{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"invariant_mode_decomposition_design__robotics_automation","trajectory_id":"R","attempt_index":0,"archetype_slug":"invariant_mode_decomposition_design","domain_slug":"robotics_automation","decision":"CANDIDATE","problem_id":"coupled_joint_mode_instability_in_high_speed_robot_motion","causal_lever_id":"damp_action_relevant_closed_loop_motion_modes","proposal":{"problem":"A multi-axis industrial robot can satisfy average joint-tracking tolerances yet develop growing coupled oscillation during high-speed motion because small errors across several joints, drive loops, and flexible links reinforce one another. Joint-by-joint alarms and tuning can miss the combination until vibration degrades accuracy, tooling, or safe operation.","actors_substrate":["Robot motion-control engineer","Robot operator and nearby workers","Multi-axis manipulator, drives, joints, flexible links, payload, sensors, and controller","Safety engineer responsible for deployment approval"],"observable_state":"Time-synchronized joint position, velocity, current or torque, end-effector error, vibration, controller commands, operating point, payload, and safety-stop events over repeated trajectories.","consequence":"An action-relevant growing or weakly damped coupled motion pattern remains hidden behind acceptable aggregate errors, producing chatter, poor path accuracy, accelerated wear, dropped payload risk, or protective stops.","affected_objective":"Maintain stable, accurate, fast robot motion without exceeding force, vibration, actuator, or human-safety limits.","structural_mapping":[{"archetype_element":"Coupled transformation","domain_realization":"A locally identified closed-loop state-transition matrix maps robot error, velocity, drive, and flexible-state deviations between control intervals.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Invariant directions","domain_realization":"Mode vectors represent joint-and-structure combinations that approximately preserve their shape during local closed-loop evolution.","claim_kind":"INFERENCE"},{"archetype_element":"Scalar modal response","domain_realization":"Eigenvalues encode local decay, growth, and oscillation; singular values separately bound possible transient amplification for a non-normal transition.","claim_kind":"INFERENCE"},{"archetype_element":"Action-relevant mode selection","domain_realization":"Modes are retained according to stability margin, vibration or path-error sensitivity, controllability, and reconstruction consequence rather than amplitude alone.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Residual and drift governance","domain_realization":"Held-out reconstruction error, structured residuals, modal rotation, and spectral-gap changes determine when the local model must be revised or retired.","claim_kind":"HYPOTHESIS"}],"component_map":[{"component":"Transformation Scope","status":"direct","domain_realization":"One robot configuration, controller version, payload class, speed band, and bounded trajectory segment."},{"component":"State-Vector Definition","status":"direct","domain_realization":"Synchronized joint errors, velocities, currents or torques, flexible-state estimates, and end-effector error."},{"component":"Invariant Mode Basis","status":"direct","domain_realization":"Eigenvectors of the locally identified closed-loop transition matrix."},{"component":"Modal Gain Spectrum","status":"direct","domain_realization":"Eigenvalues plus singular-value transient-gain guards."},{"component":"Dominant Mode Selection Rule","status":"adapted","domain_realization":"Select by stability margin and safety-weighted outcome sensitivity, subject to residual tolerance."},{"component":"Stable/Unstable Mode Partition","status":"direct","domain_realization":"Classify discrete-time modes as decaying, marginal, growing, or oscillatory within the fitted regime."},{"component":"Modal Intervention Map","status":"adapted","domain_realization":"Map bounded controller-parameter changes to modal damping, path error, actuator demand, and cross-mode effects."},{"component":"Reconstruction Residual Check","status":"direct","domain_realization":"Reconstruct held-out state trajectories and inspect both error magnitude and structured vibration remnants."},{"component":"Mode Drift Monitor","status":"direct","domain_realization":"Track mode direction, ordering, gain, and residual drift across payloads and operating periods."},{"component":"Interpretation Scope Contract","status":"direct","domain_realization":"Modes are local diagnostic and control-design constructs, not globally valid physical causes."},{"component":"Mode-Coupling Register","status":"direct","domain_realization":"Record near-degenerate, non-orthogonal, and intervention-induced cross-mode behavior."},{"component":"Local Linearization Window","status":"direct","domain_realization":"Explicit bounds on configuration, speed, acceleration, payload, contact state, and disturbance size."},{"component":"Spectral Gap Threshold","status":"direct","domain_realization":"Minimum retained-versus-discarded separation needed for stable selection and mode identity."}],"mechanism_dispositions":[{"slug":"eigendecomposition_workflow","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Decompose the explicit local closed-loop transition operator into the full eigenbasis and spectrum; report conditioning.","counterfactual_removal":"Without it, coupled growth directions and their local gains are not identified."},{"slug":"modal_sensitivity_sweep","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Use only bounded offline or shadow perturbations to rank controller changes by safety-weighted modal outcomes and register cross-effects.","counterfactual_removal":"The spectrum would diagnose instability but would not identify which permissible adjustment has leverage."},{"slug":"modal_stability_analysis","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Partition discrete-time modes relative to the unit circle and attach the fitted operating window.","counterfactual_removal":"No defensible distinction would exist between decaying and growing modes."},{"slug":"mode_shape_testing","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Compare predicted shapes with low-energy excitation or ordinary trajectory response inside a guarded cell.","counterfactual_removal":"The analytical modes would lack an independent physical-response check, reducing pilot credibility."},{"slug":"network_spectral_centrality_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Joint connectivity importance is not the target; centrality does not establish closed-loop dynamic stability.","counterfactual_removal":"No causal or viability change."},{"slug":"power_iteration_probe","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A dominant-only estimate can miss several weakly damped modes and is unreliable near the spectral-gap boundary.","counterfactual_removal":"No change because the bounded operator is decomposed fully."},{"slug":"principal_component_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"High-variance directions need not be dynamically growing or control-relevant.","counterfactual_removal":"No change to the transition-based causal test."},{"slug":"reduced_order_model","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Run the retained-mode model only as a shadow surrogate for bounded controller comparisons.","counterfactual_removal":"Diagnosis remains possible, but rapid safe comparison of candidate adjustments becomes less viable."},{"slug":"residual_reconstruction_test","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Test retained modes on held-out trajectories against magnitude, structure, and safety-weighted residual budgets.","counterfactual_removal":"Omitted dynamics could be mistaken for safe compression and invalidate proposed control changes."},{"slug":"singular_value_decomposition","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Use singular values to detect transient amplification and eigenbasis fragility in a non-normal operator, not as invariant dynamics.","counterfactual_removal":"An eigenvalue-stable but transiently amplifying controller could pass the screen."},{"slug":"spectral_decomposition_report","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Document conditioning, coupling, residuals, permitted interpretations, and operating limits for approvers.","counterfactual_removal":"Technical results could be operationally misread outside their valid regime."},{"slug":"spectral_gap_monitor","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Monitor gap, mode rotation, gains, and residuals before any later production reliance.","counterfactual_removal":"A once-valid modal basis could silently remain in use after payload or regime drift."}],"causal_chain":["Coupled robot states evolve through a locally repeatable closed-loop transition.","Its action-relevant modes reveal combinations that decay slowly, grow, oscillate, or transiently amplify.","Sensitivity tests identify bounded controller changes that increase damping of hazardous modes without unacceptable cross-mode or actuator effects.","Held-out residual, physical-response, conditioning, and scope checks gate the change.","Only a safety-authorized controller adjustment that passes shadow and guarded-cell tests advances; drift or residual alarms retire it."],"baseline":"Tune and alarm on individual joints, aggregate tracking error, and visible vibration using existing controller logs.","nearest_rival":"Multivariable robust or gain-scheduled controller tuning against worst-case tracking and stability margins without explicit modal prioritization.","authority_safety":{"affected_parties":["Robot operators","Nearby workers and maintenance staff","Process and safety engineers","Owners of the robot, tooling, workpiece, and payload"],"decision_authority":"The facility's designated robot safety authority jointly with the motion-control owner; the analyst may recommend but not deploy.","authorized_first_step":"Replay existing logs to fit one local model, then run a shadow simulation and a low-speed guarded-cell excitation on one robot and payload, with no production workpiece or person inside the safeguarded space.","excluded_actions":["Autonomous production controller deployment","Disabling interlocks, collision detection, speed limits, or emergency stops","Excitation near people or unsecured payloads","Extrapolation beyond the declared operating window"],"halt_rollback":"Stop on any safety-limit excursion, unexpected contact, actuator saturation, rising unmodeled vibration, structured residual above budget, eigenbasis ill-conditioning, or modal drift beyond tolerance; restore the approved controller and quarantine the candidate model."}},"negative_tests":{"strongest_counterevidence":"The apparent coupled oscillation disappears after correcting one sensor, loose fixture, damaged reducer, or single-loop fault, or the fitted modes fail to recur on held-out runs.","analogy_break":"Robot motion is nonlinear, configuration-dependent, contact-sensitive, and often non-normal; local eigenmodes cease to represent behavior after large moves, impacts, saturation, backlash, or controller switching.","failure_condition":"No operating window yields repeatable modes with adequate conditioning, spectral separation, held-out reconstruction, and physical-response agreement.","problem_falsifier":"Time-synchronized evidence shows no repeatable multivariable growth or weak-damping pattern beyond a directly observable single-component fault, and ordinary joint-level diagnostics predict failures adequately.","intervention_falsifier":"Within the valid window, controller changes predicted to damp the selected mode do not improve held-out decay or vibration, or they worsen path error, actuator demand, residuals, or another safety-relevant mode.","risks":["Unsafe excitation or destabilizing gain changes","Transient amplification despite stable eigenvalues","Missing low-amplitude but safety-critical dynamics","Mode swapping or false drift alarms near degeneracy","Overgeneralization across payloads, configurations, contact states, or controller versions","Analyst interpretation being mistaken for deployment authorization"]},"null_rationale":null,"classification":{"candidate_kind":"MECHANISM_COMPOSITION","prior_art_status":"UNSEARCHED","evidence_maturity":"HYPOTHESIS"},"revision_change_log":{"revision_kind":"ORIGINAL","prior_problem_id":null,"prior_causal_lever_id":null,"problem_changed":false,"causal_lever_changed":false,"conceptual_changes":[],"operational_changes":[],"repairs_addressed":[]},"confidence":0.86,"generator_notes":"Closed-book structural transfer. Empirical recurrence, controllability, thresholds, and safety benefit remain untested hypotheses; no novelty claim is made."}