Insights into the Constrained Hamiltonian dynamics formulation of the Unicycle

Modeling the dynamics of a unicycle problem with its nonholonomic constraints has been a prime example for validating various dynamic formulation, namely, the Hamiltonian and Lagrangian formulation. Both methods introduce Lagrange multipliers to enforce the constraints, hence adding extra variables and equations which renders the equations of motion into Differential-Algebraic-Equations. In this paper we use the constrained Hamiltonian and a Poisson structure to express the full dynamics of the Unicycle in a series of first-order differential equations which does not require the use of Lagrange multipliers. Finally, we simulate the three formulations to validate that the solutions are numerically equivalent.