Systems and methods for neural ordinary differential equation learned tire models

A system comprising:

• a processor;
• and
• a memory storing instructions that, when executed by the processor, cause the processor to:
• receive estimated tire forces and vehicle measurements;
• solve a second order differential equation in a repetitive manner until an error calculation based on a tire force function and the estimated tire forces reaches a minimum value, by:
• using a first predictive model to provide one or more inflection points and initial conditions based on the vehicle measurements,
• using a second and third predictive model to act as, respectively, exponents to a positive and a negative exponential equation based on the one or more inflection points, the initial conditions, and the vehicle measurements, and
• integrating the exponential equations to obtain the tire force function;
• and
• wherein the tire force function when applied to further vehicle measurements provides a tire force estimate.

A system comprising:

• a processor;
• and
• a memory storing instructions that, when executed by the processor, cause the processor to:
• receive vehicle measurements, one or more inflection points, and initial conditions;
• apply a first and second predictive model to act as, respectively, exponents to a positive and a negative exponential equation based on the one or more inflection points, the initial conditions, and the vehicle measurements;
• and
• perform integration of the exponential equations to obtain a tire force estimate.