Safe Beyond the Horizon: Efficient Sampling-based MPC with Neural Control Barrier Functions

A common problem when using model predictive control (MPC) in practice is the satisfaction of safety specifications beyond the prediction horizon.While theoretical works have shown that safety can be guaranteed by enforcing a suitable terminal set constraint or a sufficiently long prediction horizon, these techniques are difficult to apply and thus are rarely used by practitioners, especially in the case of general nonlinear dynamics.To solve this problem, we impose a tradeoff between exact recursive feasibility, computational tractability, and applicability to "blackbox" dynamics by learning an approximate discrete-time control barrier function and incorporating it into a variational inference MPC (VIMPC), a sampling-based MPC paradigm.To handle the resulting state constraints, we further propose a new sampling strategy that greatly reduces the variance of the estimated optimal control, improving the sample efficiency, and enabling realtime planning on a CPU.The resulting Neural Shield-VIMPC (NS-VIMPC) controller yields substantial safety improvements compared to existing sampling-based MPC controllers, even under badly designed cost functions.We validate our approach in both simulation and real-world hardware experiments.Project website: https://mit-realm.github.io/ns-vimpc/. I. INTRODUCTIONModel Predictive Control (MPC) is a versatile control approach widely used in robotics applications such as autonomous driving [76], bio-inspired locomotion [12,35], or manipulation of deformable objects [59], to name just a few.These methods address safety by incorporating state and control constraints into the finite-horizon optimization problem, ensuring that the system remains safe over the prediction horizon [12,49,59,74].However, safety of the system beyond the prediction horizon is often overlooked by practitioners, potentially leading to the violations of safety constraints at future timesteps.This is a well-known problem in the field of MPC.The question of whether a sequence of safe control actions can always be found under an MPC controller has been studied extensively in the literature under the name of recursive feasibility [14,32,42,50,52].A simple method of achieving recursive feasibility is by enforcing a control-invariant terminal set constraint at the end of the prediction horizon [14,42].However, it is difficult to find such a control-invariant set for general nonlinear systems.Methods such as bounding the system dynamics [13,14,26] often result in over-conservative sets, while methods that numerically solve the Hamilton-Jacobi