Real-time stochastic kinodynamic motion planning via multiobjective search on GPUs

Abstract

Abstract-In this paper we present the PUMP (Parallel Uncertainty-aware Multiobjective Planning) algorithm for addressing the stochastic kinodynamic motion planning problem, whereby one seeks a low-cost, dynamically-feasible motion plan subject to a constraint on collision probability (CP). To ensure exhaustive evaluation of candidate motion plans (as needed to tradeoff the competing objectives of performance and safety), PUMP incrementally builds the Pareto front of the problem, accounting for the optimization objective and an approximation of CP. This is performed by a massively parallel multiobjective search, here implemented with a focus on GPUs. Upon termination of the exploration phase, PUMP searches the Pareto set of motion plans to identify the lowest cost solution that is certified to satisfy the CP constraint (according to an asymptotically exact estimator). We introduce a novel particle-based CP approximation scheme, designed for efficient GPU implementation, which accounts for dependencies over the history of a trajectory execution. We present numerical experiments for quadrotor planning wherein PUMP identifies solutions in~100 ms, evaluating over one hundred thousand partial plans through the course of its exploration phase. The results show that this multiobjective search achieves a lower motion plan cost, for the same CP constraint, compared to a safety buffer-based search heuristic and repeated RRT trials.

Trajectory Planning Under Stochastic and Bounded Sensing Uncertainties Using Reachability Analysis

“…For details of the trajectory planning framework, we refer the readers to [19]. Here we illustrate the framework in Fig.…”

“…We account for the presence of both stochastic and bounded sensing uncertainties in our analysis. 2) Next, we combine our method to predict state uncertainty with an available trajectory planning framework [19]. In order to compare candidate trajectories within the planning framework, we design a metric for the size of the predicted state uncertainty.…”

“…We statistically validate the collision safety of the UAS by simulating multiple trajectories along the planned trajectories. The rest of the paper is organized as follows: we begin by formulating the problem in Section II; in Section III, we present the set representations and operations used in the paper; in Section IV, we mention the limitations of our prior work [1] and discuss our improved reachability analysis used to predict state uncertainty; Section V provides an overview of the trajectory planning framework [19] along with our metric for the size of the predicted state uncertainty; and in Section VI, we demonstrate the planning results for urban GNSS-based navigation of a fixed-wing UAS.…”

“…Overview of trajectory planning framework[19]. (a) The planner first builds a graph of feasible trajectories.…”

Perception-Aware Motion Planning via Multiobjective Search on GPUs

“…The multiobjective search has the further benefit of admitting a wide range of perception heuristic functions. In this work we consider additive heuristics intended to emulate the variance in a localization estimate (indeed, heuristics of this form could be addressed by state augmentation in a non-sampling-based context) but, e.g., more complicated particle-based heuristics have also been applied within a similar multiobjective search framework [17]. The final phase of MPAP computes an asymptotically exact probability of motion plan p satisfying a localization error bound through MC sampling [20].…”