Smooth road reference for autonomous driving vehicles based on 2D constrained smoothing spline

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.

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.