Trajectory optimization is a popular strategy for planning trajectories for robotic systems. However, many robotic tasks require changing contact conditions, which is difficult due to the hybrid nature of the dynamics. The optimal sequence and timing of these modes are typically not known ahead of time. In this work, we extend the Iterative Linear Quadratic Regulator (iLQR) method to a class of piecewise smooth hybrid dynamical systems by allowing for changing hybrid modes in the forward pass, using the saltation matrix to update the gradient information in the backwards pass, and using a reference extension to account for mode mismatch. We demonstrate these changes on a variety of hybrid systems and compare the different strategies for computing the gradients.

翻译：轨迹优化是规划机器人系统轨迹的流行战略。 但是,许多机器人任务需要改变接触条件,由于动态的混合性质,这很难改变接触条件。 这些模式的最佳顺序和时间通常不会事先知道。 在这项工作中,我们将线性线性二次曲线调节(iLQR)方法推广到一类零碎平稳的混合动态系统,允许改变前转路的混合模式,使用盐化矩阵更新后转路的梯度信息,并使用参考扩展来核算模式不匹配。 我们在各种混合系统中展示这些变化,比较计算梯度的不同战略。