用贝塞尔多项式构建可达多面体，高效验证分层控制系统的运动规划安全性。
Bezier Reachable Polytopes: Efficient Certificates for Robust Motion Planning with Layered Architectures
- 基于贝塞尔多项式的几何特性，生成可约束轨迹的多面体证书
- 实现长时序任务的计算可行的安全性验证
- 适合需可靠保障的机器人分层控制系统设计
控制架构常以分层方式实现，将独立设计的模块组合完成复杂任务。为确保此类分层框架的可靠性，需在设计阶段考虑各层级的能力与限制及其连接关系。为此，本文提出贝塞尔可达多面体——一种针对贝塞尔多项式参考轨迹空间中可达点的证书。该方法捕获低层控制器在满足状态和输入约束下可跟踪的轨迹集合，并利用贝塞尔多项式的几何特性保持高效的多面体表示。结果表明，这些证书可作为分层架构的构造性工具，使长时序任务能在计算可处理的范围内进行推理。
原文摘要 · Abstract (English)
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.
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