Improved Jacobian matrix estimation applied to snake robots

Two manipulator Jacobian matrix estimators for constrained planar snake robots are developed and tested, which enables the implementation of Jacobian-based obstacle-aided locomotion (OAL) control schemes. These schemes use obstacles in the robot's vicinity to obtain propulsion. The devised estimators infer manipulator Jacobians for constrained planar snake robots in situations where the positions and number of surrounding obstacle constraints might change or are not precisely known. The first proposed estimator is an adaptation of contemporary research in soft robots and builds on convex optimization. The second estimator builds on the unscented Kalman filter. By simulations, we evaluate and compare the two devised algorithms in terms of their statistical performance, execution times, and robustness to measurement noise. We find that both algorithms lead to Jacobian matrix estimates that are similarly useful to predict end-effector movements. However, the unscented filter approach requires significantly lower computing resources and is not poised by convergence issues displayed by the convex optimization-based method. We foresee that the estimators may have use in other fields of research, such as soft robotics and visual servoing. The estimators may also be adapted for use in general non-planar snake robots.