Smooth road reference for autonomous driving vehicles based on 2D constrained smoothing spline
According to some embodiments, a system determines a number of boundary areas having predetermined dimensions centered around each of a number of control points of a first reference line. The system selects a number of two-dimensional polynomials each representing a segment of an optimal reference line between adjacent control points. The system defines a set of constraints to the two-dimensional polynomials to at least ensure the two-dimensional polynomials passes through each of the boundary areas. The system performs a quadratic programming (QP) optimization on a target function such that a total cost of the target function reaches minimum while the set of constraints are satisfied. The system generates a second reference line representing the optimal reference line based on the QP optimization to control the ADV autonomously according to the second reference line.
1. A computer-implemented method to generate an optimal reference line for an autonomous driving vehicle (ADV), the method comprising:
generating a first reference line for controlling the ADV on a vehicular lane;
determining a plurality of boundary areas having predetermined dimensions centered around each of a plurality of control points of the first reference line;
selecting a plurality of two-dimensional polynomials each representing a segment of an optimal reference line between adjacent control points;
defining a set of constraints to the two-dimensional polynomials to at least ensure the plurality of two-dimensional polynomials passes through each of the plurality of boundary areas;
performing a quadratic programming (QP) optimization on a target function such that a total cost of the target function reaches minimum while the set of constraints are satisfied;
generating a second reference line representing the optimal reference line based on the QP optimization; and
controlling the ADV autonomously according to the second reference line.
2. The method of claim 1 , wherein adjacent control points of the plurality of control points are approximately equally spaced apart.
3. The method of claim 1 , wherein the boundary areas are boundary boxes having an edge facing a direction parallel to the first reference line.
4. The method of claim 1 , wherein defining a set of constraints to the two-dimensional polynomials comprises defining a set of equality or inequality constraints.
5. The method of claim 1 , wherein defining a set of constraints to the two-dimensional polynomials comprises defining a joint constraint to join segments smoothly between adjacent control points, wherein the joint constraint is configured to a third derivative smoothness.
6. The method of claim 1 , wherein the target function comprises a plurality of kernels, the plurality of kernels being one of a first derivative kernel, a second derivative kernel and a third derivative kernel, wherein the first, the second, and the third derivative kernels are generated by integration of square of the respective derivatives.
7. The method of claim 6 , wherein the target function comprises a separate weight factor for each of the plurality of kernels.
8. The method of claim 1 , wherein the target function comprises a guidance kernel based on previously collected driving route data.
9. A non-transitory machine-readable medium having instructions stored therein, which when executed by a processor, cause the processor to perform operations, the operations comprising:
generating a first reference line for controlling an autonomous driving vehicle (ADV) on a vehicular lane;
determining a plurality of boundary areas having predetermined dimensions centered around each of a plurality of control points of the first reference line;
selecting a plurality of two-dimensional polynomials each representing a segment of an optimal reference line between adjacent control points;
defining a set of constraints to the two-dimensional polynomials to at least ensure the plurality of two-dimensional polynomials passes through each of the plurality of boundary areas;
performing a quadratic programming (QP) optimization on a target function such that a total cost of the target function reaches minimum while the set of constraints are satisfied;
generating a second reference line representing the optimal reference line based on the QP optimization; and
controlling the ADV autonomously according to the second reference line.
10. The non-transitory machine-readable medium of claim 9 , wherein adjacent control points of the plurality of control points are approximately equally spaced apart.
11. The non-transitory machine-readable medium of claim 9 , wherein the boundary areas are boundary boxes having an edge facing a direction parallel to the first reference line.
12. The non-transitory machine-readable medium of claim 9 , wherein defining a set of constraints to the two-dimensional polynomials comprises defining a set of equality or inequality constraints.
13. The non-transitory machine-readable medium of claim 9 , wherein defining a set of constraints to the two-dimensional polynomials comprises defining a joint constraint to join segments smoothly between adjacent control points, wherein the joint constraint is configured to a third derivative smoothness.
14. The non-transitory machine-readable medium of claim 9 , wherein the target function comprises a plurality of kernels, the plurality of kernels being one of a first derivative kernel, a second derivative kernel and a third derivative kernel, wherein the first, the second, and the third derivative kernels are generated by integration of square of the respective derivatives.
15. The non-transitory machine-readable medium of claim 14 , wherein the target function comprises a separate weight factor for each of the plurality of kernels.
16. The non-transitory machine-readable medium of claim 9 , wherein the target function comprises a guidance kernel based on previously collected driving route data.
17. A data processing system, comprising:
a processor; and
a memory coupled to the processor to store instructions, which when executed by the processor, cause the processor to perform operations, the operations including
generating a first reference line for controlling an autonomous driving vehicle (ADV) on a vehicular lane;
determining a plurality of boundary areas having predetermined dimensions centered around each of a plurality of control points of the first reference line;
selecting a plurality of two-dimensional polynomials each representing a segment of an optimal reference line between adjacent control points;
defining a set of constraints to the two-dimensional polynomials to at least ensure the plurality of two-dimensional polynomials passes through each of the plurality of boundary areas;
performing a quadratic programming (QP) optimization on a target function such that a total cost of the target function reaches minimum while the set of constraints are satisfied;
generating a second reference line representing the optimal reference line based on the QP optimization; and
controlling the ADV autonomously according to the second reference line.
18. The system of claim 17 , wherein adjacent control points of the plurality of control points are approximately equally spaced apart.
19. The system of claim 17 , wherein the boundary areas are boundary boxes having an edge facing a direction parallel to the first reference line.
20. The system of claim 17 , wherein defining a set of constraints to the two-dimensional polynomials comprises defining a set of equality or inequality constraints.
21. The system of claim 17 , wherein defining a set of constraints to the two-dimensional polynomials comprises defining a joint constraint to join segments smoothly between adjacent control points, wherein the joint constraint is configured to a third derivative smoothness.