Abstract
Achieving versatile and explosive motion with robustness against dynamic uncertainties is a challenging task. Introducing parallel compliance in quadrupedal design is deemed to enhance locomotion performance, which, however, makes the control task even harder. This work aims to address this challenge by proposing a general template model and establishing an efficient motion planning and control pipeline. To start, we propose a reduced-order template model-the dual-legged actuated spring-loaded inverted pendulum with trunk rotation-which explicitly models parallel compliance by decoupling spring effects from active motor actuation. With this template model, versatile acrobatic motions, such as pronking, froggy jumping, and hop-turn, are generated by a dual-layer trajectory optimization, where the singularity-free body rotation representation is taken into consideration. Integrated with a linear singularity-free tracking controller, enhanced quadrupedal locomotion is achieved. Comparisons with the existing template model reveal the improved accuracy and generalization of our model. Hardware experiments with a rigid quadruped and a newly designed compliant quadruped demonstrate that i) the template model enables generating versatile dynamic motion; ii) parallel elasticity enhances explosive motion. For example, the maximal pronking distance, hop-turn yaw angle, and froggy jumping distance increase at least by 25%, 15% and 25%, respectively; iii) parallel elasticity improves the robustness against dynamic uncertainties, including modelling errors and external disturbances. For example, the allowable support surface height variation increases by 100% for robust froggy jumping.
Abstract (translated)
实现具备广泛适应性和爆发力的运动，并且能够抵御动态不确定性，是一项挑战性任务。在四足动物设计中引入并行柔顺性被认为可以提高行走性能，但这却使控制任务变得更加困难。本研究旨在通过提出一个通用模板模型并建立高效的运动规划和控制系统来解决这一问题。 首先，我们提出了一个降阶的模板模型——具有躯干旋转功能的双足驱动弹簧加载倒立摆（Dual-Legged Actuated Spring-Loaded Inverted Pendulum with Trunk Rotation）。该模型明确地通过分离弹簧效应与主动电机驱动作用来建模并行柔顺性。利用这个模板模型，诸如跳跃、蛙跳和转向跃等广泛的杂技动作可以通过双层轨迹优化生成，在此过程中考虑到了无奇点的体旋转表示。 结合线性的无奇点跟踪控制器后，实现了增强型四足动物行走性能。与现有的模板模型相比，我们的模型在准确性和泛化性方面表现出显著改进。通过刚性四足机器人和新设计的柔顺四足机器人的硬件实验发现： 1. 模板模型能够生成多样化的动态运动； 2. 并行弹性增强了爆发力动作的表现能力。例如，最大跳跃距离、转向跃偏航角度及蛙跳距离至少分别增加了25%、15%和25%； 3. 并行弹性提高了对抗动态不确定性（包括建模误差和外部干扰）的鲁棒性。例如，在稳健型蛙跳中允许的支持面高度变化增加了一倍。 这些结果表明，所提出的模板模型及控制策略在提高四足机器人运动性能方面具有显著优势，并为未来的研究提供了坚实的基础。
URL
https://arxiv.org/abs/2504.12854
