Analytical Integral Global Trajectory Optimization with Contact Dynamics

Davide De Martini, Majid Khadiv, Andrea Del Prete

Keywords: Trajectory Optimization, Global Optimization, Contact Dynamics, Analytical Integration, Robotics

TL;DR: AIGO is a new optimization method that analytically smooths and solves difficult, non-convex trajectory problems with contact dynamics, outperforming traditional gradient-based approaches.

Abstract:

Trajectory Optimization (TO) involves designing trajectories by minimizing a cost function subject to constraints, often formulated as an Optimal Control Problem (OCP). Traditional methods, such as Gradient Descent or sampling-based approaches, can converge to poor local minima due to nonconvexity or high dimensionality.
In this work, we explore Analytical Integral Global Optimization (AIGO), a novel algorithm inspired by Randomized Smoothing (RS), for TO. Unlike RS, which relies on sampling, AIGO computes the smoothed objective analytically using unitary kernels (e.g., hyperboxes) and optimizes over the integral of the function, progressively shrinking the integration domain until the original problem is recovered. We evaluate AIGO with a point-mass with collisions demonstrating its ability to reliably find feasible and efficient trajectories where traditional methods struggle.

Submission Number: 27