SUMMARYThe popular approach of assuming a control policy and then finding the largest region of attraction (ROA) (e.g., sum-of-squares optimization) may lead to conservative estimates of the ROA, especially for highly nonlinear systems. We present a sampling-based approach that starts by assuming an ROA and then finds the necessary control policy by performing trajectory optimization on sampled initial conditions. Our method works with black-box models, produces a relatively large ROA, and ensures exponential convergence of the initial conditions to the periodic motion. We demonstrate the approach on a model of hopping and include extensive verification and robustness checks.

中文翻译：

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动态平衡腿机器人的大范围吸引力控制策略：基于采样的方法

总结假设控制策略然后找到最大吸引区域（ROA）（例如平方和优化）的流行方法可能导致ROA的保守估计，特别是对于高度非线性系统。我们提出了一种基于采样的方法，首先假设 ROA，然后通过对采样的初始条件执行轨迹优化来找到必要的控制策略。我们的方法适用于黑盒模型，产生相对较大的 ROA，并确保初始条件对周期性运动的指数收敛。我们在跳跃模型上演示了该方法，并包括广泛的验证和稳健性检查。