second-order-consensus-ring-8

Second-order consensus · solved 13 of 13 agent attempts pass

The task. Textbook (neighbour PD). The reference with May gains (1.0, 1.5) passes only 0.73 of seeds within the horizon; gains (1.5, 2.0) pass 40/40, so gain tuning matters.

Gate. final error (edge disagreement in position + 0.25 * edge disagreement in velocity) <= 1e-3 after 300 steps; success rate >= 0.9 on 40 verifier-only seeds

Axes: topology:ring, n_agents:8, dynamics:double-integrator

Each video re-runs the attempt's final controller through the task's own evaluator on a public seed (never the grader's held-out ones). The table under each video is the official grade on the held-out seeds.

Best attemptGemini (cursor-cli (pre-clock), 7 min) · base

Graded on the held-out seeds: passes every gate on the grader's held-out seeds.

criterion	graded	needed
base:success	1.000	≥ 0.900

How the agent got there: 7 min · 38 tool calls · 2 edit-tool edits · 16 runs of its own Python (tests, experiments, rewrites) · no tuner runs · official verifier 3× (success rates in order: 0.00, 1.00, 1.00).

The agent's final message

The distributed second-order consensus controller has been implemented in `/app/work/controller.py`. ### Control Law & Gain Rationale For each agent \(i\) interacting with its immediate neighbors \(\mathcal{N}_i\) on the ring graph, the distributed control action is: \[ u_i = - k_p \sum_{j \in \mathcal{N}_i} A_{ij}(p_i - p_j) - k_v \sum_{j \in \mathcal{N}_i} A_{ij}(v_i - v_j) = -k_p (L p)_i - k_v (L v)_i \] where \(L = D - A\) is the graph Laplacian. - **Proportional Gain (\(k_p = 6.0\))**: Penalizes relative position disagreements between adjacent agents, providing the restorative spring stiffness needed to converge to agreement. - **Velocity Gain (\(k_v = 4.0\))**: Penalizes relative velocity disagreements, providing viscous damping to eliminate oscillatory modes and align velocities smoothly. - **Stability & Saturation**: With sample time \(\Delta t = 0.05\,\text{s}\) and graph spectrum \(\lambda_{\max} = 4.0\), the closed-loop discrete-time eigenvalues remain well inside the unit circle while respecting the \([-2, 2]\) control saturation limits. ### Verification Results Evaluated against the verification benchmark: - **Success rate**: 100% (`solved=True`, 1.000 across visible and hold-out seed evaluations) - **Mean final consensus error**: \(\sim 2.83 \times 10^{-16}\) (well below threshold \(10^{-3}\))The distributed second-order consensus controller in `/app/work/controller.py` is configured and validated. ### Summary of Results - **Controller Law**: Distributed n…

Controller family: consensus protocol

Each agent applies u = -k_p*L@p - k_v*L@v with fixed gains 6.0 and 4.0 using the graph Laplacian, then clips the result to the action limit.

Shown: public seed 0 (base); this episode passes the default rung. This episode: final_error 9.35e-16, final_position_error 8.94e-16, final_velocity_error 1.65e-16, total_reward -70.3.

controller.py · trial second-order-consensus-ring-8__N7GMi8U