We use dynamics formulation of skid-steer robot with an arc-length parametrized path description for path navigation of the robot in least possible time. We use Lagrangian formulation to derive dynamics of the robot and add the kinematic constraint to the dynamics using a parameter corresponding to internal force. This necessary conditions for the trajectory are established in terms of the path variable. The proposed methodology is experimentally evaluated for a circular and a custom trajectory. For the circular trajectory, it is demonstrated that the constraint can be removed by the choice of parameters. Moreover, the nature of the enforced constraint is demonstrated for the custom trajectory.

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