The equilibrium shape of a continuum robot is resulted from both its internal actuation and the external physical interaction with a surrounding environment. A fast and accurate shape estimation method (i) can be used as a feedback to compensate for more accurate motion; and (ii) can reveal rich information about physical interactions (e.g. instrument-anatomy contacts / forces during a surgery). From a prior work that demonstrated an offline calibration of continuum robots, we adopt its shape modal representation and error propagation models that include identification Jacobians. In this work, we present an iterative observer approach to enable online shape estimation. We develop a dual Extended Kalman Filter (EKF) to estimate both the robot state and the shape modal parameters. The dual EKF provides robust estimation on (i) the configuration space variables that are controllable and driven by internal actuation; and (ii) the modal coefficients representing homotopies of shape families that are governed by the physical interactions with the environment. We report results from simulation studies in this work, and plan to investigate methods in the future to use the proposed approach for predicting physical interactions.

翻译：连续机器人的平衡形状来自其内部振动和与周围环境的外部物理互动。快速和准确的形状估计方法(一) 可用来作为反馈,以补偿更准确的运动;和(二) 能够揭示关于物理互动的丰富信息(例如仪器-剖面接触/手术期间的力)。从先前显示连续机器人离线校准的工作来看,我们采用了其形状模式表达和错误传播模型,其中包括识别Jacobian人。在这项工作中,我们提出了一个迭代观察者方法,以便能够进行在线形状估计。我们开发了一个双倍扩展的Kalman过滤器(EKF),以估算机器人状态和形状模式参数。双倍扩展的EKF对(一) 可控制的空间变量和由内部动作驱动的空间变量提供了可靠的估计;以及(二) 代表受与环境物理互动制约的形状家庭同型体的模型系数。我们报告这项工作的模拟研究结果,并计划今后采用拟议的方法来预测物理互动。