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Trail-Braking (TB) is a common cornering technique used in rally racing to negotiate tight corners at (moderately) high speeds. In a previous paper by the authors it has been shown that TB can be generated as the solution to the minimum-time cornering problem, subject to fixed final positioning of the vehicle after the corner. A TB maneuver can then be computed by solving a non-linear programming (NLP). In this work we formulate an optimization problem by relaxing the final positioning of the vehicle with respect to the width of the road in order to study the optimality of late-apex trajectories typically followed by rally drivers. We test the results on a variety of corners. The optimal control inputs are approximated by simple piecewise linear input profiles defined by a small number of parameters. It is shown that the proposed input parameterization can generate close to optimal TB along the various corner geometries.

This paper proposes an approach that uses the road preview data to optimize a shift schedule for a vehicle equipped with an automatic transmission. The road preview is inferred here from the so-called electronic horizon of a digital map that includes road attributes such as road grade, curvature, segment speed limit, functional class, etc. The optimized shift schedule selects the gear ratio whose optimization is conducted through applying a hybrid model predictive control method to the powertrain system, which is modelled as the multiple plants associated with multiple gears together with engine models. The goal of this optimization of shift schedule includes improving real world fuel economy and drivability. The real-world fuel economy gains using the proposed approach are achieved through optimizing gear ratio w.r.t. the road grade variations of the road ahead.