Accurate prediction of shape and contact forces significantly improves the performance of a continuum robot during its operation in obstacle-laden environments. This paper presents an optimization-based mathematical framework to predict the bending profile of a cable-driven continuum robot in presence of obstacles. The kinematics model is derived from the concept of strain energy minimization and can easily incorporate obstacles as inequality constraints in the optimization-based approach. The location of point of contact can be identified by observing the Lagrange multipliers of the inequality constraints. Using the kinematics model and the principle of virtual work, a method to estimate the reaction forces at contact is proposed. The model shows high accuracy, with RMS error of 1.35 mm in prediction of the pose for experiments conducted on a 180 mm long robot prototype. Validation experiments are also conducted on the prototype by imposing contact at different locations on the robot. In all cases, the average error in predicting the contact force is found to be less than 1.0 g for applied loads ranging from 50 to 350 g.

准确预测形状和接触力可显着提高连续体机器人在充满障碍物的环境中运行时的性能。本文提出了一种基于优化的数学框架，用于预测存在障碍物的电缆驱动连续体机器人的弯曲轮廓。运动学模型源自应变能最小化的概念，并且可以轻松地将障碍物作为基于优化的方法中的不等式约束。可以通过观察不等式约束的拉格朗日乘子来确定接触点的位置。利用运动学模型和虚功原理，提出了一种估计接触反作用力的方法。该模型显示出高精度，RMS 误差为 1。35 毫米用于在 180 毫米长的机器人原型上进行的实验的姿势预测。还通过在机器人的不同位置施加接触来对原型进行验证实验。在所有情况下，对于 50 至 350 g 的施加载荷，预测接触力的平均误差小于 1.0 g。