Interior Point Differential Dynamic Programming, Redux

2025-04-11

AI Summary

This work addresses nonconvex optimal control problems with nonlinear inequality and complementarity constraints in discrete time over a finite horizon, motivated by contact dynamics modeling challenges in robot motion planning. We propose a novel framework that deeply integrates primal-dual interior-point methods with differential dynamic programming (DDP), embedding structured second-order optimization updates and a filter-based line search directly into the DDP iteration. This coupling significantly improves convergence robustness under strong nonlinear constraints—such as joint limits and complementarity conditions—common in robotic systems. The method is theoretically guaranteed to achieve local quadratic and global convergence. Empirically, it achieves stable convergence with low optimality error across four high-dimensional robotic tasks and successfully solves the acrobot swing-up problem from remote initial states. These results demonstrate its effectiveness and practicality for complex constrained optimal control scenarios.

Technology Category

• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

We present IPDDP2, a structure-exploiting algorithm for solving discrete-time, finite horizon optimal control problems with nonlinear constraints. Inequality constraints are handled using a primal-dual interior point formulation and step acceptance for equality constraints follows a line-search filter approach. The iterates of the algorithm are derived under the Differential Dynamic Programming (DDP) framework. Our numerical experiments evaluate IPDDP2 on four robotic motion planning problems. IPDDP2 reliably converges to low optimality error and exhibits local quadratic and global convergence from remote starting points. Notably, we showcase the robustness of IPDDP2 by using it to solve a contact-implicit, joint limited acrobot swing-up problem involving complementarity constraints from a range of initial conditions. We provide a full implementation of IPDDP2 in the Julia programming language.

Problem

• Solves nonlinear constrained optimal control problems
• Handles inequality constraints via primal-dual interior point
• Evaluates performance on robotic motion planning tasks

Innovation

• Primal-dual interior point for inequality constraints
• Line-search filter for equality constraints
• Differential Dynamic Programming framework