint condition between two ellipses is characterized by four inequalities. Next, a velocity-based approach is suggested on the basis of the collision detection so that an elliptic robot moves to its goal without collisions with obstacles. The proposed algorithm is decomposed into two phases: linear and angular motion planning. In the first phase, the ellipse-based velocity obstacle (EBVO) is defined as the set of linear velocities of a robot that would cause a collision within a finite time horizon. Furthermore, strategies for determining a new linear velocity with the EBVO are explained. In the second phase, the angular velocity is selected with which the robot can circumvent the obstacle blocking the path to the goal with the minimum deviation. Finally, the obstacle avoidance method was extended for multi-robot collision avoidance on the basis on the concept of reciprocity. The concept of hybrid reciprocal velocity obstacles is adopted in the part of linear motion planning, and the collision-free reciprocal rotation angles are calculated in the part of angular motion planning on the assumption that if one robot rotates, then the other robot may rotate equally or equally opposite. The proposed algorithm was validated in simulations for various scenarios in terms of travel time and distance. It was shown that it outperformed the methods that enclosed robots and obstacles by circles, by ellipses without rotation, and by polygons with rotation. In addition, it was shown that the computation time of the proposed method was much smaller than the sampling time, which means that it is fast enough for real-time applications.Chapter 1 Introduction 1 1.1 Background of the Problem 1 1.2 Statement of the Problem 5 1.3 Contributions 10 1.4 Organization 11 Chapter 2 Literature Review 13 2.1 Bounding Ellipsoid 13 2.2 Collision Detection between Ellipsoids 15 2.3 Velocity-based Local Navigation 18 Chapter 3 Collision Detection 23 3.1 Introduction 23 3.2 Problem Formulation 25 3.3 Configuration Space Obstacle 25 3.4 Algebraic Condition for the Interior-disjoint of Two Ellipses 34 3.5 Summary 50 Chapter 4 Obstacle Avoidance 51 4.1 Introduction 51 4.2 Problem Formulation and Approach 53 4.3 Preliminaries: Properties of C-obstacles for an Elliptic Robot 56 4.3.1 Tangent lines to C-obstacle 56 4.3.2 Closest point on the outline of C-obstacle 63 4.4 Ellipse-based Velocity Obstacles 65 4.5 Selection of Collision-free Linear Velocity 71 4.5.1 Conservative Approximation of the EBVOs 72 4.5.2 New Linear Velocity Selection with Multiple Obstacles 77 4.6 Collision-free Rotation Angles 81 4.6.1 The Shortest Time-to-contact 81 4.6.2 Collision-free Interval of the Rotation Angles 82 4.7 Selection of Collision-free Angular Velocity 89 4.7.1 Preferred Angular Velocities 89 4.7.2 New Angular Velocity Selection 91 4.8 Summary 93 Chapter 5 Multi-Robot Collision Avoidance 95 5.1 Introduction 95 5.2 Problem Formulation 97 5.3 Ellipse-based Reciprocal Velocity Obstacles 98 5.4 Collision-free Reciprocal Rotation Angles 103 5.4.1 Candidates of the First Contact Rotation Angle 108 5.4.2 Updating the Candidates Sets 116 5.4.3 Calculation of Collision-free Reciprocal Rotation Angles 117 5.4.4 An Example 118 5.5 Summary 123 Chapter 6 Implementation and Simulations 125 6.1 Implementation Setups 125 6.2 Obstacle Avoidance 126 6.2.1 Line scenario of a robot and an obstacle 127 6.2.2 Multiple moving obstacles scenario 135 6.2.3 Pedestrians avoidance scenario 144 6.3 Multi-Robot Collision Avoidance 148 6.3.1 Chicken scenario 149 6.3.2 Circle scenario 155 Chapter 7 Conclusion 165 Bibliography 171 초록 191Docto

A Hamilton-Jacobi Formulation for Time-Optimal Paths of Rectangular Nonholonomic Vehicles

We address the problem of optimal path planning for a simple nonholonomic vehicle in the presence of obstacles. Most current approaches are either split hierarchically into global path planning and local collision avoidance, or neglect some of the ambient geometry by assuming the car is a point mass. We present a Hamilton-Jacobi formulation of the problem that resolves time-optimal paths and considers the geometry of the vehicle

Wheeled Mobile Robots: State of the Art Overview and Kinematic Comparison Among Three Omnidirectional Locomotion Strategies

In the last decades, mobile robotics has become a very interesting research topic in the feld of robotics, mainly because of population ageing and the recent pandemic emergency caused by Covid-19. Against this context, the paper presents an overview on wheeled mobile robot (WMR), which have a central role in nowadays scenario. In particular, the paper describes the most commonly adopted locomotion strategies, perception systems, control architectures and navigation approaches. After having analyzed the state of the art, this paper focuses on the kinematics of three omnidirectional platforms: a four mecanum wheels robot (4WD), a three omni wheel platform (3WD) and a two swerve-drive system (2SWD). Through a dimensionless approach, these three platforms are compared to understand how their mobility is afected by the wheel speed limitations that are present in every practical application. This original comparison has not been already presented by the literature and it can be used to improve our understanding of the kinematics of these mobile robots and to guide the selection of the most appropriate locomotion system according to the specifc application

Repeatable Motion Planning for Redundant Robots over Cyclic Tasks

We consider the problem of repeatable motion planning for redundant robotic systems performing cyclic tasks in the presence of obstacles. For this open problem, we present a control-based randomized planner, which produces closed collision-free paths in configuration space and guarantees continuous satisfaction of the task constraints. The proposed algorithm, which relies on bidirectional search and loop closure in the task-constrained configuration space, is shown to be probabilistically complete. A modified version of the planner is also devised for the case in which configuration-space paths are required to be smooth. Finally, we present planning results in various scenarios involving both free-flying and nonholonomic robots to show the effectiveness of the proposed method

Formation control of multiple mobile robots using parametric and implicit representations

Coordination of autonomous robot groups is an active research area and much recent work has focused on modeling and control issues related to coordination. Robot groups can coordinate in many different ways. Some robot groups may execute coordination in which group members move in a scattered manner like the bees of a beehive or coordination of the group may require a more strict formation like the swallows. The shape formation is very important for the coordination of autonomous mobile robot groups because it increases the capability of a robot group by increasing the competence and the security of the group. The shape formation is applicable in many tasks like formation flight, flocking and schooling, transportation systems, searchand- rescue operations, competitive games, reconnaissance and surveillance. This thesis develops a flexible shape formation control method for autonomous mobile robots. There are different approaches in the literature for shape formation of mobile robots. Proposed method is different from these existing approaches by being applicable to complex formation curves as well as different number of robots and heterogeneous groups. It consists of two phases. In the first phase, shape formation is controlled by using potential fields generated from implicit polynomial representations and in the second phase, the control for keeping the desired shape is designed using elliptical Fourier descriptors. In this shape formation method, coordination between the robots is modeled using virtual linear springs between each robot and its nearest two neighbors. The success of the proposed method is shown through simulations on groups of different numbers of point-particle robots. Proposed method is then extended to non-holonomic mobile robots by using the desired positions in point particle model as references for the non-holonomic robots. The method is also implemented with real non-holonomic robots with a bird-eye-view camera

Distance computation between non-holonomic motions with constant accelerations

A method for computing the distance between two moving robots or between a mobile robot and a dynamic obstacle with linear or arc-like motions and with constant accelerations is presented in this paper. This distance is obtained without stepping or discretizing the motions of the robots or obstacles. The robots and obstacles are modelled by convex hulls. This technique obtains the future instant in time when two moving objects will be at their minimum translational distance - i.e., at their minimum separation or maximum penetration (if they will collide). This distance and the future instant in time are computed in parallel. This method is intended to be run each time new information from the world is received and, consequently, it can be used for generating collision-free trajectories for non-holonomic mobile robots.This work was partially funded by the Spanish government CICYT projects: DPI2010-20814-C02-02, and DPI2011-28507-C02-01.Bernabeu Soler, EJ.; Valera Fernández, Á.; Gómez Moreno, J. (2013). Distance computation between non-holonomic motions with constant accelerations. International Journal of Advanced Robotic Systems. 10:1-15. doi:10.5772/56760S11510Urmson, C., Anhalt, J., Bagnell, D., Baker, C., Bittner, R., Clark, M. N., … Ferguson, D. (2008). Autonomous driving in urban environments: Boss and the Urban Challenge. Journal of Field Robotics, 25(8), 425-466. doi:10.1002/rob.20255Redon, S., Kheddar, A., & Coquillart, S. (2002). Fast Continuous Collision Detection between Rigid Bodies. Computer Graphics Forum, 21(3), 279-287. doi:10.1111/1467-8659.t01-1-00587Canny, J. (1986). Collision Detection for Moving Polyhedra. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-8(2), 200-209. doi:10.1109/tpami.1986.4767773Buss, S. R. (2005). Collision detection with relative screw motion. The Visual Computer, 21(1-2), 41-58. doi:10.1007/s00371-004-0269-8Fiorini, P., & Shiller, Z. (1998). Motion Planning in Dynamic Environments Using Velocity Obstacles. The International Journal of Robotics Research, 17(7), 760-772. doi:10.1177/027836499801700706Gilbert, E. G., Johnson, D. W., & Keerthi, S. S. (1988). A fast procedure for computing the distance between complex objects in three-dimensional space. IEEE Journal on Robotics and Automation, 4(2), 193-203. doi:10.1109/56.2083Bernabeu, E. J., & Tornero, J. (2002). Hough transform for distance computation and collision avoidance. IEEE Transactions on Robotics and Automation, 18(3), 393-398. doi:10.1109/tra.2002.1019476Simon, D. (2006). Optimal State Estimation. doi:10.1002/047004534

Avoiding local minima in the potential field method using input-to-state stability

International audienceSupported by a novel field definition and recent control theory results, a new method to avoid local minima is proposed. It is formally shown that the system has an attracting equilibrium at the target point, repelling equilibriums in the obstacles centers and saddle points on the borders. Those unstable equilibriums are avoided capitalizing on the established Input-to-State Stability (ISS) property of this multistable system. The proposed modification of the PF method is shown to be effective by simulation for a two variables integrator and then applied to an unicycle-like wheeled mobile robots which is subject to additive input disturbances

Design and Development of an Integrated Mobile Robot System for Use in Simple Formations

In recent years, formation control of autonomous unmanned vehicles has become an active area of research with its many broad applications in areas such as transportation and surveillance. The work presented in this thesis involves the design and implementation of small unmanned ground vehicles to be used in leader-follower formations. This mechatronics project involves breadth in areas of mechanical, electrical, and computer engineering design. A vehicle with a unicycle-type drive mechanism is designed in 3D CAD software and manufactured using 3D printing capabilities. The vehicle is then modeled using the unicycle kinematic equations of motion and simulated in MATLAB/Simulink. Simple motion tasks are then performed onboard the vehicle utilizing the vehicle model via software, and leader-follower formations are implemented with multiple vehicles

Nonlinear Model Predictive Path Following Controller with Obstacle Avoidance

In the control systems community, path-following refers to the problem of tracking an output reference curve. This work presents a novel model predictive path-following control formulation for nonlinear systems with constraints, extended with an obstacle avoidance strategy. The method proposed in this work simultaneously provides an optimizing solution for both, path-following and obstacle avoidance tasks in a single optimization problem, using Nonlinear Model Predictive Control (NMPC). The main idea consists in extending the existing NMPC controllers by the introduction of an additional auxiliary trajectory that maintains the feasibility of the successive optimization problems even when the reference curve is unfeasible, possibly discontinuous, relaxing assumptions required in previous works. The obstacle avoidance is fulfilled by introducing additional terms in the value functional, rather than imposing state space constraints, with the aim of maintaining the convexity of the state and output spaces. Simulations results considering an autonomous vehicle subject to input and state constraints are carried out to illustrate the performance of the proposed control strategy.Fil: Sánchez, Ignacio Julián Rodolfo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: D'jorge, Agustina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Raffo, Guilherme V.. Universidade Federal de Minas Gerais; BrasilFil: González, Alejandro Hernán. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Ferramosca, Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin