Vehicle operation around obstacles
A computer includes a processor and a memory, and the memory stores instructions executable by the processor to formulate a plurality of constraints, determine a final input modification to a nominal input that minimizes a cost function subject to the constraints, and actuate a component of a vehicle according to the nominal input and the final input modification. Each constraint indicates a respective obstacle relative to the vehicle. Each constraint is represented as a linear inequality in a two-dimensional space with dimensions for acceleration and steering angle. The nominal input includes a nominal acceleration and a nominal steering angle. The final input modification includes a final change to the nominal acceleration and a final change to the nominal steering angle. The computer determines the final input modification by individually calculating the cost function for a plurality of potential input modifications that are on the constraints.
1 . A computer comprising a processor and a memory, the memory storing instructions executable by the processor to:
formulate a plurality of constraints, each constraint indicating a respective obstacle relative to a vehicle, each constraint represented as a linear inequality in a two-dimensional space with dimensions for acceleration and steering angle;
determine a final input modification to a nominal input that minimizes a cost function subject to the constraints, the nominal input including a nominal acceleration and a nominal steering angle, the final input modification including a final change to the nominal acceleration and a final change to the nominal steering angle, by individually calculating the cost function for a plurality of potential input modifications that are on the constraints; and
actuate a component of the vehicle according to the nominal input and the final input modification to affect motion of the vehicle.
2 . The computer of claim 1 , wherein the instructions further include instructions to actuate a brake system of the vehicle according to a sum of the nominal acceleration and the final change to the nominal acceleration.
3 . The computer of claim 1 , wherein the instructions further include instructions to actuate a steering system of the vehicle according to a sum of the nominal steering angle and the final change to the nominal steering angle.
4 . The computer of claim 1 , wherein the instructions further include instructions to select at least one intersection point between two of the constraints in the two-dimensional space as one of the potential input modifications for individually calculating the cost function.
5 . The computer of claim 1 , wherein the instructions further include instructions to select at least one minimal-cost point having a lowest value of the cost function along one of the constraints in the two-dimensional space as one of the potential input modifications for individually calculating the cost function.
6 . The computer of claim 5 , wherein the instructions to select the at least one minimal-cost point include instructions to solve a closed-form expression for the at least one minimal-cost point.
7 . The computer of claim 1 , wherein the instructions further include instructions to sequentially calculate the cost function for the potential input modifications in a rule-based order.
8 . The computer of claim 1 , wherein the cost function is quadratic.
9 . The computer of claim 8 , wherein the cost function lacks a linear term.
10 . The computer of claim 1 , wherein the instructions further include instructions to:
determine that none of the constraints are constraining the final input modification; and
upon determining that none of the constraints are constraining the final input modification, select zero as the final change to the nominal acceleration and zero as the final change to the nominal steering angle.
11 . The computer of claim 1 , wherein at least one of the constraints is based on a control barrier function.
12 . The computer of claim 11 , wherein the at least one of the constraints is equivalent to a sum of a change with respect to time of the control barrier function and a function of the control barrier function exceeding a value.
13 . The computer of claim 1 , wherein the cost function increases with increasing change to the nominal acceleration.
14 . The computer of claim 1 , wherein the cost function increases with increasing change to the nominal steering angle.
15 . The computer of claim 1 , wherein the constraints are first constraints, minimizing the cost function is subject to a second constraint, and the second constraint is that a sum of the nominal acceleration and the final change to the nominal acceleration is within a preset value.
16 . The computer of claim 1 , wherein the constraints are first constraints, minimizing the cost function is subject to a second constraint, and the second constraint is that a sum of the nominal steering angle and the final change to the nominal steering angle is within a preset value.
17 . The computer of claim 1 , wherein the nominal input includes at least one of a value inputted by an operator or a value outputted by an algorithm for at least partially autonomously operating the vehicle.
18 . A method comprising:
formulating a plurality of constraints, each constraint indicating a respective obstacle relative to a vehicle, each constraint represented as a linear inequality in a two-dimensional space with dimensions for acceleration and steering angle;
determining a final input modification to a nominal input that minimizes a cost function subject to the constraints, the nominal input including a nominal acceleration and a nominal steering angle, the final input modification including a final change to the nominal acceleration and a final change to the nominal steering angle, by individually calculating the cost function for a plurality of potential input modifications that are on the constraints; and
actuating a component of the vehicle according to the nominal input and the final input modification to affect motion of the vehicle.
19 . The method of claim 18 , further comprising:
actuating a brake system of the vehicle according to a sum of the nominal acceleration and the final change to the nominal acceleration; and
actuating a steering system of the vehicle according to a sum of the nominal steering angle and the final change to the nominal steering angle.
20 . The method of claim 18 , further comprising sequentially calculating the cost function for the potential input modifications in a rule-based order.