gatekeeper: Online Safety Verification and Control for Nonlinear Systems in Dynamic Environments

This article presents the gatekeeper algorithm, a real-time and computationally lightweight method that ensures that trajectories of a nonlinear system satisfy safety constraints despite sensing limitations. gatekeeper integrates with existing path planners and feedback controllers by introducing an additional verification step to ensure that proposed trajectories can be executed safely, despite nonlinear dynamics subject to bounded disturbances, input constraints, and partial knowledge of the environment. Our key contribution is that 1) we propose an algorithm to recursively construct safe trajectories by numerically forward propagating the system over a (short) finite horizon, and 2) we prove that tracking such a trajectory ensures the system remains safe for all future time, i.e., beyond the finite horizon. We demonstrate the method in a simulation of a dynamic firefighting mission, and in physical experiments of a quadrotor navigating in an obstacle environment that is sensed online. We also provide comparisons against the state-of-the-art techniques for similar problems.