Development of Linear Battery Model for Path Planning with Mixed Integer Linear Programming: Simulated and Experimental Validation

Abstract

Mixed Integer Linear Programs (MILPs) are often used in the path planning of both ground and aerial vehicles. Such a formulation of the path planning problem requires a linear objective function and constraints, limiting the fidelity of the tracking of vehicle states. One such state often used is the charge level of the on board battery. High-fidelity battery state estimation requires nonlinear differential equations to be solved. This state estimation is vital in path planning to ensure flyable paths, however when using a linear path planning problem cannot implement these nonlinear models. Poor accuracy in battery estimation during the path planning runs the risk of the planned path being feasible by the estimation model but in reality will deplete the battery to a critical level, resulting in a dangerous planned path. To the end of higher accuracy battery estimation within a linear framework, we test a simple linear battery model which predicts the change in state-of-charge (SOC) of a battery given a power draw, time duration, and current SOC in the context of an a-priori path planning problem. This context differentiates itself from real-time estimation. In ahead-of-time path planning, the changes to battery draw are often assumed as a series of constant power draws as opposed to rapidly changing power draw which may occur in real-time battery tracking and estimation. The linear battery model is presented and then tested against alternate models in both numerical and in experimental tests. Further, the effect of the proposed linear model on the time-to-solve a resource constrained shortest path problem is also evaluated, where two different algorithms are used to solve the path planning problem. It is seen that the linear model performs well in battery state estimation while remaining implementable in a Linear Program or MILP, with minimal effect on the time-to-solve. This provides what we consider to be a worthwhile trade-off in improved accuracy relative to increased time-to-solve.