PiP-X: Online feedback motion planning/replanning in dynamic environments using invariant funnels

TL;DR

PiP-X is an innovative online motion re-planning algorithm that uses invariant funnels and sampling-based methods to enable safe, kinodynamically feasible navigation in dynamic environments for robots like quadrotors.

Contribution

The paper introduces PiP-X, a novel framework combining sampling, control theory, and graph-based methods for real-time feedback motion re-planning in nonlinear, dynamic environments.

Findings

Successfully navigates a 6DOF quadrotor in complex maze scenarios.

Ensures kinodynamic feasibility through Lyapunov stability analysis.

Demonstrates quick online re-planning in cluttered, dynamic settings.

Abstract

Computing kinodynamically feasible motion plans and repairing them on-the-fly as the environment changes is a challenging, yet relevant problem in robot-navigation. We propose a novel online single-query sampling-based motion re-planning algorithm - PiP-X, using finite-time invariant sets - funnels. We combine concepts from sampling-based methods, nonlinear systems analysis and control theory to create a single framework that enables feedback motion re-planning for any general nonlinear dynamical system in dynamic workspaces. A volumetric funnel-graph is constructed using sampling-based methods, and an optimal funnel-path from robot configuration to a desired goal region is then determined by computing the shortest-path subtree in it. Analysing and formally quantifying the stability of trajectories using Lyapunov level-set theory ensures kinodynamic feasibility and guaranteed set-invariance of the solution-paths. The use of incremental search techniques and a pre-computed library of motion-primitives ensure that our method can be used for quick online rewiring of controllable motion plans in densely cluttered and dynamic environments. We represent traversability and sequencibility of trajectories together in the form of an augmented directed-graph, helping us leverage discrete graph-based replanning algorithms to efficiently recompute feasible and controllable motion plans that are volumetric in nature. We validate our approach on a simulated 6DOF quadrotor platform in a variety of scenarios within a maze and random forest environment. From repeated experiments, we analyse the performance in terms of algorithm-success and length of traversed-trajectory.