We present a novel approach to perform probabilistic collision detection between a high-DOF robot and imperfect obstacle representations in dynamic and uncertain environments. Our formulation is designed for high-DOF robot trajectory planning in dynamic scenes, where the uncertainties are modeled using Gaussian distributions. We present an efficient algorithm to compute collision probabilities between the robot and the obstacles. Furthermore, we present a prediction algorithm for obstacle positions that takes into account spatial and temporal uncertainties and uses that for trajectory optimization. We highlight the performance of our trajectory planning algorithm in challenging simulated and real-world environments with robot arms operating next to dynamically moving human obstacles.

Blue noise sampling has proved useful for many graphics applications, but remains underexplored in high-dimensional spaces due to the difficulty of generating distributions and proving properties about them. We present a blue noise sampling method with good quality and performance across different dimensions. The method, spoke-dart sampling, shoots rays from prior samples and selects samples from these rays. It combines the advantages of two major high-dimensional sampling methods: the locality of advancing front with the dimensionality-reduction of hyperplanes, specifically line sampling. We prove that the output sampling is saturated with high probability, with bounds on distances between pairs of samples and between any domain point and its nearest sample. We demonstrate spoke-dart applications for approximate Delaunay graph construction, global optimization, and robotic motion planning. Both the blue-noise quality of the output distribution and the adaptability of the intermediate processes of our method are useful in these applications.

We present a contact planner for complex legged locomotion tasks: standing up, climbing stairs using a handrail, crossing rubble, and getting out of a car. The need for such a planner was shown at the DARPA Robotics Challenge, where such behaviors could not be demonstrated (except for egress). Current planners suffer from their prohibitive algorithmic complexity because they deploy a tree of robot configurations projected in contact with the environment. We tackle this issue by introducing a reduction property: the reachability condition. This condition defines a geometric approximation of the contact manifold, which is of low dimension, presents a Cartesian topology, and can be efficiently sampled and explored. The hard contact planning problem can then be decomposed into two subproblems: first, we plan a path for the root without considering the whole-body configuration, using a sampling-based algorithm; then, we generate a discrete sequence of whole-body configurations in static equilibrium along this path, using a deterministic contact-selection algorithm. The reduction breaks the algorithm complexity encountered in previous works, resulting in the first interactive implementation of a contact planner (open source). While no contact planner has yet been proposed with theoretical completeness, we empirically show the interest of our framework: in a few seconds, with high success rates, we generate complex contact plans for various scenarios and two robots: HRP-2 and HyQ. These plans are validated in dynamic simulations or on the real HRP-2 robot.

We present new algorithms to perform fast probabilistic collision queries between convex as well as non-convex objects. Our approach is applicable to general shapes, where one or more objects are represented using Gaussian probability distributions. We present a fast new algorithm for a pair of convex objects, and extend the approach to non-convex models using hierarchical representations. We highlight the performance of our algorithms with various convex and non-convex shapes on complex synthetic benchmarks and trajectory planning benchmarks for a 7-DOF Fetch robot arm.

We present a rapidly exploring-random-tree-based parallel motion planning algorithm that uses the maximal Poisson-disk sampling scheme. Our approach exploits the free-disk property of the maximal Poisson-disk samples to generate nodes and perform tree expansion. Furthermore, we use an adaptive scheme to generate more samples in challenging regions of the configuration space. The Poisson-disk sampling results in improved parallel performance and we highlight the performance benefits on multicore central processing units as well as manycore graphics processing units on different benchmarks.

We present an algorithmic framework for the early classification of human intentions, and use it to accurately predict future human motions when planning the path of a robot in an environment that is shared with humans. During an off-line learning phase, a classifier that can recognize when a human intends to interact with the robot is trained. At runtime, this trained classifier allows us to recognize humans who intend to interact with, or obstruct, the robot in some way. We validate our approach using both recorded and simulated data in an environment in which some humans intentionally obstruct the robot. Our classifier identifies these potential blockers, thus allowing the robot to safely and efficiently navigate the environment by minimizing the chances of being blocked.

We present an interactive motion planning algorithm to compute plausible trajectories for high-DOF human-like characters. Given a discrete sequence of contact configurations, we use a three-phase optimization approach to ensure that the resulting trajectory is collision-free, smooth, and satisfies dynamic balancing constraints. Our approach can directly compute dynamically balanced and natural-looking motions at interactive frame rates and is considerably faster than prior methods. We highlight its performance on complex human motion benchmarks corresponding to walking, climbing, crawling, and crouching, where the discrete configurations are generated from a kinematic planner or extracted from motion capture datasets.

We present a multi-agent simulation algorithm to compute the trajectories and full-body motion of human-like agents. Our formulation uses a coupled approach that combines 2D collision-free navigation with high-DOF human motion simulation using a behavioral finite state machine. In order to generate plausible pedestrian motion, we use a closed-loop hierarchical planner that satisfies dynamic stability, biomechanical, and kinematic constraints, and is tightly integrated with multi-agent navigation. Furthermore, we use motion capture data to generate natural looking human motion. The overall system is able to generate plausible motion with upper and lower body movements and avoid collisions with other human-like agents. We highlight its performance in indoor and outdoor scenarios with tens of human-like agents.

We present an RRT-based motion planning algorithm that uses the maximal Poisson-disk sampling scheme. Our approach exploits the free-disk property of the maximal Poisson-disk samples to generate nodes and perform tree expansion. Furthermore, we use an adaptive scheme to generate more samples in challenging regions of the configuration space. Our approach can be easily parallelized on multi-core CPUs and many-core GPUs. We highlight the performance of our algorithm on different benchmarks.

We present a novel algorithm to compute collision-free trajectories in dynamic environments. Our approach is general and does not require a priori knowledge about the obstacles or their motion. We use a replanning framework that interleaves optimization-based planning with execution. Furthermore, we describe a parallel formulation that exploits a high number of cores on commodity graphics processors (GPUs) to compute a high-quality path in a given time interval. We derive bounds on how parallelization can improve the responsiveness of the planner and the quality of the trajectory.

We present a novel algorithm to compute collision-free trajectories in dynamic environments. Our approach is general and makes no assumption about the obstacles or their motion. We use a replanning framework that interleaves optimization-based planning with execution. Furthermore, we describe a parallel formulation that exploits high number of cores on commodity graphics processors (GPUs) to compute a high-quality path in a given time interval. Overall, we show that search in configuration spaces can be significantly accelerated by using GPU parallelism.