Roadmaps with Gaps over Controllers: Achieving Efficiency in Planning under Dynamics

TL;DR

The accompanying experimental evaluation shows that the approach significantly improves the computational efficiency of motion planning on various benchmarks, including physics-based vehicular models on uneven and varying friction terrains as well as a quadrotor under air pressure effects.

Abstract

This paper aims to improve the computational efficiency of motion planning for mobile robots with non-trivial dynamics through the use of learned controllers. Offline, a system-specific controller is first trained in an empty environment. Then, for the target environment, the approach constructs a data structure, a "Roadmap with Gaps," to approximately learn how to solve planning queries using the learned controller. The roadmap nodes correspond to local regions. Edges correspond to applications of the learned controller that approximately connect these regions. Gaps arise as the controller does not perfectly connect pairs of individual states along edges. Online, given a query, a tree sampling-based motion planner uses the roadmap so that the tree's expansion is informed towards the goal region. The tree expansion selects local subgoals given a wavefront on the roadmap that guides towards the goal. When the controller cannot reach a subgoal region, the planner resorts to random exploration to maintain probabilistic completeness and asymptotic optimality. The accompanying experimental evaluation shows that the approach significantly improves the computational efficiency of motion planning on various benchmarks, including physics-based vehicular models on uneven and varying friction terrains as well as a quadrotor under air pressure effects.

Figures (10)

• Figure 1: Solution trajectories (thick lines) and planning trees (thin lines) for a MuSHR vehicle over an uneven terrain in MuJoCo. The cost function is trajectory duration, which is impacted by the uneven terrain. The proposed expansion method for kinodynamic planning (left) leverages a "Roadmap with Gaps" to avoid difficult terrain resulting in shorter duration solutions. The alternative expansion (right), which samples random local goals, navigates the rough hills less effectively. It results in a shorter distance path but a much slower trajectory. Planning time was 60s for both methods.
• Figure 2: Stages of the proposed pipeline. Offline: A controller is trained in an empty environment. The roadmap with gaps is built over the robot's free C-space in a target environment. Online: Given a new query $(x_0,x_G)$, a wavefront is computed over the roadmap. At every iteration of the tree sampling-based planner, a local goal is computed given the wavefront information, and a candidate control is propagated towards the local goal via the trained controller.
• Figure 3: (a) A Roadmap with Gaps consists of vertices (configurations, represented as dotted boxes). The roadmap's directional edges (dotted lines) correspond to where the controller was successfully executed from the source to the target configuration, given some tolerance. (b) For a new planning query $(x_0, x_G)$, the start $q_0$ and goal $q_G$ are added to the roadmap. (c) Due to gaps, naively following the roadmap's shortest path to the goal may not be feasible.
• Figure 4: Roadmap-Guided Expansion ( RoGuE): Given the roadmap with gaps in an environment (transparent) and the current planning tree (opaque), RoGuE selects informed local goals for the controller $\pi$. The closest roadmap node $q_\text{near}$ to the selected tree node $x_\text{sel}$ is identified. Its successor is passed as the local goal $q_\text{lg}$ to the controller. This expansion adds a new tree node $x_\text{new}$.
• Figure 5: Physically simulated benchmarks using MuJoCo. Top: (L-R) Maze, Terrain. Bottom: (L-R) Friction, Quadrotor.