Equality Constrained Differential Dynamic Programming

Trajectory optimization is an important tool in task-based robot motion planning, due to its generality and convergence guarantees under some mild conditions. It is often used as a post-processing operation to smooth out trajectories that are generated by probabilistic methods or to directly control the robot motion. Unconstrained trajectory optimization problems have been well studied, and are commonly solved using Differential Dynamic Programming methods that allow for fast convergence at a relatively low computational cost. In this paper, we propose an augmented Lagrangian approach that extends these ideas to equality-constrained trajectory optimization problems, while maintaining a balance between convergence speed and numerical stability. We illustrate our contributions on various standard robotic problems and highlights their benefits compared to standard approaches.

Authors

• Sarah El Kazdadi
• Justin Carpentier
• Jean Ponce

Keywords

• Robot motion
• Tools
• Probabilistic logic
• Dynamic programming
• Planning
• Task analysis
• Trajectory optimization
• Differentiation Program
• Differential Dynamic Programming
• Optimization Problem
• Convergence Rate
• Probabilistic Method
• Numerical Stability
• Convergence Guarantees
• Trajectory Optimization Problem
• Objective Function
• Optimal Control
• State Space
• Feasible Solution
• Lagrange Multiplier
• Additional Constraints
• Direct Approach
• Equality Constraints
• Quadratic Programming
• Constrained Optimization
• Forward Pass
• Backward Pass
• Feedback Term
• Pontryagin Maximum Principle
• Sequential Quadratic Programming
• Line Search
• Optimal Control Problem
• Error Constraint
• Constrained Optimization Problem