trajectory optimization on Lie group

2023-RSS-Convex Geometric Motion Planning on Lie Groups via Moment Relaxation

Background

local search methods: fast, but depends on good initialization
sampling-based methods: only probabilistic complete
global optimization:
- (discrete)Mixed-integer programming
- (continuous)Polynomial programming

Global optimization does not scale well: - robot models - problem structure

This methods: - geometric formulation for robot dynamics - exploit the problem sparsity - leverage the Lasserre's hierarchy of moment relaxation

for kinodynamic motion planning

Method