Adwait Verulkar, Behzad Danaei, Srikanth Sivaramakrishnan, Ryan Trinter
原文摘要
A track fitting pipeline is presented that converts a measured racetrack point cloud into a closed, $C^4$ differentiable, three-dimensional surface model suitable for high-fidelity Modelica race-car optimization. The surface is a Monge patch, parametrised by a curvilinear arc-length coordinate measured along the minimum-curvature line (MCL) and a signed lateral offset, with a height polynomial of user-selectable degree capturing the cross-sectional elevation profile. The choice of MCL as the reference line is deliberate since anchoring the same surface on the geometric centre-line can cause adjacent normals to cross inside the drivable region on tight corners. The resulting non-injective parametrisation assigns multiple curvilinear addresses to the same three-dimensional point and returns invalid road geometry. The MCL is obtained from a quadratic program that minimises integrated curvature subject to track-boundary, periodicity, and jerk-regularisation constraints. By reducing total curvature while remaining within the track bounds, the MCL moves the region of parametrisation breakdown outside the drivable strip on all circuits studied, keeps the normal map injective across the full track width, and yields a more linear time-to-arc-length transformation for minimum lap-time problems. The fitted surface and the associated track widths are exported as periodic piecewise-quintic $C^4$ B-splines, solved as a nonlinear program.
Srikanth Sivaramakrishnan, Behzad Danaei, Adwait Verulkar, Ryan Trinter
原文摘要
TrackJoint is a Modelica MultiBody component that turns a three-dimensional road surface into a joint with two degrees of freedom. The two joint coordinates are the distance travelled along a reference line and the sideways offset from that line. Together they give the position, orientation and angular velocity of a single frame_b connector. All road geometry reaches the joint as a small set of periodic piecewise-quintic splines, so one component can represent any circuit whose splines have been fitted beforehand. The road constraint is closed with d'Alembert's principle. The two generalized forces that belong to the joint coordinates are set to zero, so no Lagrange multipliers are needed. The joint is connected to a multibody race car in Dymola and the pair is exported as one FMI~3.0 FMU. The same FMU is then used for time-domain simulation and for CasADi/IPOPT minimum lap-time optimization, with no change to the model in between. This works because the joint keeps the arc-length coordinate as a real state and publishes its time derivative, which is the quantity that lets the problem be rewritten with distance We report results for minimum lap time simulations on the Singapore Formula~1 circuit.