Bayesian Safety Guarantees for Port-Hamiltonian Systems with Learned Energy Functions
This work addresses safety guarantees for control systems with learned models, which is an incremental improvement in robust control for robotics and automation.
The paper tackles the problem of ensuring safety in port-Hamiltonian systems with learned energy functions by propagating model uncertainty into a safety filter, resulting in an end-to-end safety guarantee of at least 1 - (η_dr + η_ptB) and a larger safe set compared to an unstructured alternative.
Control barrier functions for port-Hamiltonian systems inherit model uncertainty when the Hamiltonian is learned from data. We show how to propagate this uncertainty into a safety filter with independently tunable credibility budgets. To propagate this uncertainty, we employ a two-stage Bayesian approach. First, posterior prediction over the Hamiltonian yields credible bands for the energy storage, producing Bayesian barriers whose safe sets are high-probability inner approximations of the true allowable set with credibility $1 - (η_{\mathrm{ptB}})$. Independently, a drift credible ellipsoid accounts for vector field uncertainty in the CBF inequality with credibility $1 - (η_{\rm dr})$. Since energy and drift uncertainties enter through disjoint credible sets, the end-to-end safety guarantee is at least $1 - (η_{\rm dr} + η_{\mathrm{ptB}})$. Experiments on a mass-spring oscillator with a GP-learned Hamiltonian show that the proposed filter preserves safety despite limited and noisy observations. Moreover, we show that the proposed framework yields a larger safe set than an unstructured GP-CBF alternative on a planar manipulator.