On Trajectory Optimization of an Electric Vehicle Eligius M.T. Hendrix 1[0000-0003-1572-1436] , Ana Maria A.C. Rocha 2[0000-0001-8679-2886] , and Inmaculada Garc´ ıa 1[0000-0002-1138-2118] 1 Computer Architecture, Universidad de M´ alaga, 29080 M´ alaga, Spain {eligius,igarciaf}@uma.es 2 ALGORITMI Center, University of Minho, 4710-057 Braga, Portugal arocha@dps.uminho.pt Abstract. The efficient control of electrical vehicles may contribute to sustainable use of energy. In recent studies, a model has been analyzed and several algorithms based on branch and bound have been presented. In this work, we discuss a reformulated model on the control of an elec- tric vehicle based on the minimization of the energy consumption during an imposed displacement. We will show that similar results can be ob- tained by applying standard software. Moreover, this paper shows that the specified control problem can be handled from a dynamic program- ming perspective. Keywords: Electric vehicle; Energy optimization; Dynamic program- ming; Nonlinear optimization; Optimal Control; Real-Time Control 1 Introduction Efficient use of energy for transportation is of utmost importance. Efficient con- trol of electric vehicles may lead to a more sustainable world. The literature on control of hybrid and electric vehicles has increased considerably over the last decade [6, 10, 11, 14]. Literature on control typically focuses on continuous control using theory on the use of the Hamiltonian and co-states. A simplified electric vehicle energy consumption model is presented in [7] and evaluated on standard driving cycles, whereas [15] presents a method to evalu- ate the real driving energy consumptions of electric vehicles. A simple electric vehicle energy consumption model that captures instantaneous braking energy regeneration as a function of the vehicle deceleration level can be found in [3]. A computationally efficient simulation model for estimating the energy consump- tion of electric vehicles is developed in [4]. In [13], a general formulation of energy-efficient driving of electric vehicles is presented, that covers several dis- tinct scenarios and the most-adopted solution techniques. In [8, 9], a model for the control of a trajectory of a completely electric vehicle has been described. The final methodology suggested in those papers is a branch and bound (B&B) approach. This approach is counter-intuitive, as it does not make use of the dynamic characteristic of the problem. Similarly, a