Developing inverse motion planning technique for autonomous vehicles using integral nonlinear constraints.

Area of Science:

• Robotics and Control Systems
• Computational Mathematics

Background:

• Autonomous vehicle motion planning requires sophisticated trajectory and speed optimization.
• Existing methods often face challenges with differentiability and constraint satisfaction.

Purpose of the Study:

• To elaborate and validate a novel technique for autonomous vehicle motion planning.
• To compare two models with varying degrees of freedom (DOF) for optimization quality, stability, and real-time performance.

Main Methods:

• Utilizing finite elements (FE) to represent functions, a vehicle kinematic model, and sequential quadratic programming for optimization.
• Implementing an inverse approach with integrated polynomials for curvature and speed, and Gaussian N-point quadrature integration.
• Employing piecewise functions with 2 and 3 DOF, and replacing nodal linear constraints with integral nonlinear ones.

Main Results:

• The developed technique ensures higher differentiability, resulting in simple and unambiguous reference curves for improved control accuracy.
• Integral nonlinear constraints guarantee non-violation of boundary limits within each finite element.
• Simulation results demonstrate smoothed geometric and kinematic parameters up to the highest derivatives.

Conclusions:

• The proposed motion planning technique is efficient and provides high-quality prognosis for autonomous vehicles.
• The study highlights the trade-offs between optimization quality, stability, and rapidity for different DOF models in real-time applications.