The complex dynamics characterizing deformable terrain presents significant impediments toward the real-world viability of locomotive robotics, particularly for legged machines. We explore vertical, robotic jumping as a model task for legged locomotion on presumed-uncharacterized, nonrigid terrain. By integrating Gaussian process (GP)-based regression and evaluation to estimate ground reaction forces as a function of the state, a 1-D jumper acquires the capability to learn forcing profiles exerted by its environment in tandem with achieving its control objective. The GP-based dynamical model initially assumes a baseline rigid, noncompliant surface. As part of an iterative procedure, the optimizer employing this model generates an optimal control strategy to achieve a target jump height. Experiential data recovered from execution on the true surface model are applied to train the GP, in turn, providing the optimizer a more richly informed dynamical model of the environment. The iterative control-learning procedure was rigorously evaluated in experiment, over different surface types, whereby a robotic hopper was challenged to jump to several different target heights. Each task was achieved within ten attempts, over which the terrain’s dynamics were learned. With each iteration, GP predictions of ground forcing became incrementally refined, rapidly matching experimental force measurements. The few-iteration convergence demonstrates a fundamental capacity to both estimate and adapt to unknown terrain dynamics in application-realistic time scales, all with control tools amenable to robotic legged locomotion.

中文翻译：

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学习地形动力学：应用于机器人跳跃的高斯过程建模和优化控制适应框架

表征可变形地形的复杂动力学严重阻碍了机车机器人在现实世界中的可行性，特别是对于腿式机器。我们探索垂直、机器人跳跃作为在假定无特征、非刚性地形上进行腿运动的模型任务。通过集成基于高斯过程 (GP) 的回归和评估来估计作为状态函数的地面反作用力，一维跳线获得了学习其环境施加的强迫剖面的能力，同时实现其控制目标。基于 GP 的动力学模型最初假设基线刚性非柔顺表面。作为迭代过程的一部分，采用该模型的优化器生成最佳控制策略以实现目标跳跃高度。从在真实表面模型上执行恢复的经验数据用于训练 GP，反过来，为优化器提供更丰富的环境动态模型。迭代控制学习程序在不同表面类型的实验中得到了严格评估，其中机器人料斗面临跳跃到几个不同目标高度的挑战。每项任务都在十次尝试内完成，通过这些尝试了解地形的动态。随着每次迭代，地面强迫的 GP 预测逐渐完善，快速匹配实验力测量值。几次迭代收敛证明了在应用现实时间尺度上估计和适应未知地形动态的基本能力，所有这些都具有适合机器人腿运动的控制工具。