상대적 안전비행영역과 상대적 번스타인 다항식을 이용한 다수 쿼드로터의 경로 계획

학위논문 (석사) -- 서울대학교 대학원 : 공과대학 기계항공공학부, 2020. 8. 김현진.Multi-agent systems consisting of unmanned aerial vehicles (UAVs) are receiving attention from many industrial domains due to their mobility, and applicability. To safely operate these multiagent systems, path planning algorithm that can generate safe, dynamically feasible trajectory is required. However, existing multi-agent trajectory planning methods may fail to generate multiagent trajectory in obstacle-dense environment due to deadlock or optimization failure caused by infeasible collision constraints. In this paper, we presents a new e client algorithm which guarantees a solution for a class of multi-agent trajectory planning problems in obstacle-dense environments. Our algorithm combines the advantages of both grid-based and optimization-based approaches, and generates safe, dynamically feasible trajectories without su ering from an erroneous optimization setup such as imposing infeasible collision constraints. We adopt a sequential optimization method with dummy agents to improve the scalability of the algorithm, and utilize the convex hull property of Bernstein polynomial to replace non-convex collision avoidance constraints to convex ones. We validate the proposed algorithm through the comparison with our previous work and SCP-based method. The proposed method reduces more than 50% of the objective cost compared to our previous work, and reduces more than 75% of the computation time compared to SCP-based method. Furthermore, the proposed method can compute the trajectory for 64 agents on average 6.36 seconds with Intel Core i7-7700 @ 3.60GHz CPU and 16G RAM.무인비행체(UAV)로 구성된 다중 에이전트 시스템은 높은 기동성 및 응용 가능성으로 많은 산업 분야에서 관심을 받고 있다. 이러한 다중 에이전트 시스템을 안전하게 운용하려면 안전하고 동적으로 실현 가능 경로를 생성할 수 있는 경로 계획 알고리즘이 필요하다. 그러나 기존의 다중 에이전트 경로 계획 방법은 장애물 환경에서 교착 상태나 부적절한 충돌 회피 조건으로 인한 최적화 실패가 일어날 수 있다는 한계가 있다. 본 논문에서는 장애물 환경에서 해의 존재를 보장하도록 다중 에이전트 경로 계획 문제를 변환한 뒤 이를 효율적으로 풀어낼 수 있는 새로운 경로 계획 알고리즘을 제시한다. 이 알고리즘은 그리드 기반 접근법과 최적화 기반 접근법의 장점을 모두 가지도록 설계되었으며, 불가능한 충돌 구속조건을 부과하지 않고 안전하고 동적으로 실현 가능한 궤적을 생성할 수 있다. 이 알고리즘은 더미 에이전트(dummy agents)을 이용한 순차 최적화 방법을 사용하여 알고리즘의 확장성(scalability)을 높였으며, 번스타인(Bernstein) 다항식의 볼록 껍질(convex hull) 성질을 활용하여 볼록하지 않은 충돌 회피 제약 조건을 볼록화하였다. 제안된 알고리즘의 성능은 선행 연구와 SCP 기반 방법과의 비교를 통해 검증되었다. 제안된 방법은 선행 연구에 비해 목표 비용의 50% 이상 절감하였으며, SCP 기반 방법에 비해 계산 시간의 75% 이상 감소하였다. 또한 제안된 방법은 인텔 코어 i7-7700 @ 3.60GHz CPU 및 16G RAM 환경에서 64개 에이전트의 궤적을 계산하는데 평균 6.36초가 소요된다.1 Introduction 1 1.1 Literature review 2 1.2 Thesis contribution 3 1.3 Thesis outline 3 2 Bernstein polynomial 4 2.1 Definition 4 2.2 Properties 5 2.2.1 Convex hull property 5 2.2.2 Endpoint interpolation property 5 2.2.3 Arithmetic operations and derivatives 6 3 Multi-agent trajectory optimization 7 3.1 Problem formulation 7 3.1.1 Assumption 7 3.1.2 Trajectory Representation 8 3.1.3 Objective function 9 3.1.4 Convex constraints 9 3.1.5 Non-convex collision avoidance constraints 10 3.2 Collision constraints construction 11 3.2.1 Initial trajectory planning 12 3.2.2 Safe flight corridor 14 3.2.3 Relative safe flight corridor 16 3.3 Trajectory optimization 18 4 Sequential optimization with dummy agents 20 5 Experimental results 24 5.1 Comparison with the previous work 24 5.1.1 Success rate 25 5.1.2 Solution quality 26 5.1.3 Scalability analysis 26 5.2 Comparison with SCP-based method 27 5.3 Flight test 29 6 Conclusion 31Maste

Survey on Motion Planning for Multirotor Aerial Vehicles in Plan-based Control Paradigm

In general, optimal motion planning can be performed both locally and globally. In such a planning, the choice in favour of either local or global planning technique mainly depends on whether the environmental conditions are dynamic or static. Hence, the most adequate choice is to use local planning or local planning alongside global planning. When designing optimal motion planning both local and global, the key metrics to bear in mind are execution time, asymptotic optimality, and quick reaction to dynamic obstacles. Such planning approaches can address the aforesaid target metrics more efficiently compared to other approaches such as path planning followed by smoothing. Thus, the foremost objective of this study is to analyse related literature in order to understand how the motion planning, especially trajectory planning, problem is formulated, when being applied for generating optimal trajectories in real-time for Multirotor Aerial Vehicles, impacts the listed metrics. As a result of the research, the trajectory planning problem was broken down into a set of subproblems, and the lists of methods for addressing each of the problems were identified and described in detail. Subsequently, the most prominent results from 2010 to 2022 were summarized and presented in the form of a timeline

AMSwarmX: Safe Swarm Coordination in CompleX Environments via Implicit Non-Convex Decomposition of the Obstacle-Free Space

Quadrotor motion planning in complex environments leverage the concept of safe flight corridor (SFC) to facilitate static obstacle avoidance. Typically, SFCs are constructed through convex decomposition of the environment's free space into cuboids, convex polyhedra, or spheres. However, when dealing with a quadrotor swarm, such SFCs can be overly conservative, substantially limiting the available free space for quadrotors to coordinate. This paper presents an Alternating Minimization-based approach that does not require building a conservative free-space approximation. Instead, both static and dynamic collision constraints are treated in a unified manner. Dynamic collisions are handled based on shared position trajectories of the quadrotors. Static obstacle avoidance is coupled with distance queries from the Octomap, providing an implicit non-convex decomposition of free space. As a result, our approach is scalable to arbitrary complex environments. Through extensive comparisons in simulation, we demonstrate a $60\%$ improvement in success rate, an average $1.8\times$ reduction in mission completion time, and an average $23\times$ reduction in per-agent computation time compared to SFC-based approaches. We also experimentally validated our approach using a Crazyflie quadrotor swarm of up to 12 quadrotors in obstacle-rich environments. The code, supplementary materials, and videos are released for reference.Comment: Submitted to ICRA 202

Accelerating Trajectory Generation for Quadrotors Using Transformers

In this work, we address the problem of computation time for trajectory generation in quadrotors. Most trajectory generation methods for waypoint navigation of quadrotors, for example minimum snap/jerk and minimum-time, are structured as bi-level optimizations. The first level involves allocating time across all input waypoints and the second step is to minimize the snap/jerk of the trajectory under that time allocation. Such an optimization can be computationally expensive to solve. In our approach we treat trajectory generation as a supervised learning problem between a sequential set of inputs and outputs. We adapt a transformer model to learn the optimal time allocations for a given set of input waypoints, thus making it into a single step optimization. We demonstrate the performance of the transformer model by training it to predict the time allocations for a minimum snap trajectory generator. The trained transformer model is able to predict accurate time allocations with fewer data samples and smaller model size, compared to a feedforward network (FFN), demonstrating that it is able to model the sequential nature of the waypoint navigation problem.Comment: Accepted at L4DC 202