System and method for determining friction curve of tire

A method for calibrating a function of a tire friction of a vehicle traveling on a road, wherein the method uses a processor coupled to a memory, wherein the processor is coupled with stored instructions implementing the method, wherein the instructions, when executed by the processor carry out at least some steps of the method comprising:

• storing, by the memory, a probability distribution of the tire friction function, a motion model relating control inputs to the vehicle with a state of the vehicle, and a measurement model relating measurements of motion of the vehicle with the state of the vehicle, wherein the tire friction function is a nonlinear function describing a friction between a surface of the road and a tire of the vehicle as a function of wheel slip of a wheel of the vehicle, wherein the motion model includes the tire friction function, and wherein one or combination of the motion model and the measurement model is subject to noise;
• accepting motion data indicative of motion of the vehicle on the road, wherein the motion data include a sequence of the control inputs to the vehicle that moves the vehicle on the road and a corresponding sequence of the measurements of the motion of the vehicle moved by the sequence of the control inputs;
• updating iteratively the probability distribution of the tire friction function until a termination condition is met, wherein an iteration comprises:
• sampling the probability distribution of the tire friction function;
• determining a state trajectory of the vehicle to fit the sequence of the measurements according to the measurement model and the sequence of the control inputs according to the motion model including the sample of the tire friction function;
• and
• updating the probability distribution of the tire friction function based on the state trajectory of the vehicle;
• outputting at least one or a combination of the probability distribution of the tire friction function and the sample of the probability distribution of the tire friction function when the termination condition is met;
• determining, by a controller, a control command based on the tire friction function associated with the updated probability distribution of the tire friction function;
• and
• transmitting, by the controller, the control command to an actuator of the vehicle to move the vehicle on the road.

A non-transitory computer readable storage medium embodied thereon a program executable by a processor for performing a method, the method comprising:

• controlling the medium to store a probability distribution of the tire friction function, a motion model relating control inputs to the vehicle with a state of the vehicle, and a measurement model relating measurements of motion of the vehicle with the state of the vehicle, wherein the tire friction function is a nonlinear function describing a friction between a surface of a road and a tire of the vehicle as a function of wheel slip of a wheel of the vehicle, wherein the motion model includes the tire friction function, and wherein one or combination of the motion model and the measurement model is subject to noise, the method comprising:
• accepting motion data indicative of motion of the vehicle on the road, wherein the motion data include a sequence of the control inputs to the vehicle that moves the vehicle on the road and a corresponding sequence of the measurements of the motion of the vehicle moved by the sequence of the control inputs;
• updating iteratively the probability distribution of the tire friction function until a termination condition is met, wherein an iteration comprises:
• sampling the probability distribution of the tire friction function;
• determining a state trajectory of the vehicle to fit the sequence of the measurements according to the measurement model and the sequence of the control inputs according to the motion model including the sample of the tire friction function;
• and
• updating the probability distribution of the tire friction function based on the state trajectory of the vehicle;
• rendering at least one or a combination of the probability distribution of the tire friction function and the sample of the probability distribution of the tire friction function when the termination condition is met;
• determining, by a controller, a control command based on the tire friction function associated with the updated probability distribution of the tire friction function;
• and
• transmitting, by the controller, the control command to an actuator of the vehicle to move the vehicle on the road.