TurboADMM: A Structure-Exploiting Parallel Solver for Multi-Agent Trajectory Optimization

TL;DR

TurboADMM is introduced, a specialized single-machine QP solver that achieves empirically near linear complexity in agent count through systematic co-design of three complementary components.

Abstract

Multi-agent trajectory optimization with dense interaction networks require solving large coupled QPs at control rates, yet existing solvers fail to simultaneously exploit temporal structure, agent decomposition, and iteration similarity. One usually treats multi-agent problems monolithically when using general-purpose QP solvers (OSQP, MOSEK), which encounter scalability difficulties with agent count. Structure-exploiting solvers (HPIPM) leverage temporal structure through Riccati recursion but can be vulnerable to dense coupling constraints. We introduce TurboADMM, a specialized single-machine QP solver that achieves empirically near linear complexity in agent count through systematic co-design of three complementary components: (1) ADMM decomposition creates per-agent subproblems solvable in parallel, preserving block-tridiagonal structure under dense coupling; (2) Riccati warmstart exploits temporal structure to provide high-quality primal-dual initialization for each agent's QP; (3) parametric QP hotstart \footnote{In the paper, we refer warmstart as the technique that uses the Riccati equation results as auxiliary QP initialization for a single QP solve, while hotstart as reusing the QR factorization across QP solve iterations.}in qpOASES reuses similar KKT system factorizations across ADMM iterations.

Figures (4)

• Figure 1: TurboADMM pipeline: Coordinator broadcasts consensus variables encoding collision status. Each agent solves Riccati warm-started QPs in parallel for first ADMM iteration, and leverages hotstart mechanism for following ADMM iterations. Coordinator updates dual variables via closed-form consensus.
• Figure 2: Solve time comparison (log scale) averaged over 20 runs with ±1 std. dev. error bars. TurboADMM achieves 5-22× speedup over OSQP/MOSEK with near-linear scaling. HPIPM fails at 4+ agents (red dots). Ablation shows complementary contributions of hotstart (2-118×) and Riccati warmstart (1.3-2.4×).
• Figure 3: Multi-agent trajectory optimization results using TurboADMM in a highly congested crossover scenario. The plot displays the spatial paths of 14 agents maneuvering within a $20\text{m} \times 20\text{m}$ workspace. Agents are tasked with navigating from starting positions (circles, $\circ$) to target destinations (squares, $\square$) while maintaining a strict safety clearance of $d_{\text{safe}} = 2.0m$. Solid colored lines indicate the computed trajectories, with stars ($\star$) denoting the final positions reached at $T=20s$. Dotted lines connecting stars to squares illustrate the terminal position tracking error. To visualize collision avoidance in the dense center, the figure overlays a snapshot of all agent collision volumes (shaded circles) at the critical time step where the global minimum separation occurred. The red link highlights the closest pair of agents at this bottleneck moment, explicitly verifying that the minimum distance ($2.05m$) satisfies the safety constraint.
• Figure 4: Final Position Tracking Error Comparisons