Path optimization based on constrained smoothing spline for autonomous driving vehicles
According to some embodiments, a system segments a first path trajectory selected from an initial location of the ADV into a number of path segments, where each path segment is represented by a polynomial function. The system selects an objective function in view of the polynomial functions of the path segments for smoothing connections between the path segments. The system defines a set of constraints to the polynomial functions based on adjacent path segments in view of at least a road boundary and an obstacle perceived by the ADV. The system performs a quadratic programming (QP) optimization on the objective function in view of the added constraints, such that an output of the objective function reaches a minimum. The system generates a second path trajectory representing a path trajectory with an optimized objective function based on the QP optimization to control the ADV autonomously.
1. A computer-implemented method to optimize a path trajectory for an autonomous driving vehicle (ADV), the method comprising:
segmenting a first path trajectory selected from an initial location of the ADV into a plurality of path segments, wherein each path segment is represented by a polynomial function;
selecting an objective function in view of the polynomial functions of the path segments for smoothing connections between the path segments;
defining a set of constraints to the polynomial functions of the path segments based on adjacent path segments in view of at least a road boundary and an obstacle perceived by the ADV;
performing a quadratic programming (QP) optimization on the objective function in view of added constraints, such that an output of the objective function reaches a minimum; and
generating a second path trajectory representing a path trajectory with an optimized objective function based on the QP optimization to control the ADV autonomously according to the second path trajectory.
2. The method of claim 1 , wherein defining the set of constraints to the polynomial functions of the path segments comprises defining a set of initial constraints representing the initial location, a direction, and a curvature of the ADV.
3. The method of claim 1 , wherein defining the set of constraints to the polynomial functions of the path segments comprises defining an upper and a lower boundary constraints representing the road boundary.
4. The method of claim 1 , wherein the polynomial functions of the path segments are fifth order polynomial functions.
5. The method of claim 1 , wherein the polynomial functions are lateral units expressed as a function of station units in a station-lateral coordinate system.
6. The method of claim 1 , wherein the objective function comprises a smoothing kernel.
7. The method of claim 1 , wherein the objective function comprises a guidance kernel when the ADV is changing lanes.
8. The method of claim 1 , further comprising interpolating a plurality of points of the second path trajectory that are absent from the first path trajectory.
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:
segmenting a first path trajectory selected from an initial location of the ADV into a plurality of path segments, wherein each path segment is represented by a polynomial function;
selecting an objective function in view of the polynomial functions of the path segments for smoothing connections between the path segments;
defining a set of constraints to the polynomial functions of the path segments based on adjacent path segments in view of at least a road boundary and an obstacle perceived by the ADV;
performing a quadratic programming (QP) optimization on the objective function in view of added constraints, such that an output of the objective function reaches a minimum; and
generating a second path trajectory representing a path trajectory with an optimized objective function based on the QP optimization to control the ADV autonomously according to the second path trajectory.
10. The non-transitory machine-readable medium of claim 9 , wherein defining the set of constraints to the polynomial functions of the path segments comprises defining a set of initial constraints representing the initial location, a direction, and a curvature of the ADV.
11. The non-transitory machine-readable medium of claim 9 , wherein defining the set of constraints to the polynomial functions of the path segments comprises defining an upper and a lower boundary constraints representing the road boundary.
12. The non-transitory machine-readable medium of claim 9 , wherein the polynomial functions of the path segments are fifth order polynomial functions.
13. The non-transitory machine-readable medium of claim 9 , wherein the polynomial functions are lateral units expressed as a function of station units in a station-lateral coordinate system.
14. The non-transitory machine-readable medium of claim 9 , wherein the objective function comprises a smoothing kernel.
15. The non-transitory machine-readable medium of claim 9 , wherein the objective function comprises a guidance kernel when the ADV is changing lanes.
16. The non-transitory machine-readable medium of claim 9 , further comprising interpolating a plurality of points of the second path trajectory that are absent from the first path trajectory.
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
segmenting a first path trajectory selected from an initial location of the ADV into a plurality of path segments, wherein each path segment is represented by a polynomial function;
selecting an objective function in view of the polynomial functions of the path segments for smoothing connections between the path segments;
defining a set of constraints to the polynomial functions of the path segments based on adjacent path segments in view of at least a road boundary and an obstacle perceived by the ADV;
performing a quadratic programming (QP) optimization on the objective function in view of added constraints, such that an output of the objective function reaches a minimum; and
generating a second path trajectory representing a path trajectory with an optimized objective function based on the QP optimization to control the ADV autonomously according to the second path trajectory.
18. The system of claim 17 , wherein defining the set of constraints to the polynomial functions of the path segments comprises defining a set of initial constraints representing the initial location, a direction, and a curvature of the ADV.
19. The system of claim 17 , wherein defining the set of constraints to the polynomial functions of the path segments comprises defining an upper and a lower boundary constraints representing the road boundary.
20. The system of claim 17 , wherein the polynomial functions of the path segments are fifth order polynomial functions.
21. The system of claim 17 , wherein the polynomial functions are lateral units expressed as a function of station units in a station-lateral coordinate system.