Controllability and Stability Analysis of Planar Snake Robot Locomotion

• Published in: IEEE transactions on automatic control Vol. 56; no. 6; pp. 1365 - 1380
• Main Authors: Liljeback, P, Pettersen, K Y, Stavdahl, Øyvind, Gravdahl, J T
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-06-2011; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Biologically-inspired robots; Computer science; control theory; systems; Control system analysis; Control system synthesis; Control theory. Systems; Controllability; Drives; Exact sciences and technology; Friction; Joints; Linkage mechanisms, cams; Mechanical engineering. Machine design; Mobile robots; motion control; Orbits; Poincaré maps; Robotics; snake robot; Stability analysis; underactuated robots; Moving robot; Control program; Non linear control; Robot dynamics; snake robot; Exponential stability; Modeling; Local time; Poincaré maps; Robotics; Stabilizability; Time varying system; Biomimetics; Controllability; Poincaré map; Planar mechanism; Path following method; underactuated robots; Viscous friction; Periodic orbit; Non linear system; Equilibrium point; Locomotion; Underactuation; Asymptotic approximation; Feedback linearization; Motion control; Reptation model; Biologically-inspired robots
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2010.2088830

This paper contributes to the understanding of snake robot locomotion by employing nonlinear system analysis tools for investigating fundamental properties of snake robot dynamics. The paper has five contributions: 1) a partially feedback linearized model of a planar snake robot influenced by viscous ground friction is developed. 2) A stabilizability analysis is presented proving that any asymptotically stabilizing control law for a planar snake robot to an equilibrium point must be time-varying. 3) A controllability analysis is presented proving that planar snake robots are not controllable when the viscous ground friction is isotropic, but that a snake robot becomes strongly accessible when the viscous ground friction is anisotropic. The analysis also shows that the snake robot does not satisfy sufficient conditions for small-time local controllability (STLC). 4) An analysis of snake locomotion is presented that easily explains how anisotropic viscous ground friction enables snake robots to locomote forward on a planar surface. The explanation is based on a simple mapping from link velocities normal to the direction of motion into propulsive forces in the direction of motion. 5) A controller for straight line path following control of snake robots is proposed and a Poincaré map is investigated to prove that the resulting state variables of the snake robot, except for the position in the forward direction, trace out an exponentially stable periodic orbit.