The trident snake robot is a mechanical device that serves as a demanding testbed for motion planning and control algorithms of constrained non-holonomic systems. This paper provides the equations of motion and addresses the motion planning problem of the trident snake with dynamics, equipped with either active joints (undulatory locomotion) or active wheels (wheeled locomotion). Thanks to a partial feedback linearization of the dynamics model, the motion planning problem basically reduces to a constrained kinematic motion planning. Two kinds of constraints have been taken into account, ensuring the regularity of the feedback and the collision avoidance between the robot's arms and body. Following the guidelines of the endogenous configuration space approach, two Jacobian motion planning algorithms have been designed: the singularity robust Jacobian algorithm and the imbalanced Jacobian algorithm. Performance of these algorithms have been illustrated by computer simulations.
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