Risk-aware trajectory generation with application to safe quadrotor landing

In navigation tasks, mobile robots often have to deal with substantial uncertainty due to imperfect actuators and noisy sensor measurements. In this paper, we consider the problem of online trajectory generation for safe navigation in the presence of state uncertainty and the resulting deviations from the desired trajectory. Our approach combines probabilistic estimation of the a priori collision risk with efficient trajectory generation, exploiting the differential flatness of many robotic systems in an explicitly constrained polynomial trajectory representation. Through trajectory optimization, our approach allows to flexibly trade off risk against, for example, the duration of the trajectory. It is computationally efficient because each optimization step has polynomial complexity. In contrast to other approaches, our method can also optimize the trajectory duration and supports cost functions that facilitate higher-order smoothness of the trajectory. Our experiments demonstrate the performance of the approach and show that our trajectories result in substantially lower collisions probabilities compared to minimum-snap trajectories in a quadrotor landing task.