Chapter 5 Sampling-Based Motion Planning

2013 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2013

: The induced sampling distribution of an augmented kd-tree after 10 4 , 10 5 , and 10 6 samples are shown in (a), (b), and (c), respectively. Whiteblack represent low-high sampling probability density. The actual obstacle configuration appears in (d), obstacles are red.

2013 European Modelling Symposium, 2013

Sampling based algorithms provide efficient methods of solving robot motion planning problem. The advantage of these approaches is the ease of their implementation and their computational efficiency. These algorithms are probabilistically complete i.e. they will find a solution if one exists, given a suitable run time. The drawback of sampling based planners is that there is no guarantee of the quality of their solutions. In fact, it was proven that their probability of reaching an optimal solution approaches zero. A breakthrough in sampling planning was the proposal of optimal based sampling planners. Current optimal planners are characterized with asymptotic optimality i.e. they reach an optimal solutions as time approaches infinity. Motivated by the slow convergence of optimal planners, post-processing and heuristic approach have been suggested. Due to the nature of the sampling based planners, their implementation requires tuning and selection of a large number of parameters that are often overlooked. This paper presents the performance study of an optimal planner under different parameters and heuristics. We also propose a modification in the algorithm to improve the convergence rate towards an optimal solution.

Proceedings - IEEE International Conference on Robotics and Automation, 2005

The last decade, sampling based planners like the Probabilistic Roadmap Method have proved to be successful in solving complex motion planning problems. We give a reachability based analysis for these planners which leads to a better understanding of the success of the approach and enhancements of the techniques suggested. This also enables us to study the effect of using new local planners.

Mutation Research-fundamental and Molecular Mechanisms of Mutagenesis, 2004

The probabilistic roadmap approach is a commonly used motion planning technique. A crucial ingredient of the approach is a sampling algorithm that samples the cong- uration space of the moving object for free congurations. Over the past decade many sampling techniques have been proposed. It is dicult to compare the dieren t techniques because they were tested on dieren t

Springer Tracts in Advanced Robotics, 2010

While spatial sampling of points has already received much attention, the motion planning problem can also be viewed as a process which samples the function space of paths. We define a search space to be a set of candidate paths and consider the problem of designing a search space which is most likely to produce a solution given a probabilistic representation of all possible environments. We introduce the concept of relative completeness which is the prior probability, before the environment is specified, of producing a solution path in a bounded amount of computation. We show how this probability is related to the mutual separation of the set of paths searched. The problem of producing an optimal set can be related to the maximum k-facility dispersion problem which is known to be NP-hard. We propose a greedy algorithm for producing a good set of paths and demonstrate that it produces results with both low dispersion and high prior probability of success.

2003

In this paper, we describe a planning and control approach in terms of sampling using Rapidlyexploring Random Trees (RRTs), which were introduced in [7, 9]. We review RRTs for motion planning and show how to use them to solve standard nonlinear control problems. We extend them to the case of hybrid systems and describe our modifications to LaValle's Motion Strategy Library to allow for hybrid motion planning. Finally, we extend them to purely discrete spaces (using heuristic evaluation as a distance metric) and provide computational experiments comparing them to conventional methods, such as A*.

49th IEEE Conference on Decision and Control (CDC), 2010

In this paper, an Adaptive Sampling strategy is presented for the generalized sampling based motion planner, Generalized Probabilistic Roadmap (GPRM) [18, 19]. These planners are designed to account for stochastic map and model uncertainty and provide a feedback solution to the motion planning problem. Sampling intelligently, in this framework, can result in huge speedups when compared to naive uniform sampling. By using the information of transition probabilities, encoded in these generalized planners, the proposed strategy biases sampling to improve the efficiency of sampling, and increase the overall success probability of GPRM. The strategy was used to solve the motion planning problem of a fully actuated point robot on several maps of varying difficulty levels, and results show that the strategy helps solve the problem efficiently while simultaneously increasing the success probability of the solution. Results also show that these rewards increase with an increase in map complexity.

IEEE Transactions on Systems, Man, and Cybernetics, 2011

In this paper, generalized versions of the probabilistic sampling based planners, Probabilistic Road Maps (PRM) and Rapidly exploring Random Tree (RRT), are presented. The generalized planners, Generalized Probabilistic Road Map (GPRM) and the Generalized Rapidly Exploring Random Tree (GRRT), result in hybrid hierarchical feedback planners that are robust to the uncertainties in the robot motion model as well as uncertainties in the robot map/ workspace. The proposed planners are analyzed and shown to be probabilistically complete. The algorithms are tested on fully actuated, as well as underactuated robots, on several maps of varying degrees of difficulty, and the results show that the generalized methods have a significant advantage over the traditional methods when planning under uncertainty.

arXiv (Cornell University), 2022

Many path planning algorithms are based on sampling the state space. While this approach is very simple, it can become costly when the obstacles are unknown, since samples hitting these obstacles are wasted. The goal of this paper is to efficiently identify obstacles in a map and remove them from the sampling space. To this end, we propose a preprocessing algorithm for space exploration that enables more efficient sampling. We show that it can boost the performance of other space sampling methods and path planners. Our approach is based on the fact that a convex obstacle can be approximated provably well by its minimum volume enclosing ellipsoid (MVEE), and a non-convex obstacle may be partitioned into convex shapes. Our main contribution is an algorithm that strategically finds a small sample, called the activecoreset, that adaptively samples the space via membershiporacle such that the MVEE of the coreset approximates the MVEE of the obstacle. Experimental results confirm the effectiveness of our approach across multiple planners based on Rapidly-exploring random trees, showing significant improvement in terms of time and path length.

Journal of Intelligent & Robotic Systems

This paper introduces an enhancement to traditional sampling-based planners, resulting in efficiency increases for high-dimensional holonomic systems such as hyperredundant manipulators, snake-like robots, and humanoids. Despite the performance advantages of modern sampling-based motion planners, solving high dimensional planning problems in near real-time remains a considerable challenge. The proposed enhancement to popular sampling-based planning algorithms is aimed at circumventing the exponential dependence on dimensionality, by progressively exploring lower dimensional volumes of the configuration space. Extensive experiments comparing the enhanced and traditional version of RRT, RRT-Connect, and Bidirectional T-RRT on both a planar hyper-redundant manipulator and the Baxter humanoid robot show significant acceleration, up to two orders of magnitude, on computing a solution. We also explore important implementation issues in the sampling process and discuss the limitations of this method.