Bezier Reachable Polytopes: Efficient Certificates for Robust Motion Planning with Layered Architectures

TL;DR

This paper introduces Bezier Reachable Polytopes, a novel method for certifying the set of feasible trajectories in layered control architectures, enhancing the efficiency and reliability of long-horizon motion planning.

Contribution

The paper proposes Bezier Reachable Polytopes as a new geometric certification tool that captures feasible trajectories in hierarchical control systems, improving tractability.

Findings

Efficient polytopic representation of reachable trajectories.

Enables reasoning about long-horizon tasks in layered architectures.

Provides guarantees for hierarchical control performance.

Abstract

Control architectures are often implemented in a layered fashion, combining independently designed blocks to achieve complex tasks. Providing guarantees for such hierarchical frameworks requires considering the capabilities and limitations of each layer and their interconnections at design time. To address this holistic design challenge, we introduce the notion of Bezier Reachable Polytopes -- certificates of reachable points in the space of Bezier polynomial reference trajectories. This approach captures the set of trajectories that can be tracked by a low-level controller while satisfying state and input constraints, and leverages the geometric properties of Bezier polynomials to maintain an efficient polytopic representation. As a result, these certificates serve as a constructive tool for layered architectures, enabling long-horizon tasks to be reasoned about in a computationally tractable manner.