Complete Tracking Scenarios

The planner result matters only if it survives the local execution layer. The experiments here propagate the same harmonic reference through the existing physical-agent environment and keep planner and formation errors separate.

Matched multi-agent run

Both runs use the repository's existing examples/multi_agent_target_tracking configuration. The experiment builds its 13-agent, four-target sheaf, advances the configured 3-D target figure-eights, solves every harmonic reference, applies the implemented Tikhonov planner, and advances the local reference controller. Targets, initial states, gains, and $\epsilon=0.2$ are matched; only feedforward changes.

Stars are generated targets, open circles are solved harmonic references, and filled circles are physical agents. Short solid trails show recent agent motion; each thin connector is the instantaneous formation error. Nothing in this animation is positioned by the renderer.

Error propagation through the cascade

The upper trace measures only $x-q^\star$. The lower trace measures physical position relative to the ideal harmonic formation. This exposes how planner lag survives an otherwise stable local tracking loop.

Feedforward restores the direct harmonic rollout to numerical precision. The remaining $3.17$ is local execution lag at the scenario's spatial scale, not a residual harmonic-solve error.

Stationary targets

With the target boundary held fixed, $q^\star$ is constant. The planner follows the measured $e^{-t/\epsilon}$ decay on the stability page, and the local tracking errors also vanish. The complete cascade therefore converges to the stationary target-relative formation.

Reproduction

Regenerate every trajectory, figure, and reported metric with:

julia --project=docs docs/scripts/tikhonov_figures.jl
julia docs/scripts/tikhonov_deployment.jl

The first command regenerates the controlled theorem checks. The second runs the deployed environment and writes its figures directly from the recorded rollout.