The problem of calculating the minimum lap or maneuver time of a nonlinear vehicle, which is linearized at each time step, is formulated as a convex optimization problem. The formulation provides an alternative to previously used quasi-steady-state analysis or nonlinear optimization. Key steps are: the use of model predictive control; expressing the minimum time problem as one of maximizing distance traveled along the track centerline; and linearizing the track and vehicle trajectories by expressing them as small displacements from a fixed reference. A consequence of linearizing the vehicle dynamics is that nonoptimal steering control action can be generated, but attention to the constraints and the cost function minimizes the effect. Optimal control actions and vehicle responses for a 90 deg bend are presented and compared to the nonconvex nonlinear programming solution.
Minimum Maneuver Time Calculation Using Convex Optimization
Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement, and Control. Manuscript received July 29, 2011; final manuscript received January 1, 2013; published online March 28, 2013. Assoc. Editor: Alexander Leonessa.
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Timings, J. P., and Cole, D. J. (March 28, 2013). "Minimum Maneuver Time Calculation Using Convex Optimization." ASME. J. Dyn. Sys., Meas., Control. May 2013; 135(3): 031015. https://doi.org/10.1115/1.4023400
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