Summary. 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. 1

Abstract — This paper shows how to effectively combine a sampling-based method primarily designed for multiple query motion planning (Probabilistic Roadmap Method- PRM) with sampling-based tree methods primarily designed for single query motion planning (Expansive Space Trees, Rapidly-Exploring Random Trees, and others) in a novel planning framework that can be efficiently parallelized. Our planner not only achieves a smooth spectrum between multiple query and single query planning but it combines advantages of both. We present experiments which show that our planner is capable of solving problems that cannot be addressed efficiently withPRM or single-query planners. A key advantage of our planner is that it is significantly more decoupled thanPRM and sampling-based tree planners. Exploiting this property, we designed and implemented a parallel version of our planner. Our experiments show that our planner distributes well and can easily solve high-dimensional problems that exhaust resources available to single machines and cannot be addressed with existing planners. Index Terms — Motion planning, sampling-based planning, parallel algorithms, roadmap, tree, PRM, EST, RRT, SRT.

We present two motion planning algorithms, based on the Rapidly Exploring Random Tree (RRT) family of algorithms. These algorithms represent the first work in the direction of derandomizing RRTs; this is a very challenging problem due to the way randomization is used in RRTs. In RRTs, randomization is used to create Voronoi bias, which causes the search trees to rapidly explore the state space. Our algorithms take steps to increase the Voronoi bias and to retain this property without the use of randomization. Studying these and related algorithms will improve our understanding of how efficient exploration can be accomplished, and will hopefully lead to improved planners. We give experimental results that illustrate how the new algorithms explore the state space and how they compare with existing RRT algorithms.

Motion planning for robots with many degrees of freedom requires the exploration of an exponentially large configuration space. Single-query motion planners restrict exploration to regions of configuration space determined to be relevant to a particular planning query. The heuristics employed by existing single-query planners to estimate the relevance of a region, however, remain unchanged throughout the planning process. An incorrect estimate by the heuristic for a configuration space region will only be corrected by explicit exploration. As a result, unnecessary exploration is performed. In this paper we propose an alternative approach. We observe that every incremental sample improves the planner’s understanding of configuration space. This improved understanding can be exploited to inform the singlequery heuristic of a motion planner. We formalize the improvement in understanding by employing the notion of entropy from information theory and derive a principled method of configuration space exploration in the single-query setting. Experiments show that the proposed single-query entropy-guided motion planner outperforms existing single-query techniques. 1

We present an approach to the problem of differentially constrained mobile robot motion planning in arbitrary cost fields. The approach is based on deterministic search in a specially discretized state space. We compute a set of elementary motions that connects each discrete state value to a set of its reachable neighbors via feasible motions. Thus, this set of motions induces a connected search graph. The motions are carefully designed to terminate at discrete states, whose dimensions include relevant state variables (e.g., position, heading, curvature, and velocity). The discrete states, and thus the motions, repeat at regular intervals, forming a lattice. We ensure that all paths in the graph encode feasible motions via the imposition of continuity constraints on state variables at graph vertices and compliance of the graph edges with a differential equation comprising the vehicle model. The resulting state lattice permits fast full configuration space cost evaluation and collision detection. Experimental results with research prototype rovers demonstrate that the planner allows us to exploit the entire envelope of vehicle maneuverability in rough terrain, while featuring real-time performance. C ○ 2009 Wiley Periodicals, Inc. 1.

We present an approach to the problem of mobile robot motion planning in arbitrary cost fields subject to differential constraints. Given a model of vehicle maneuverability, a trajectory generator solves the two point boundary value problem of connecting two points in state space with a feasible motion. We use this capacity to compute a control set which connects any state to its reachable neighbors in a limited neighborhood. Equivalence classes of paths are used to implement a path sampling policy which preserves expressiveness while eliminating redundancy. The implicit repetition of the resulting minimal control set throughout state space produces a reachability graph that encodes all feasible motions consistent with this sampling policy. The graph encodes only feasible motions by construction and, by appropriate choice of state space dimension, can permit full configuration space collision detection while imposing heading and curvature continuity constraints at nodes. Nonholonomic constraints are satisfied by construction in the trajectory generator. We also use the trajectory generator to compute an ideal admissible heuristic and significantly improve planning efficiency. Comparisons

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The problem of humanoid agents and robots reaching to arbitrary targets in environments with static and dynamic obstacles has not yet been investigated in detail. Typical approaches include using randomized motion planning or constructing uninformed trajectories (e.g., linear interpolation between initial and target positions and orientations of the hand) in operational space, in hopes that inter-link and agent-environment collisions do not occur. In this paper, we test the most popular algorithms for motion generation for single-arm reaching in environments with randomly placed obstacles of random sizes. Additionally, we attempt to formalize the concept of motor primitives, and test a motor primitive implementation in the same experiments. We conduct an analysis of the efficacy of the algorithms for reaching in static environments, and discuss the extensibility of the algorithms towards reaching in dynamic environments.

The development of practical motion planning algorithms and obstacle avoidance techniques is considered as one of the most important fields of study in the task of building autonomous or semiautonomous robot systems. The motion planners designed for humanoid robots combine both path planning generation and the ability of executing the resulting path with respect to their characteristics. These planners should consider the specific dynamical constraints and stability problems of the humanoid robots. In this paper, we present a time-efficient hybrid motion planning system for a Fujitsu HOAP-2 humanoid robot in indoor and miniature city environments. The proposed technique is a combination of sampling-based planner and D * Lite search to generate dynamic footstep placements in unknown environments. It generates the search space depending on non-uniform sampling of the free configuration space to direct the computational resources to troubled and difficult regions. D * Lite search is then implemented to find dynamic and low-cost footstep placements within the resulting configuration space. The proposed hybrid algorithm reduces the searching time and produces a smoother path for the humanoid robot with low cost. 1

Randomized, sampling-based planning has a long history of success, and although the benefits associated with this use of randomization are widely-recognized, its costs are not well-understood. We examine a variety of problem instances solved with the Rapidly-exploring Random Tree algorithm, demonstrating that heavy-tailed runtime distributions are both common and potentially exploitable. We show that runtime mean and variability can be reduced simultaneously by a straightforward strategy such as restarts and that such a strategy can apply broadly across sets of queries. Our experimental results indicate that several-fold improvements can be achieved in the mean and variance for restrictive problem environments.