To be applicable to real world scenarios trajectory planning schemes for mobile autonomous systems must be able to efficiently deal with obstacles in the area of operation. In the context of optimization based trajectory planning and control a number of different approaches to formulate collision avoidance constraints can be found in the literature. Here the contribution of the present work is twofold. First, the most popular methods to represent obstacles are summarized, namely the simple ellipsoidal representation, the constructive solid geometry (CSG) method as well as a direct and an indirect implementation of a signed distance based approach. The formulations are characterized with respect to the impact on the complexity of the optimization problem, as well as the ability to meet different problem requirements. Second, this work presents a novel variant of the CSG method to describe collision avoidance constraints. It is highly efficient due to a very low number of nonlinear inequality constraints required for a given number of obstacles and sample points and in contrast to the original CSG formulation allows to consider the controlled system's shape. The good performance of the proposed formulation is demonstrated by a comparison to the previously mentioned alternatives. To this end optimal trajectory planning for marine surface vessels formulated as a nonlinear programming problem is used as a benchmark example where the scenario is designed based on the maritime test field in Kiel, Germany.
Singularity Avoidance with Application to Online Trajectory Optimization for Serial Manipulators
Automation and Control Institute (ACIN), TU Wien（维也纳工业大学自动化与控制研究所（ACIN））；Center for Vision, Automation and Control, AIT Austrian Institute of Technology（奥地利技术研究所（AIT）视觉、自动化与控制中心）
Path Planning and Obstacle Avoidance Scheme for Autonomous Robots using Raspberry Pi
University of Moratuwa（莫拉图瓦大学）
随着机器人平台的逐步发展，使手动过程自动化，路径规划已成为一个关键领域，无论是否了解室内和室外环境。算法可以是智能的或预结构化的，并且应该最有效地到达目的地。在这一领域的主要挑战是找到一条路径，这是免费的静态障碍以及动态障碍。在本文中，提出了一种方法与机器人平台的实施细节，以覆盖关键点，并在动态环境中到达原来的关键点。主要的计算发生在Raspberry Pi B+模块中，指南针，车轮编码器和超声波传感器用于实现机器人到相关关键点的定位。
A Circle Grid-based Approach for Obstacle Avoidance Motion Planning of Unmanned Surface Vehicles
Intelligent Transportation System Research Center, Wuhan University of Technology（武汉理工大学智能交通系统研究中心）；National Engineering Research Center for Water Transport Safety（国家水运安全工程技术研究中心）；School of Navigation, Wuhan University of Technology（武汉理工大学航运学院）
Flatness-based trajectory planning for 3D overhead cranes with friction compensation and collision avoidance
Departamento de Informatica e Ingenieria de Sistemas (DIIS)（信息与系统工程系（DIIS））；Instituto de Investigacion en Ingenieria de Aragon (I3A)（阿列尼亚工程研究所（I3A））；Universidad de Zaragoza（萨拉戈塔大学）
Self-Supervised Learning-Based Path Planning and Obstacle Avoidance Using PPO and B-Splines in Unknown Environments
Department of Mechanical Engineering Univerisity of New Hampshire Durham, New Hampshire, USA（机械工程系 新罕布什尔大学 布鲁克林, 新罕布什尔州, 美国）；Department of Mechanical Engineering The Citadel School of Engineering Charleston County, South Carolina, USA（机械工程系 蒂 Citadel 工程学院 查尔斯顿县, 南卡罗来纳州, 美国）
Graph-based Path Planning with Dynamic Obstacle Avoidance for Autonomous Parking
Honda Research Institute (HRI)（本田研究院）；GRASP Lab（GRASP实验室）；University of Pennsylvania（宾夕法尼亚大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；University of California at Riverside（加州大学河滨分校）
本文提出时间索引Hybrid A star算法，将动态障碍物预测融入在线规划框架，在垂直、斜向和平行泊车场景中实现高效安全的动态避障路径规划。
Department of Cybernetics, Czech Technical University in Prague（捷克技术大学布拉格分校自动化系）；Mechanical and Aerospace Engineering, Old Dominion University（旧 Dominion 大学机械与航空航天工程系）；Mechanical Engineering Faculty, Sahand University of Technology（沙赫德大学机械工程系）；Aksaray University（阿克萨雷大学）
TRUST-Planner: Topology-guided Robust Trajectory Planner for AAVs with Uncertain Obstacle Spatial-temporal Avoidance
School of Aerospace Engineering, Beijing Institute of Technology（北京理工大学航空航天工程学院）；Key Laboratory of Dynamics and Control of Flight Vehicle, Ministry of Education（教育部飞行器动力学与控制重点实验室）
DikpolaSat Mission: Improvement of Space Flight Performance and Optimal Control Using Trained Deep Neural Network -- Trajectory Controller for Space Objects Collision Avoidance
Tod’Aérs - Transparent Organization for Aeronautics and Space Research（Tod'Aérs - 航空航天研究透明组织）；Space Generation Advisory Council（太空世代咨询委员会）；Moscow Aviation Institute（莫斯科航空学院）；Univerité Sultan Moulay Slimane（苏丹穆莱·斯利曼大学）
Fast Safe Rectangular Corridor-based Online AGV Trajectory Optimization with Obstacle Avoidance
State Key Laboratory of Intelligent Manufacturing Equipment and Technology（智能制造装备与技术国家重点实验室）；School of Mechanical Science and Engineering（机械科学与工程学院）；Huazhong University of Science and Technology（华中科技大学）
RobotDiffuse: Diffusion-Based Motion Planning for Redundant Manipulators with the ROP Obstacle Avoidance Dataset
School of Computer Science and Engineering, Beihang University, Beijing, China（北京航空航天大学计算机科学与工程学院）；School of Software, Beihang University, Beijing, China（北京航空航天大学软件学院）；Hangzhou Innovation Institute, Beihang University, Hangzhou, China（北京航空航天大学杭州创新研究院）
Trajectory Optimization for UAV-Based Medical Delivery with Temporal Logic Constraints and Convex Feasible Set Collision Avoidance
State Key Laboratory of Multimodal Artificial Intelligence Systems（多模态人工智能系统国家重点实验室）；Vanke School of Public Health（万科公共卫生学院）；School of Automation（自动化学院）
Trajectory Planning with Model Predictive Control for Obstacle Avoidance Considering Prediction Uncertainty
Institute of Electromobility, RPTU University Kaiserslautern-Landau（电磁移动研究所，科隆-兰道大学）；Institute of Wireless Communications and Navigation, RPTU University Kaiserslautern-Landau（无线通信与导航研究所，科隆-兰道大学）
A Relaxed Quadratic-Program-based Framework for Trajectory Tracking of Unicycle Robots with Singularity Avoidance
Department of Mechanical；Industrial Engineering at the New Jersey Institute of Technology (NJIT), NJ, USA；School of Engineering, Infrastructure；Sustainability De Montfort University, Leicester, LE1 9BH, UK
Local Path Planning and Obstacle Avoidance for an Omnicopter Platform
Faculty of Aerospace Engineering, Delft University of Technology（代尔夫特理工大学航空航天工程学院）；Mohamed Bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Center for Artificial Intelligence and Robotics, New York University Abu Dhabi（纽约大学阿布扎比分校人工智能与机器人中心）
