Trajectory Optimization L1-450
Unclaimed Principle — open for contribution
This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.
To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.
Forward model E
Trajectory Optimization: Trajectory optimization: find minimum-time or minimum-effort robot trajectory satisfying dynamics and obstacle constraints. The forward operator produces the measurement through a 3-node primitive DAG (M.collocation.direct_transcription…); recovery is posed as a nonlinear_inverse problem. Difficulty tier delta=5 with effective condition number kappa_eff~2000; dynamic_obstacle_uncertainty, model_uncertainty set the accuracy floor at the Omega boundary. See the forward_model field for the closed-form equation.
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- true
- Stability:
- conditional
- κ:
- 100000
Existence of the recovered optimal_trajectory is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 2000); dynamic_obstacle_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Deterministic sets the irreducible data-fidelity floor.
Solvability C
- Solver class:
- sparse-recovery [direct_collocation_IPOPT or DDP_iLQR or CHOMP]
- Convergence rate q:
- 2
- Complexity:
- O(N_nodes * n_state ** 2 * N_iter) for direct methods per iteration