Sampling-based motion planners are an effective means for generating collision-free motion paths. However, the quality of these motion paths (with respect to quality measures such as path length, clearance, smoothness or energy) is often notoriously low, especially in high-dimensional configuration spaces. We introduce a simple algorithm for merging an arbitrary number of input motion paths into a hybrid output path of superior quality, for a broad and general formulation of path quality. Our approach is based on the observation that the quality of certain sub-paths within each solution may be higher than the quality of the entire path. A dynamic-programming algorithm, which we recently developed for comparing and clustering multiple motion paths, reduces the running time of the merging algorithm significantly. We tested our algorithm in motion-planning problems with up to 12 degrees of freedom. We show that our algorithm is able to merge a handful of input paths produced by several different motion planners to produce output paths of much higher quality.
In many virtual environment applications, paths have to be planned for characters to traverse from a start to a goal position in the virtual world while avoiding obstacles. Contemporary applications require a path planner that is fast (to ensure real-time interaction with the environment) and flexible (to avoid local hazards such as small and dynamic obstacles). In addition, paths need to be smooth and short to ensure natural looking motions. Current path planning techniques do not obey these criteria simultaneously. For example, A* approaches generate unnatural looking paths, potential field-based methods are too slow, and sampling-based path planning techniques are inflexible. We propose a new technique, the Corridor Map Method (CMM), which satisfies all criteria. In an off-line construction phase, the CMM creates a system of collision-free corridors for the static obstacles in an environment. In the query phase, paths can be planned inside the corridors for different types of characters while avoiding dynamic obstacles. Experiments show that high-quality paths for single characters or groups of characters can be obtained in real-time. Many algorithms have been proposed that create a path for a robot in an environment with obstacles. Most methods are aimed at finding a solution. However, for many applications, the path must be of a good quality as well. That is, a path should be short and should keep some amount of minimum clearance to the obstacles. Traveling along such a path reduces the chances of collisions due to the difficulty of measuring and controlling the precise position of the robot. This paper reports a new technique, called Partial shortcut, which decreases the path length. While current methods have difficulties in removing all redundant motions, the technique efficiently removes these motions by interpolating one degree of freedom at a time. Two algorithms are also studied that increase the clearance along paths. The first one is fast but can only deal with rigid, translating bodies. The second algorithm is slower but can handle a broader range of robots, including three-dimensional free-flying and articulated robots, which may reside in arbitrary high-dimensional configuration spaces. A big advantage of these algorithms is that clearance along paths can now be increased efficiently without using complex data structures and algorithms. Finally, we combine the two criteria and show that high-quality paths can be obtained for a broad range of robots. Several motion planning methods using networks of randomly generated nodes in the free space have been shown to perform well in a number of cases, however their performance degrades when paths are required to pass through narrow passages in the free space. In previous work we proposed MAPRM, a method of sampling the configuration space in which randomly generated configurations, free or not, are retracted onto the medial axis of the free space without having to first compute the medial axis; this was shown to increase sampling in narrow passages. In this paper we give details of the MAPRM algorithm for the case of a rigid body moving in three dimensions, and show that the retraction may be carried out without explicitly computing the C-obstacles or the medial axis. We give theoretical and experimental results to show this improves performance on problems involving narrow corridors and compare the performance to uniform random sampling from the free space. Many motion planning techniques, like the probabilistic roadmap method (PRM), generate low quality paths. In this paper, we study a number of different quality criteria on paths in particular length and clearance. We describe a number of techniques to improve the quality of paths. These are based on a new approach to increase the path clearance. Experiments showed that the heuristics were able to generate paths of a much higher quality than previous approaches.