Controlling the automatic starting of a motor vehicle uphill in a μ split situation

A vehicle control system comprising:

• sensors for determining a road gradient and a driven wheel speed;
• and
• a controller programmed to
• while the vehicle is stationary, set an initial locking torque of an electronic limited slip differential based on the road gradient;
• and
• in response to detecting vehicle movement, set the locking torque based on a slip ratio of a slowest driven wheel, wherein the slip ratio SRxx for the slowest driven wheel is calculated according to
• SRxx=(Vxx−VRef)/VCrit in response to a reference velocity VRef being between 0 and a critical velocity VCrit, and according to
• SRxx=(Vxx−VRef)/VRef in response to the reference velocity being greater than the critical velocity.

A vehicle comprising:

• a first axle having first and second driven wheels;
• a second axle having third and fourth wheels;
• an electronic limited slip differential connected between the first and second driven wheels, wherein the differential is configured to control rotation of the first and second driven wheels based on a locking torque of the differential;
• and
• a controller programmed to
• while the vehicle is stationary, set an initial valve for the locking torque based on a road gradient, wherein the initial locking torque is greater than a lower limiting value of torque capacity required for the vehicle to travel uphill at the road gradient with only one of the driven wheels being powered, and the initial locking torque is less than an upper limiting value of torque capacity such that powertrain torque does not cause the slowest of the driven wheels to spin;
• and
• in response to detecting vehicle movement and detecting a mu split condition in which the first wheel has a higher coefficient of friction with the road than the second wheel, adjust the locking torque based on a slip ratio of the first wheel, wherein the slip ratio of the first wheel is based on a ratio of a speed of the first wheel and a critical velocity if a speed of a slower of the third and fourth wheels is between 0 and the critical velocity, and is based on a ratio of the speed of the first wheel and the speed of the slower of the third and fourth wheels if the speed of the slower of the third and fourth wheels is greater than the critical velocity.