We present a new method for generating collision-free paths for robots operating in changing environments. Our approach is closely related to recent probabilistic roadmap approaches. These planners use preprocessing and query stages, and are aimed at planning many times in the same environment. In contrast, our preprocessing stage creates a representation of the configuration space that can be easily modified in real time to account for changes in the environment, thus facilitating real-time planning. As with previous approaches, we begin by constructing a graph that represents a roadmap in the configuration space, but we do not construct this graph for a specific workspace. Instead, we construct the graph for an obstacle-free workspace, and encode the mapping from workspace cells to nodes and arcs in the graph. When the environment changes, this mapping is used to make the appropriate modifications to the graph, and plans can be generated by searching the modified graph.
In this paper, we first discuss the construction of the roadmap, including how random samples of the configuration space are generated using an importance sampling approach and how these samples are connected to form the roadmap. We then discuss the mapping from the workspace to the configuration space roadmap, explaining how the mapping is generated and how it can be encoded efficiently using compression schemes that exploit redundancy in the mapping. We then introduce quantitative robustness measures and show how these can be used to enhance the robustness of the roadmap to changes in the environment. Finally, we evaluate an implementation of our approach for serial-link manipulators with up to 20 joints.
Coordinating the motions of multiple robots operating in a shared workspace without collisions is an important capability. We address the task of coordinating the motions of multiple robots when their trajectories (defned by both the path and velocity along the path) are specijied. This problem of collision-pee trajectory coordination arises in welding and painting workcells in the automotive industry. We identify suficient and necessary conditions for collision-free coordination of the robots when only the robot start times can be varied, and defne corresponding optimization problems. We develop mixed integer programming formulations of these problems to automatically generate minimum time solutions. This method is applicable to both mobile robots and articulated arms, and places no restrictions on the number of degrees offeedom of the robots. The primary advantage of this method is its ability to coordinate the motions of several robots, with as many as 20 robots being considered. We show that, even when the robot trajectories are specijied, minimum time coordination of multiple robots is NP-hard.
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