テンプレートモデルとアンカーモデルの近似シミュレーションによる形式的接続
Formal Connections between Template and Anchor Models via Approximate Simulation
LIPモデルで計画したバランサ制御がLIPを近似シミュレートすることを示し、接地制約を満たす線形条件を導出して二次計画法で高速な計画・再計画を実現した。
著者: Vince Kurtz, Rafael Rodrigues da Silva, Patrick M. Wensing, Hai Lin
分類: cs.RO
原文アブストラクト
Reduced-order template models like the Linear Inverted Pendulum (LIP) and Spring-Loaded Inverted Pendulum (SLIP) are widely used tools for controlling high-dimensional humanoid robots. However, connections between templates and whole-body models have lacked formal underpinnings, preventing formal guarantees when it comes to integrated controller design. We take a small step towards addressing this gap by considering the notion of approximate simulation. Derived from simulation relations for discrete transition systems in formal methods, approximate similarity means that the outputs of two systems can remain $\epsilon$-close. In this paper, we consider the case of controlling a balancer via planning with the LIP model. We show that the balancer approximately simulates the LIP and derive linear constraints that are sufficient conditions for maintaining ground contact. This allows for rapid planning and replanning with the template model by solving a quadratic program that enforces contact constraints in the full model. We demonstrate the efficacy of this planning and control paradigm in a simulated push recovery scenario for a planar 4-link balancer.
