Randomized single-query motion planning in expansive spaces

Random sampling is a fundamental technique for motion planning of objects with many degrees of freedom (dof). This thesis presents efficient randomized algorithms for single-query motion planning of objects with many dofs and under complex motion constraints. Unlike most other probabilistic roadmap planners, our algorithms perform no preprocessing of the environment. They sample collision-free configurations incrementally in the connected components of the space that contain the query configurations, thus avoiding the high cost of pre-computing a roadmap for the entire space. Two specific planners are discussed. One addresses the simpler problem of path planning. The other extends the basic idea and takes into account kinematic and dynamic constraints on motion as well. A control system is used to represent both types of constraints in a unified framework. Our algorithms have been tested extensively on both synthesized examples and real-life CAD data from the industry; they have shown strong performance on rigid-body and articulated objects with up to 18 dofs. We also demonstrate their generality and effectiveness in three practical applications: assembly maintainability checking, motion synthesis for animated characters, and kinodynamic motion planning for an integrated real-time robot system in environments with moving obstacles. The lack of theoretical explanation for the randomized motion planners' success in experiments has motivated us to introduce the notion of expansive spaces as a new way to characterize the complexity of input environments. It provides us a conceptual framework to understand why randomized motion planners work well and under what conditions. We prove that in an expansive space, our algorithms find a solution trajectory with probability that converges to 1 at an exponential rate, if a solution exists. An efficient motion planner is also useful as a primitive for accomplishing more complex tasks. An example of this is the robot placement problem, an important application from the manufacturing industry. By combining a randomized path planner with local iterative optimization, our placement algorithm computes simultaneously a base location and a corresponding collision-free path for a fixed-base robot manipulator to execute specified tasks as efficiently as possible.