A branch-and-bound algorithm for energy-efficient control allocation with applications to planar motion control of electric ground vehicles

A globally optimal energy-efficient control allocation (EECA) is developed for planar motion control of electric ground vehicles (EGVs) with four in-wheel motors. Different from the distribution processes in previous EECA designs [19][21], which obtained optimal torque distributions locally due to the nonlinear/nonconvex characteristics of EECA formulation, this EECA approach based a branch-and-bound (B&B) method that can make the distributed control actuation achieve the global energy-optimal operating points. Based on a sequence of equivalent problem transformations and a linear relaxation programming, the global optimal programming can be solved by the B&B method through rewriting the EECA formulation into a polynomial fractional optimization problem. Simulation results of different EGV maneuvers indicate that less energy are consumed when the EECA scheme based on the B&B method is applied, in comparison with the energy consumptions of the identical maneuvers with the active-set algorithm.