Improving the Efficiency of Rapidly-exploring Random Trees Using a Potential Function Planner

Abstract

Abstract-This paper presents an improvement of the standard randomized path planning algorithm, and uses this new approach to design reconfiguration maneuvers for large formations of spacecraft. A spacecraft reconfiguration maneuver is a difficult 6 DOF trajectory design problem with nonlinear attitude dynamics and non-convex constraints. In addition, some of the constraints couple the positions and attitudes of the spacecraft, which makes the problems high-dimensional. A key step in the overall design is to find a feasible trajectory using a randomized path planner, which typically requires a large fraction of the total computation time. This paper presents an improvement to the path planner that greatly reduces the solution time and enables the solution of very large problems. The primary modification is to change the function that connects two points, which is a key component of the randomized planner. The standard approach is to use a simple and fast function, which is changed here to one that is slower, but much more effective in linking two points. The new connection function finds a link between the points by minimizing a distance function to the target point with a feasible optimizer that accounts for the constraints. The examples presented demonstrate the significant speed improvement of the new planner and that the algorithm can solve problems with up to 16 spacecraft with numerous constraints.

Triangular geometry based optimal motion planning using RRT*-motion planner

“…In these algorithms, the probability of finding a path solution in a given environment is one, if number of iterations utilized are allowed to approach infinity. Rapidly exploring random trees quickly find their initial path in a given problem, and due to their effectiveness, have been improved in number of ways [7], [8], [9], [10], [11], [12]. Most recent advancement of RRTs algorithm is the RRT*, which ensures asymptotic optimality [12], unlike 978-1-4799-2323-6114/$3l.00 ©2014 IEEE 380…”

Potentially guided bidirectionalized RRT* for fast optimal path planning in cluttered environments

“…In order to improve the rates of convergence to optimal solution of RRT*, techniques such as sample-biasing [28] [29] [30], sample-rejection [31], sampling-heuristics [25], multiple trees [32], iterative searches [31] and anytime searches [26] were used. Qureshi et al [29] used potential biasing on the randomly sampled states in RRT* to get to the optimal solution faster in his P-RRT* algorithm, which is an extension of previously proposed APGD-RRT* algorithm [33].…”

Discovering and synthesizing humanoid climbing movements

“…To summarize our technical approach, we grow a tree of paths in the climber's state space, inspired by Rapidly-Exploring Random Trees (RRT:s, [Lavalle 1998]). Planning in high-dimensional space using randomized actions can, however, take a long time and sometimes makes it impossible to find a feasible path [Garcia and How 2005]. Instead, we grow the tree informed by graph search in the lower-dimensional stance graph, which represents all possible 4-hold configurations or climber stances.…”