Learning Safe, Generalizable Perception-Based Hybrid Control With Certificates

Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods

“…In this combined CLF-CBF QP, the constraint (15c) ensures safety at all times while the stability constraint (15b) is relaxed by some variable amount r. This relaxation allows the system to temporarily cease progress towards the goal in order to remain safe, and k > 0 is a tunable parameter governing the trade-off between control effort and relaxation of the CLF condition. It is important to note that this combined QP can suffer from deadlock when there is no safe direction that moves closer to the goal, although there are proposals for switched controllers [17] and unified Lyapunov-barrier certificates [9] that alleviate this concern.…”

“…Contraction is a property of the closed-loop system, not of any particular trajectory, and thus the existence of a metric satisfying condition (17) suffices to prove that a control system is capable of exponentially stabilizing any dynamically feasible nominal trajectory. Additionally, if a system is contracting, then bounded disturbances will produce a bounded worst-case tracking error, and this tracking error will be proportional to the magnitude of the disturbance [13].…”

“…This approach provides the foundation for many certificate-based learning works; early examples include [28], and later works include [3], [29], [30], [31], [32], [33]. Examples that learn CLF or CBF certificates that imply controllers include [34], [35], [36], [37], [9], [17], [38]. A related class of works assume that a certificate is given for a nominal system and use supervised learning to adapt that certificate to the uncertain true model [2], [39], [40], [12].…”

“…Since Chang et al's work, other authors have expanded this joint control-certificate learning approach to other certificate functions. For instance, [10] jointly learns a barrier function and controller, while [35], [36], [37], [9], [17], [38] learn control Lyapunov and control barrier functions (implicitly combining the certificate and control policy). Other authors, notably Tsukamoto, Chung, and Slotine [34], [51] have extended the neural certificate approach to contraction metrics (see [5] for an overview of these approaches).…”

“…To enable generalization to new environments, the CBF and CLF are learned as functions of observations (Lidar data and range and bearing to the goal) rather than states. More details on this example can be found in [17]. This example shows how learned certificates can be used to ensure safety as part of a larger robotics architecture.…”