Popular high-dimensional motion planning algorithms seem to pay an overly high price in terms of trajectory quality for their performance. In domains sparsely populated by obstacles, the heuristics used by sampling-based planners to navigate narrow passages can be needlessly complex; furthermore, additional post-processing is required to remove the jerky or extraneous motions from the paths that such planners generate. In this paper, we present CHOMP, a novel method for continuous path refinement that uses covariant gradient techniques to improve the quality of sampled trajectories. Our optimization technique converges over a wider range of input paths and is able to optimize higher- order dynamics of trajectories than previous path optimization strategies. As a result, CHOMP can be used as a standalone motion planner in many real-world planning queries. The effectiveness of our proposed method is demonstrated in manipulation planning for a 6-DOF robotic arm as well as in trajectory generation for a walking quadruped robot. 1

Abstract — We propose a framework, called Lightning, for planning paths in high-dimensional spaces that is able to learn from experience, with the aim of reducing computation time. This framework is intended for manipulation tasks that arise in applications ranging from domestic assistance to robot-assisted surgery. Our framework consists of two main modules, which run in parallel: a planning-from-scratch module, and a module that retrieves and repairs paths stored in a path library. After a path is generated for a new query, a library manager decides whether to store the path based on computation time and the generated path’s similarity to the retrieved path. To retrieve an appropriate path from the library we use two heuristics that exploit two key aspects of the problem: (i) A correlation between the amount a path violates constraints and the amount of time needed to repair that path, and (ii) the implicit division of constraints into those that vary across environments in which the robot operates and those that do not. We evaluated an implementation of the framework on several tasks for the PR2 mobile manipulator and a minimally-invasive surgery robot in simulation. We found that the retrieve-andrepair module produced paths faster than planning-fromscratch in over 90 % of test cases for the PR2 and in 58% of test cases for the minimally-invasive surgery robot. I.

Abstract In this paper, we describe a method of improving trajectory optimization based on predicting good initial guesses from previous experiences. In order to generalize to new situations, we propose a paradigm shift: predicting qualitative attributes of the trajectory that place the initial guess in the basin of attraction of a low-cost solution. We start with a key such attribute, the choice of a goal within a goal set that describes the task, and show the generalization capabilities of our method in extensive experiments on a personal robotics platform. 1

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.

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