Symbolic-numeric efficient solution of optimal control problems for multibody systems

Abstract

This paper presents an efficient symbolic-numerical approach for generating and solving the Boundary Value Problem-Differential Algebraic Equation (BVP-DAE) originating from the variational form of the Optimal Control Problem (OCP). This paper presents the Method for the symbolic derivation, by means of symbolic manipulation software (Maple), of the equations of the OCP applied to a generic multibody system. The constrained problem is transformed into a non-constrained problem, by means of the Lagrange multipliers and penalty functions. From the first variation of the nonconstrained problem a BVP-DAE is obtained, and the finite difference discretization yields a non-linear systems. For the numerical solution of the non-linear system a damped Newton scheme is used. The sparse and structured jacobians is quickly inverted by exploiting the sparsity pattern in the solution strategy. The proposed method is implemented in an object oriented fashion, and coded in C++ language. Efficiency is ensured in core routines by using Lapack and Blas for linear algebra.

Green driving optimization of a series hybrid electric vehicle

“…Road geometry has been taken from maps.google.it and then converted into the curvature model (19), while edges have been removed by constraining the curvature to a maximum value |Θ| < 0.12 m −1 . Traffic is not considered and therefore the speed is not constrained to the behavior of other vehicles.…”

“…In this work the indirect approach has been used and the optimization problem has been converted into a two point boundary value problem. More details on the adopted approach may be found in [19], [30].…”

“…The contribution of the SCS developed in this paper results from its main features: it does not presuppose any specific shape for the optimal solution, instead it simultaneously optimises fuel consumption, power split and speed profile; it is developed and tested on a symbolic dynamic vehicle model that maintains an appropriate balance between complexity and accuracy of transient behaviour; and, it utilises computationally efficient optimal control software [19] with excellent convergence speed appropriate for real-time application.…”

A Virtual Rider for Motorcycles: Maneuver Regulation of a Multi-Body Vehicle Model

“…[26]. Written in the original coordinates, the nonlinear feedback (15) exponentially stabilizes the maneuver for (1). Such a might be developed using an LQR strategy if the transverse linearization is, e.g., uniformly or instantaneously controllable.…”

“…In the latter, the proposed rider model is composed of two parts. A path planning procedure, the optimal maneuver method [15], is used to compute the reference ground path and speed to be followed. The reference optimal trajectory is then stabilized using independent proportional-integral-derivative (PID) loops to control speed and lateral deviation.…”