Operating complex real-world systems, such as soft robots, can benefit from precise predictive control schemes that require accurate state and model knowledge. This knowledge is typically not available in practical settings and must be inferred from noisy measurements. In particular, it is challenging to simultaneously estimate unknown states and learn a model online from sequentially arriving measurements. In this paper, we show how a recently proposed gray-box system identification tool enables the estimation of a soft robot's current pose while at the same time learning a bending stiffness model. For estimation and learning, we rely solely on a nominal constant-curvature robot model and measurements of the robot's base reactions (e.g., base forces). The estimation scheme -- relying on a marginalized particle filter -- allows us to conveniently interface nominal constant-curvature equations with a Gaussian Process (GP) bending stiffness model to be learned. This, in contrast to estimation via a random walk over stiffness values, enables prediction of bending stiffness and improves overall model quality. We demonstrate, using real-world soft-robot data, that the method learns a bending stiffness model online while accurately estimating the robot's pose. Notably, reduced multi-step forward-prediction errors indicate that the learned bending-stiffness GP improves overall model quality.

翻译：操作复杂的现实世界系统（如软体机器人）可从精确的预测控制方案中获益，这类方案需要准确的状态和模型知识。在实际应用中，这类知识通常无法直接获取，必须从含噪声的测量数据中推断得出。尤其具有挑战性的是如何从顺序到达的测量数据中同时估计未知状态并在线学习模型。本文展示了最近提出的一种灰箱系统辨识工具如何能够同时估计软体机器人的当前位姿并学习其弯曲刚度模型。对于估计与学习过程，我们仅依赖于标称的等曲率机器人模型以及对机器人基座反作用力（例如基座力）的测量。该估计方案——基于边缘化粒子滤波器——使我们能够方便地将标称等曲率方程与待学习的高斯过程（GP）弯曲刚度模型相结合。与通过对刚度值进行随机游走来估计的方法相比，此方法能够预测弯曲刚度并提升整体模型质量。我们利用真实世界的软体机器人数据证明，该方法能够在准确估计机器人位姿的同时在线学习弯曲刚度模型。值得注意的是，降低的多步前向预测误差表明，学习到的高斯过程弯曲刚度模型提升了整体模型质量。