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In this paper we derive the dynamic equations of a race-car model viaLie-group methods. Lie-group methods are nowadays quite familiar tocomputational dynamicists and roboticists, but their diffusion within thevehicle dynamics community is still limited. We try to bridge this gap byshowing that this framework merges gracefully with the Articulated BodyAlgorithm (ABA) and enables a fresh and systematic formulation of the vehicledynamics. A significant contribution is represented by a rigorousreconciliation of the ABA steps with the salient features of vehicle dynamics,such as road-tire interactions, aerodynamic forces and load transfers. Theproposed approach lends itself both to the definition of direct simulationmodels and to the systematic assembly of vehicle dynamics equations required,in the form of equality constraints, in numerical optimal control problems. Weput our approach on a test in the latter context which involves the solution ofminimum lap-time problem (MLTP). More specifically, a MLTP for a race car onthe N\"urburgring circuit is systematically set up with our approach. Theequations are then discretized with the direct collocation method and solvedwithin the CasADi optimization suite. Both the quality of the solution and thecomputational efficiency demonstrate the validity of the presented approach.

A Lie Group-Based Race Car Model for Systematic Trajectory Optimization on 3D Tracks