Deeply-learnt damped least-squares (DL-DLS) method for inverse kinematics of snake-like robots.

Recently, snake-like robots are proposed to assist experts during medical procedures on internal organs via natural orifices. Despite their well-spelt advantages, applications in radiosurgery is still hindered by absence of suitable designs required for spatial navigations within clustered and confined parts of human body, and inexistence of precise and fast inverse kinematics (IK) models. In this study, a deeply-learnt damped least squares method is proposed for solving IK of spatial snake-like robot. The robot's model consists of several modules, and each module has a pair of serial-links connected with orthogonal twists. For precise control of the robot's end-effector, damped least-squares approach is used to minimize error magnitude in a function modeled over analytical Jacobian of the robot. This is iteratively done until an apt joint vector needed to converge the robot to desired positions is obtained. For fast control and singularity avoidance, a deep network is built for prediction of unique damping factor required for each target point in the robot's workspace. The deep network consists of 11 x 15 array of neurons at the hidden layer, and deeply-learnt with a huge dataset of 877,500 data points generated from workspace of the snake robot. Implementation results for both simulated and actual prototype of an eight-link model of the robot show the effectiveness of the proposed IK method. With error tolerance of 0.01 mm, the proposed method has a very high reachability measure of 91.59% and faster mean execution time of 9.20 (±16.92) ms for convergence. In addition, the method requires an average of 33.02 (±39.60) iterations to solve the IK problem. Hence, approximately 3.6 iterations can be executed in 1 ms. Evaluation against popularly used IK methods shows that the proposed method has very good performance in terms of accuracy and speed, simultaneously.