Solving Trajectory Optimization Problems in the Presence of Probabilistic Constraints.

Area of Science:

• Optimization Theory
• Aerospace Engineering
• Control Systems

Background:

• Trajectory optimization problems often involve complex nonlinear dynamics and uncertainties.
• Probabilistic constraints introduce significant challenges in finding feasible and optimal solutions.
• Existing methods for chance-constrained optimization can be computationally intensive and may lack convergence guarantees.

Purpose of the Study:

• To develop an approximation-based strategy for solving nonlinear trajectory optimization problems with probabilistic constraints.
• To convert chance-constrained models into deterministic parametric nonlinear programming models.
• To ensure the convergence of the approximation method to the original problem's optimal solution.

Main Methods:

• A smooth and differentiable approximation function is proposed to replace probabilistic constraints with deterministic ones.
• The chance-constrained trajectory optimization model is reformulated as a parametric nonlinear programming model.
• Theoretical proofs are provided to demonstrate the convergence of the approximation function, set, and optimal solution.

Main Results:

• The proposed approximation strategy successfully converts chance-constrained problems into solvable deterministic models.
• Numerical results from space vehicle and unmanned vehicle trajectory optimization validate the approach's feasibility and effectiveness.
• Comparative studies show the proposed method outperforms other typical chance-constrained optimization techniques.

Conclusions:

• The approximation-based strategy offers an effective solution for nonlinear trajectory optimization with probabilistic constraints.
• The method provides a robust framework for handling uncertainties in trajectory planning.
• This approach demonstrates significant potential for applications in aerospace and robotics.