Knowing the state of a robot is critical for many problems, such as feedback control. For continuum robots, state estimation is incredibly challenging. First, the motion of a continuum robot involves many kinematic states, including poses, strains, and velocities. Second, all these states are infinite-dimensional due to the robot's flexible property. It has remained unclear whether these infinite-dimensional states are observable at all using existing sensing techniques. Recently, we presented a solution to this challenge. It was a mechanics-based dynamic state estimation algorithm, called a Cosserat theoretic boundary observer, which could recover all the infinite-dimensional robot states by only measuring the velocity twist of the tip. In this work, we generalize the algorithm to incorporate tip pose measurements for more tuning freedom. We also validate this algorithm offline using recorded experimental data of a tendon-driven continuum robot. Specifically, we feed the recorded tension of the tendon and the recorded tip measurements into a numerical solver of the Cosserat rod model based on our continuum robot. It is observed that, even with purposely deviated initialization, the state estimates by our algorithm quickly converge to the recorded ground truth states and closely follow the robot's actual motion.

翻译：了解机器人的状态对于反馈控制等许多问题至关重要。对于连续体机器人，状态估计极具挑战性。首先，连续体机器人的运动涉及多种运动学状态，包括位姿、应变和速度。其次，由于机器人的柔性特性，所有这些状态都是无限维的。目前尚不清楚利用现有传感技术是否能够观测这些无限维状态。近期，我们提出了一种解决这一挑战的方案。这是一种基于力学原理的动态状态估计算法，称为Cosserat理论边界观测器，其通过仅测量末端的速度旋量即可恢复所有无限维机器人状态。在本工作中，我们对该算法进行推广，引入末端位姿测量以提供更多调优自由度。同时，我们利用肌腱驱动连续体机器人的实验记录数据对该算法进行离线验证。具体而言，我们将记录的肌腱张力与末端测量数据输入基于连续体机器人的Cosserat杆模型数值求解器。观测结果表明，即使初始化存在刻意偏差，我们的算法所估计的状态仍能快速收敛到记录的真实状态，并紧密跟踪机器人的实际运动。