Quadrotor stabilizing controllers often require careful, model-specific tuning for safe operation. We use reinforcement learning to train policies in simulation that transfer remarkably well to multiple different physical quadrotors. Our policies are low-level, i.e., we map the rotorcrafts' state directly to the motor outputs. The trained control policies are very robust to external disturbances and can withstand harsh initial conditions such as throws. We show how different training methodologies (change of the cost function, modeling of noise, use of domain randomization) might affect flight performance. To the best of our knowledge, this is the first work that demonstrates that a simple neural network can learn a robust stabilizing low-level quadrotor controller (without the use of a stabilizing PD controller) that is shown to generalize to multiple quadrotors. The video of our experiments can be found at https://sites.google.com/ view/sim-to-multi-quad.
We describe a method for formation-change trajectory planning for large quadrotor teams in obstacle-rich environments. Our method decomposes the planning problem into two stages: a discrete planner operating on a graph representation of the workspace, and a continuous refinement that converts the non-smooth graph plan into a set of C k -continuous trajectories, locally optimizing an integral-squared-derivative cost. We account for the downwash effect, allowing safe flight in dense formations. We demonstrate the computational efficiency in simulation with up to 200 robots and the physical plausibility with an experiment with 32 nano-quadrotors. Our approach can compute safe and smooth trajectories for hundreds of quadrotors in dense environments with obstacles in a few minutes.All authors are with the
We describe a trajectory optimization framework that maximizes observability of one or more user-chosen states in a nonlinear system. Our framework is based on a novel metric for quality of observability that is state-estimator agnostic and offers improved numerical stability over prior methods in some cases where the states of interest do not appear directly in the observation. We apply this metric to trajectory optimization problems for closed-loop self-calibration, maintaining observability while navigating through an environment, and rapidly modifying an already-planned trajectory for online recalibration. We include a statistical procedure to balance observability of several states with heterogeneous units and magnitudes. As an example, we apply our framework to online calibration of GPS-IMU and visual-inertial navigation systems on a quadrotor helicopter. Extensive simulations and a real-robot experiment demonstrate the effectiveness of our framework, showing better convergence of the states and the resulting higher precision in navigation.
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