A 2-DOF MultiBody Track Joint for Race Car Optimization

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.

We present a closed-loop framework for autonomous raceline optimization that combines NURBS-based trajectory representation, CMA-ES global trajectory optimization, and controller-guided spatial feedback. Instead of treating tracking errors as transient disturbances, our method exploits them as informative signals of local track characteristics via a Kalman-inspired spatial update. This enables the construction of an adaptive, acceleration-based constraint map that iteratively refines trajectories toward near-optimal performance under spatially varying track and vehicle behavior. In simulation, our approach achieves a 17.38% lap time reduction compared to a controller parametrized with maximum static acceleration. On real hardware, tested with different tire compounds ranging from high to low friction, we obtain a 7.60% lap time improvement without explicitly parametrizing friction. This demonstrates robustness to changing grip conditions in real-world scenarios.

Articulated objects used in simulation and embodied AI are typically specified by geometry and kinematic structure, but lack the fine-grained dynamical effects that govern realistic mechanical behavior, such as frictional holding, detents, soft closing, and snap latching. Existing approaches either ignore the detailed structure of dynamics entirely, or use simple models with limited expressiveness. We introduce JODA, a framework for generating joint-level dynamics as a structured three-channel field over the joint degree of freedom, capturing conservative forces, dry friction, and damping. Instantiated using shape-constrained piecewise cubic interpolation (PCHIP), this formulation defines a compact and expressive function space that is both interpretable and compatible with differentiable simulation. Building on this representation, we develop methods for inferring and refining joint dynamics from multimodal inputs. Given visual observations and joint context, a vision-language model proposes structured dynamical primitives, which are composed into a unified dynamics field. The resulting representation supports both direct manipulation and gradient-based refinement. We demonstrate that JODA enables plausible and controllable modeling of diverse joint behaviors, providing a unified interface for inference, editing, and optimization. Code and example assets with their generated profiles will be released upon publication.