Reciprocally-rotating Velocity Obstacles

Modern multi-agent systems frequently use high-level planners to extract basic paths for agents, and then rely on local collision avoidance to ensure that the agents reach their destinations without colliding with one another or dynamic obstacles. One state-of-the-art local collision avoidance technique is Optimal Reciprocal Colli- sion Avoidance (ORCA). Despite being fast and efficient for circular-shaped agents, ORCA may deadlock when polygonal shapes are used. To address this shortcom- ing, we introduce Reciprocally-Rotating Velocity Obstacles (RRVO). RRVO extends ORCA by introducing a notion of rotation. This extension permits more realistic motion than ORCA for polygonally-shaped agents and does not suffer from as much deadlock. In this thesis, we present the theory of RRVO and show empirically that it does not suffer from the deadlock issue ORCA has, that it permits agents to reach goals faster, and that it has a comparable collision rate at the cost of some performance overhead

Reciprocally-rotating Velocity Obstacles

Modern multi-agent systems frequently use high-level planners to extract basic paths for agents, and then rely on local collision avoidance to ensure that the agents reach their destinations without colliding with one another or dynamic obstacles. One state-of-the-art local collision avoidance technique is Optimal Reciprocal Colli- sion Avoidance (ORCA). Despite being fast and efficient for circular-shaped agents, ORCA may deadlock when polygonal shapes are used. To address this shortcom- ing, we introduce Reciprocally-Rotating Velocity Obstacles (RRVO). RRVO extends ORCA by introducing a notion of rotation. This extension permits more realistic motion than ORCA for polygonally-shaped agents and does not suffer from as much deadlock. In this thesis, we present the theory of RRVO and show empirically that it does not suffer from the deadlock issue ORCA has, that it permits agents to reach goals faster, and that it has a comparable collision rate at the cost of some performance overhead

Doctor of Philosophy

dissertationThis dissertation solves the collision avoidance problem for single- and multi-robot systems where dynamic effects are significant. In many robotic systems (e.g., highly maneuverable and agile unmanned aerial vehicles) the dynamics cannot be ignored and collision avoidance schemes based on kinematic models can result in collisions or provide limited performance, especially at high operating speeds. Herein, real-time, model-based collision avoidance algorithms that explicitly consider the robots' dynamics and perform real-time input changes to alter the trajectory and steer the robot away from potential collisions are developed, implemented, and verified in simulations and physical experiments. Such algorithms are critical in applications where a high degree of autonomy and performance are needed, for example in robot-assisted first response where aerial and/or mobile ground robots are required to maneuver quickly through cluttered and dangerous environments in search of survivors. Firstly, the research extends reciprocal collision avoidance to robots with dynamics by unifying previous approaches to reciprocal collision avoidance under a single, generalized representation using control obstacles. In fact, it is shown how velocity obstacles, acceleration velocity obstacles, continuous control obstacles, and linear quadratic regulator (LQR)-obstacles are special instances of the generalized framework. Furthermore, an extension of control obstacles to general reciprocal collision avoidance for nonlinear, nonhomogeneous systems where the robots may have different state spaces and different nonlinear equations of motion from one another is described. Both simulations and physical experiments are provided for a combination of differential-drive, differential-drive with a trailer, and car-like robots to demonstrate that the approach is capable of letting a nonhomogeneous group of robots with nonlinear equations of motion safely avoid collisions at real-time computation rates. Secondly, the research develops a stochastic collision avoidance algorithm for a tele-operated unmanned aerial vehicle (UAV) that considers uncertainty in the robot's dynamics model and the obstacles' position as measured from sensors. The model-based automatic collision avoidance algorithm is implemented on a custom-designed quadcopter UAV system with on-board computation and the sensor data are processed using a split-and-merge segmentation algorithm and an approximate Minkowski difference. Flight tests are conducted to validate the algorithm's capabilities for providing tele-operated collision-free operation. Finally, a set of human subject studies are performed to quantitatively compare the performance between the model-based algorithm, the basic risk field algorithm (a variant on potential field), and full manual control. The results show that the model-based algorithm performs significantly better than manual control in both the number of collisions and the UAV's average speed, both of which are extremely vital, for example, for UAV-assisted search and rescue applications. Compared to the potential-field-based algorithm, the model-based algorithm allowed the pilot to operate the UAV with higher average speeds

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

Game-Theoretic Safety Assurance for Human-Centered Robotic Systems

In order for autonomous systems like robots, drones, and self-driving cars to be reliably introduced into our society, they must have the ability to actively account for safety during their operation. While safety analysis has traditionally been conducted offline for controlled environments like cages on factory floors, the much higher complexity of open, human-populated spaces like our homes, cities, and roads makes it unviable to rely on common design-time assumptions, since these may be violated once the system is deployed. Instead, the next generation of robotic technologies will need to reason about safety online, constructing high-confidence assurances informed by ongoing observations of the environment and other agents, in spite of models of them being necessarily fallible.This dissertation aims to lay down the necessary foundations to enable autonomous systems to ensure their own safety in complex, changing, and uncertain environments, by explicitly reasoning about the gap between their models and the real world. It first introduces a suite of novel robust optimal control formulations and algorithmic tools that permit tractable safety analysis in time-varying, multi-agent systems, as well as safe real-time robotic navigation in partially unknown environments; these approaches are demonstrated on large-scale unmanned air traffic simulation and physical quadrotor platforms. After this, it draws on Bayesian machine learning methods to translate model-based guarantees into high-confidence assurances, monitoring the reliability of predictive models in light of changing evidence about the physical system and surrounding agents. This principle is first applied to a general safety framework allowing the use of learning-based control (e.g. reinforcement learning) for safety-critical robotic systems such as drones, and then combined with insights from cognitive science and dynamic game theory to enable safe human-centered navigation and interaction; these techniques are showcased on physical quadrotors—flying in unmodeled wind and among human pedestrians—and simulated highway driving. The dissertation ends with a discussion of challenges and opportunities ahead, including the bridging of safety analysis and reinforcement learning and the need to ``close the loop'' around learning and adaptation in order to deploy increasingly advanced autonomous systems with confidence

Interactive Motion Planning for Multi-agent Systems with Physics-based and Behavior Constraints

Man-made entities and humans rely on movement as an essential form of interaction with the world. Whether it is an autonomous vehicle navigating crowded roadways or a simulated pedestrian traversing a virtual world, each entity must compute safe, effective paths to achieve their goals. In addition, these entities, termed agents, are subject to unique physical and behavioral limitations within their environment. For example, vehicles have a finite physical turning radius and must obey behavioral constraints such as traffic signals and rules of the road. Effective motion planning algorithms for diverse agents must account for these physics-based and behavior constraints. In this dissertation, we present novel motion planning algorithms that account for constraints which physically limit the agent and impose behavioral limitations on the virtual agents. We describe representational approaches to capture specific physical constraints on the various agents and propose abstractions to model behavior constraints affecting them. We then describe algorithms to plan motions for agents who are subject to the modeled constraints. First, we describe a biomechanically accurate elliptical representation for virtual pedestrians; we also describe human-like movement constraints corresponding to shoulder-turning and side-stepping in dense environments. We detail a novel motion planning algorithm extending velocity obstacles to generate collisionfree paths for hundreds of elliptical agents at interactive rates. Next, we describe an algorithm to encode dynamics and traffic-like behavior constraints for autonomous vehicles in urban and highway environments. We describe a motion planning algorithm to generate safe, high-speed avoidance maneuvers using a novel optimization function and modified control obstacle formulation, and we also present a simulation framework to evaluate driving strategies. Next, we present an approach to incorporate high-level reasoning to model the motions and behaviors of virtual agents in terms of verbal interactions with other agents or avatars. Our approach leverages natural-language interaction to reduce uncertainty and generate effective plans. Finally, we describe an application of our techniques to simulate pedestrian behaviors for gathering simulated data about loading, unloading, and evacuating an aircraft.Doctor of Philosoph