Affiliation: College of Arts and Sciences, Department of Computer Science
The configuration space is a fundamental concept that is widely used in algorithmic robotics. Many applications in robotics, computer-aided design, and related areas can be reduced to computational problems in terms of configuration spaces. In this dissertation, we address three main computational challenges related to configuration spaces: 1) how to efficiently compute an approximate representation of high-dimensional configuration spaces; 2) how to efficiently perform geometric, proximity, and motion planning queries in high dimensional configuration spaces; and 3) how to model uncertainty in configuration spaces represented by noisy sensor data. We present new configuration space construction algorithms based on machine learning and geometric approximation techniques. These algorithms perform collision queries on many configuration samples. The collision query results are used to compute an approximate representation for the configuration space, which quickly converges to the exact configuration space. We highlight the efficiency of our algorithms for penetration depth computation and instance-based motion planning. We also present parallel GPU-based algorithms to accelerate the performance of optimization and search computations in configuration spaces. In particular, we design efficient GPU-based parallel k-nearest neighbor and parallel collision detection algorithms and use these algorithms to accelerate motion planning. In order to extend configuration space algorithms to handle noisy sensor data arising from real-world robotics applications, we model the uncertainty in the configuration space by formulating the collision probabilities for noisy data. We use these algorithms to perform reliable motion planning for the PR2 robot.