通过近似模拟实现模板模型和锚模型之间的形式化连接
Formal Connections between Template and Anchor Models via Approximate Simulation
摘要：
线性倒立摆（LIP）和弹簧加载倒立摆（SLIP）等降阶模板模型是控制高维人形机器人的常用工具。然而，模板和全身模型之间的联系缺乏正式的基础，在集成控制器设计方面无法提供正式的保证。通过考虑近似模拟的概念，我们朝着解决这一差距迈出了一小步。从形式化方法中离散变迁系统的模拟关系出发，近似相似是指两个系统的输出保持$ε$ -接近。在本文中，我们考虑的情况下，通过规划与LIP模型的平衡控制。我们表明，平衡器近似模拟LIP和线性约束，保持地面接触的充分条件。这允许通过求解在完整模型中强制接触约束的二次规划来快速规划和重新规划模板模型。我们证明了这种规划和控制模式的有效性，在一个模拟的推恢复方案的平面4链路平衡器。
英文摘要：
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 $ε$-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.
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