Probabilistic completeness of RRT for geometric and kinodynamic planning with forward propagation

The Rapidly-exploring Random Tree (RRT) algorithm has been one of the most prevalent and popular motion-planning techniques for two decades now. Surprisingly, in spite of its centrality, there has been an active debate under which conditions RRT is probabilistically complete. We provide two new proofs of probabilistic completeness (PC) of RRT with a reduced set of assumptions. The first one for the purely geometric setting, where we only require that the solution path has a certain clearance from the obstacles. For the kinodynamic case with forward propagation of random controls and duration, we only consider in addition mild Lipschitz-continuity conditions. These proofs fill a gap in the study of RRT itself. They also lay sound foundations for a variety of more recent and alternative sampling-based methods, whose PC property relies on that of RRT

Balancing Global Exploration and Local-connectivity Exploitation with Rapidly-exploring Random disjointed-Trees

Sampling efficiency in a highly constrained environment has long been a major challenge for sampling-based planners. In this work, we propose Rapidly-exploring Random disjointed-Trees* (RRdT*), an incremental optimal multi-query planner. RRdT* uses multiple disjointed-trees to exploit local-connectivity of spaces via Markov Chain random sampling, which utilises neighbourhood information derived from previous successful and failed samples. To balance local exploitation, RRdT* actively explore unseen global spaces when local-connectivity exploitation is unsuccessful. The active trade-off between local exploitation and global exploration is formulated as a multi-armed bandit problem. We argue that the active balancing of global exploration and local exploitation is the key to improving sample efficient in sampling-based motion planners. We provide rigorous proofs of completeness and optimal convergence for this novel approach. Furthermore, we demonstrate experimentally the effectiveness of RRdT*'s locally exploring trees in granting improved visibility for planning. Consequently, RRdT* outperforms existing state-of-the-art incremental planners, especially in highly constrained environments.Comment: Submitted to IEEE International Conference on Robotics and Automation (ICRA) 201

UAV Path Planning System Based on 3D Informed RRT* for Dynamic Obstacle Avoidance

A path planning system based on the Informed RRT* path planner was developed to enable an unmanned aerial vehicle (UAV) to avoid moving obstacles in a cluttered 3D environment. For congested environments such as a construction site, path planning systems that help a UAV to safely manoeuvre around dynamic objects and potential co-workers operating within the same workspace is needed. Instead of using a general RRT* path planner approach which will generate a sinuous path, we proposed a flexible approach to increase the convergence of our path planner by re-defining the search space based on 2D Informed RRT* path planner. General RRT* has a relatively low convergence speed to optimize its original solution. By using motion tracking cameras, we obtained real-time feedback of the UAVs pose as well as map structuring and obstacle positions. With this setup, the performance of our proposed path planning approach was assessed using a set of diverse scenarios to compare against general RRT* in convergence rate, quality of solution and ability to handle multiple obstacle situation

Anytime informed path re-planning and optimization for robots in changing environments

In this paper, we propose a path re-planning algorithm that makes robots able to work in scenarios with moving obstacles. The algorithm switches between a set of pre-computed paths to avoid collisions with moving obstacles. It also improves the current path in an anytime fashion. The use of informed sampling enhances the search speed. Numerical results show the effectiveness of the strategy in different simulation scenarios.Comment: Submitted to IROS 2021. "This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

Advanced BIT* (ABIT*): Sampling-Based Planning with Advanced Graph-Search Techniques

Path planning is an active area of research essential for many applications in robotics. Popular techniques include graph-based searches and sampling-based planners. These approaches are powerful but have limitations. This paper continues work to combine their strengths and mitigate their limitations using a unified planning paradigm. It does this by viewing the path planning problem as the two subproblems of search and approximation and using advanced graph-search techniques on a sampling-based approximation. This perspective leads to Advanced BIT*. ABIT* combines truncated anytime graph-based searches, such as ATD*, with anytime almost-surely asymptotically optimal sampling-based planners, such as RRT*. This allows it to quickly find initial solutions and then converge towards the optimum in an anytime manner. ABIT* outperforms existing single-query, sampling-based planners on the tested problems in $\mathbb{R}^{4}$ and $\mathbb{R}^{8}$, and was demonstrated on real-world problems with NASA/JPL-Caltech.Comment: IEEE International Conference on Robotics and Automation (ICRA) 2020, 6 + 1 pages, 3 figures, video available at https://youtu.be/VFdihv8Lq2

Adaptively Informed Trees (AIT*): Fast Asymptotically Optimal Path Planning through Adaptive Heuristics

Informed sampling-based planning algorithms exploit problem knowledge for better search performance. This knowledge is often expressed as heuristic estimates of solution cost and used to order the search. The practical improvement of this informed search depends on the accuracy of the heuristic. Selecting an appropriate heuristic is difficult. Heuristics applicable to an entire problem domain are often simple to define and inexpensive to evaluate but may not be beneficial for a specific problem instance. Heuristics specific to a problem instance are often difficult to define or expensive to evaluate but can make the search itself trivial. This paper presents Adaptively Informed Trees (AIT*), an almost-surely asymptotically optimal sampling-based planner based on BIT*. AIT* adapts its search to each problem instance by using an asymmetric bidirectional search to simultaneously estimate and exploit a problem-specific heuristic. This allows it to quickly find initial solutions and converge towards the optimum. AIT* solves the tested problems as fast as RRT-Connect while also converging towards the optimum.Comment: IEEE International Conference on Robotics and Automation (ICRA) 2020, 6 + 2 pages, 5 figures, video available at https://youtu.be/twM723QM9T

Informed anytime fast marching tree for asymptotically-optimal motion planning

In many applications, it is necessary for motion planning planners to get high-quality solutions in high-dimensional complex problems. In this paper, we propose an anytime asymptotically-optimal sampling-based algorithm, namely Informed Anytime Fast Marching Tree (IAFMT*), designed for solving motion planning problems. Employing a hybrid incremental search and a dynamic optimal search, the IAFMT* fast finds a feasible solution, if time permits, it can efficiently improve the solution toward the optimal solution. This paper also presents the theoretical analysis of probabilistic completeness, asymptotic optimality, and computational complexity on the proposed algorithm. Its ability to converge to a high-quality solution with the efficiency, stability, and self-adaptability has been tested by challenging simulations and a humanoid mobile robot