Systems and methods for the real-time determination of tire normal forces

A method for determining a tire normal force (Fz) in a device having a plurality of tires, a controller and a suspension system with at least one suspension sensor and at least one inertial measurement unit (IMU), the method comprising:

• obtaining suspension data (S) via the at least one suspension sensor;
• obtaining acceleration data (u) via the at least one IMU;
• obtaining a transformation matrix (T) based on a plurality of predefined parameters, via the controller,
• using the controller, obtaining the respective tire normal forces (Fzi(t), i=1 . . . n) by multiplying the suspension data (S) with the sum transformation matrix (Ts) and a suspension compliance matrix (τs) that takes into account the effects of suspension compliance, and adding a horizontal dynamics matrix (Tu) that characterizes the influence of horizontal dynamics through unsprung inertia forces, multiplied by the IMU accelerations matrix (u), a the matrix column of detected accelerations such that:
• {tilde over (F)}z=[TS+τS(p)]{tilde over (S)}+Tuũ;
• wherein the plurality of tires includes two laterally-spaced tires, such that the two laterally-spaced tires are both on one of the front axle and the rear axle;
• wherein the plurality of predefined parameters includes:
• a first distance (a) from a front axle of the device to a center of gravity of the device;
• a second distance (b) from a rear axle of the device to the center of gravity of the device;
• a track width (2d) between respective first and second centerlines of the two laterally-spaced tires;
• a roll moment of inertia (Ixx) of the device;
• a pitch moment of inertia (Iyy) of the device;
• a sprung mass (M) of the device;
• and
• respective masses (mi) of each of the plurality of tires,
• wherein the first tire has a first mass (m1);
• and
• wherein the transformation matrix (T) includes a first row having first, second, third and fourth coefficients (T11, T12, T13, T14) based at least partially on the first mass (m1), the first distance (a), the second distance (b), the track width (2d), the roll moment of inertia (Ixx), the pitch moment of inertia (Iyy) and the sprung mass (M).

A device comprising:

• a plurality of tires;
• a suspension system operatively connected to the plurality of tires;
• at least one suspension sensor operatively connected to the suspension system and configured to provide suspension data (S);
• at least one inertial measurement unit (IMU) configured to detect and provide an accelerations matrix (u) defined as:
• u=[ax ay aψ]T, and
• a controller operatively connected to the at least one suspension sensor and having a processor and tangible, non-transitory memory on which is recorded instructions for executing a method for determining respective tire normal forces (Fzi(t), i=1 . . . n) for one or more of the plurality of tires, based at least partially on the suspension data (S), the respective tire normal forces being operative to adjust operation of the wheeled device;
• wherein execution of the instructions by the processor causes the controller to determine a transformation matrix (Ts) based on a plurality of predefined parameters;
• wherein the suspension data (S) includes respective real-time suspension forces (Si(t), i=1 . . . n) for each of the plurality of tires;
• and
• wherein the controller is configured to obtain the respective tire normal forces (Fzi(t), i=1 . . . n) by multiplying the suspension data (S) with the sum transformation matrix (Ts) and a suspension compliance matrix (τs) that takes into account the effects of suspension compliance, and adding a horizontal dynamics matrix (Tu) that characterizes the influence of horizontal dynamics through unsprung inertia forces, multiplied by the IMU accelerations matrix (u), a the matrix column of detected accelerations such that:
• {tilde over (F)}z=[TS+τS(p)]{tilde over (S)}+Tuũ.