In manufacturing and automation settings, robots often have to perform highly-repetitive manipulation tasks in structured environments. In this work we are interested in settings where tasks are similar, yet not identical (e.g., due to uncertain orientation of objects) and motion planning needs to be extremely fast. Preprocessing-based approaches prove to be very beneficial in these settings; they analyze the configuration-space offline to generate some auxiliary information which can then be used in the query phase to speedup planning times. Typically, the tighter the requirement is on query times the larger the memory footprint will be. In particular, for high-dimensional spaces, providing real-time planning capabilities is extremely challenging. While there are planners that guarantee real-time performance by limiting the planning horizon, we are not aware of general-purpose planners capable of doing it for infinite horizon (i.e., planning to the goal). To this end, we propose a preprocessing-based method that provides provable bounds on the query time while incurring only a small amount of memory overhead in the query phase. We evaluate our method on a 7-DOF robot arm and show a speedup of over tenfold in query time when compared to the PRM algorithm, while provably guaranteeing a maximum query time of less than 3 milliseconds.
 Provides an analysis of a path planning method which uses probabilistic roadmaps. This method has proven very successful in practice, but the theoretical understanding of its performance is still limited. Assuming that a path spl gamma exists between two configurations a and b of the robot, we study the dependence of the failure probability to connect a and b on (i) the length of spl gamma , (ii) the distance function of spl gamma from the obstacles, and (iii) the number of nodes N of the probabilistic roadmap constructed. Importantly, our results do not depend strongly on local irregularities of the configuration space, as was the case with previous analysis. These results are illustrated with a simple but illuminating example. In this example, we provide estimates for N, the principal parameter of the method, in order to achieve failure probability within prescribed bounds. We also compare, through this example, the different approaches to the analysis of the planning method. A landmark based heuristic is investigated for reducing query phase run-time of the probabilistic roadmap (PRM) motion planning method. The heuristic is generated by storing minimum spanning trees from a small number of vertices within the PRM graph and using these trees to approximate the cost of a shortest path between any two vertices of the graph. The intermediate step of preprocessing the graph increases the time and memory requirements of the classical motion planning technique in exchange for speeding up individual queries making the method advantageous in multi-query applications. This paper investigates these trade-offs on PRM graphs constructed in randomized environments as well as a practical manipulator simulation. We conclude that the method is preferable to Dijkstra's algorithm or the A∗ algorithm with conventional heuristics in multi-query applications. A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collision-free configurations and whose edges correspond to feasible paths between these configurations. These paths are computed using a simple and fast local planner. In the query phase, any given start and goal configurations of the robot are connected to two nodes of the roadmap; the roadmap is then searched for a path joining these two nodes. The method is general and easy to implement. It can be applied to virtually any type of holonomic robot. It requires selecting certain parameters (e.g., the duration of the learning phase) whose values depend on the scene, that is the robot and its workspace. But these values turn out to be relatively easy to choose, Increased efficiency can also be achieved by tailoring some components of the method (e.g., the local planner) to the considered robots. In this paper the method is applied to planar articulated robots with many degrees of freedom. Experimental results show that path planning can be done in a fraction of a second on a contemporary workstation ( spl ap 150 MIPS), after learning for relatively short periods of time (a few dozen seconds).