2023/03/31 by Simoes, Alexandre Anahory, Liñán, Maria Barbero, Colombo, Leonardo +1
#FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2303.17917
Retractions maps are used to define a discretization of the tangent bundle of the configuration manifold as two copies of the configuration manifold where the dynamics take place. Such discretization maps can be conveniently lifted to a higher-order tangent bundle to construct geometric integrators for the higher-order Euler-Lagrange equations. Given a cost function, an optimal control problem for fully actuated mechanical systems can be understood as a higher-order variational problem. In this paper we introduce the notion of a higher-order discretization map associated with a retraction map to construct geometric integrators for the optimal control of mechanical systems. In particular, we study applications to path planning for obstacle avoidance of a planar rigid body.