Feasible trajectory planning for minimum time manoeuvring

Path planning models are often only founded by geometric calculations and do not consider the vehicle's limitations. In critical situations, path following is crucial, as a departure from the trajectory can have significant consequences. It is therefore necessary to define trajectories which the vehicle has the capacity to follow, i.e. feasible trajectories. This paper presents a framework for feasible trajectory generation for use in minimum time manoeuvres (MTM). The feasibility of trajectories is evaluated against a Quasi-Steady-State (QSS) acceleration envelope and jerk constraints. The vehicle's dynamics feasibility is assessed through a new exact relation of vehicle trajectory curvature that is expressed relative to a track reference line. The physical restriction of these constraints, relative to the vehicle's transient capabilities, implies that QSS feasibility assessments also extend to the transient vehicle. Minimum curvature trajectories are also reviewed. Results are presented for four examples. First, a constant radius example highlights differences in the minimum curvature cost models. The second example compares minimum curvature trajectories against MTM solutions for the Tempelhof Airport Street Circuit (Berlin), resulting in a new minimum curvature objective. The last two examples, straight road and Adria International Raceway, show that the feasible trajectory model is a good predictor of the QSS handling limits, indicating its ability to define feasible trajectories. The maximum spread of results is $ 3.2\% $ 3.2%. A friction ellipse model is additionally presented for comparison against the Normal-Tangential-Acceleration (NTA) surface. Friction ellipse results showed to be comparable if the acceleration envelope alignment is sufficient.