The Jacobian is a matrix which relates the robot joint velocities to its end-effector velocities through a linear transformation parameterized by the joint states (see Section 3 for more details).

To do so, a generic strategy consists of calculating and then exploiting the manipulator Jacobian (or simply Jacobian) of the system. In contrast, the present work is part of an effort to achieve efficient, robust, and intelligent locomotor behavior by exploiting information about the geometry and mechanical properties of the surroundings of the robot. Many experimental systems for obstacle-aided locomotion (OAL) adapt to the environment in an implicit or heuristical manner only, with little utilization of mechanical sensor information. As of now, this is largely an unrealized potential. In principle, this makes snake robots suitable for moving and adapting to unknown and challenging environments, such as in rubble following landslides or collapsed buildings. Like their biological counterparts, and as explained in detail in Ariizumi and Matsuno (2017) Gray (1946), mechanical snakes move using an array of different propulsion techniques, such as lateral undulation, sinus lifting, and sidewinding. Snake robots are mechanisms designed to mimic biological snakes, which aspire to inherit the robustness and stability of biological snake locomotion. The estimators may also be adapted for use in general non-planar snake robots. We foresee that the estimators may have use in other fields of research, such as soft robotics and visual servoing. 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 find that both algorithms lead to Jacobian matrix estimates that are similarly useful to predict end-effector movements. By simulations, we evaluate and compare the two devised algorithms in terms of their statistical performance, execution times, and robustness to measurement noise. The second estimator builds on the unscented Kalman filter. The first proposed estimator is an adaptation of contemporary research in soft robots and builds on convex optimization. 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. These schemes use obstacles in the robot’s vicinity to obtain propulsion. 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.

Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway.Jostein Løwer*, Damiano Varagnolo and Øyvind Stavdahl

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