Seminar Details
2015-06-16 (14.00) : Numerical optimal control on Lie groups with applications to constrained motion planning of multiple vehicles in SE(3)
At Euler building (A002)
Organized by Mathematical Engineering
Speaker :
Alessandro Saccon (Eindhoven University of Technology (TU/e))
Abstract :
The Lie group Projection Operator Approach is a recently developed iterative algorithm for solving continuous-time optimal control problems on Lie groups. In the talk, we will discuss the main ideas lying behind this numerical method. In particular, we will detail the role played by the second covariant derivative of a map between Lie groups in obtaining a linear-quadratic approximation to the optimal control problem. This approximation is key to compute the descent direction at each iteration of the algorithm. The implementation of this numerical method on a computer requires the integration of the system dynamics and of a differential Riccati equation (DRE) associated with the linear-quadratic approximation of the optimal control problem. Numerical examples will be provided to demonstrate the effectiveness of the numerical method and its quadratic converge rate to local minima satisfying the second order sufficient conditions (SSC) for optimality. The application of the algorithm to solving minimum energy constrained motion planning problems or multiple vehicles will conclude the talk.