Locomotion Dynamics of an Underactuated Three-Link Robotic Vehicle

The wheeled three-link snake robot is a well-known example of an underactuated system modelled using nonholonomic constraints, preventing lateral slippage (skid) of the wheels. A kinematically controlled configuration assumes that both joint angles are directly prescribed as phase-shifted periodic input. In another configuration of the robot, only one joint is periodically actuated while the second joint is passively governed by a visco-elastic torsion spring. In our work, we constructed the two configurations of the wheeled robot and conducted motion experiments under different actuation inputs. Analysis of the motion tracking measurements reveals a significant amount of wheels' skid, in contrast to the assumptions used in standard nonholonomic models. Therefore, we propose modified dynamic models which include wheels' skid and viscous friction forces, as well as rolling resistance. After parameter fitting, these dynamic models reach good agreement with the motion measurements, including effects of input's frequency on the mean speed and net displacement per period. This illustrates the importance of incorporating wheels' skid and friction into the system's model.