We consider a finite element approximation of the Hamilton-Jacobi-Bellman equation for the optimal control of switched systems. In particular, we show that the obtained finite dimensional problem belongs to a special class of problems that we already studied in a previous work. In that work, we also presented a simple and efficient solution algorithm.As an application, we present the problem of generating parking maneuvers for self-driving vehicles. The vehicle is described by a switched system. Each change between forward and backward motion is associated to a switching cost. This added cost penalizes the maneuvers with a larger number of direction changes and allows obtaining simpler and more human-like trajectories.

Fast numerical solution of optimal control problems for switched systems: An application to path planning / Laurini, M.; Consolini, L.; Locatelli, M.. - ELETTRONICO. - 2020-:(2020), pp. 9304280.4105-9304280.4110. (Intervento presentato al convegno 59th IEEE Conference on Decision and Control, CDC 2020 tenutosi a kor nel 2020) [10.1109/CDC42340.2020.9304280].

### Fast numerical solution of optimal control problems for switched systems: An application to path planning

#### Abstract

We consider a finite element approximation of the Hamilton-Jacobi-Bellman equation for the optimal control of switched systems. In particular, we show that the obtained finite dimensional problem belongs to a special class of problems that we already studied in a previous work. In that work, we also presented a simple and efficient solution algorithm.As an application, we present the problem of generating parking maneuvers for self-driving vehicles. The vehicle is described by a switched system. Each change between forward and backward motion is associated to a switching cost. This added cost penalizes the maneuvers with a larger number of direction changes and allows obtaining simpler and more human-like trajectories.
##### Scheda breve Scheda completa Scheda completa (DC)
2020
978-1-7281-7447-1
Fast numerical solution of optimal control problems for switched systems: An application to path planning / Laurini, M.; Consolini, L.; Locatelli, M.. - ELETTRONICO. - 2020-:(2020), pp. 9304280.4105-9304280.4110. (Intervento presentato al convegno 59th IEEE Conference on Decision and Control, CDC 2020 tenutosi a kor nel 2020) [10.1109/CDC42340.2020.9304280].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11381/2894708`
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