A Robust Invariant Set Planner For Quadrotors

We propose a motion planner for quadrotors implemented as a search on a graph constructed from robust positively invariant (PI) sets. We model the position error dynamics of the quadrotor in closed-loop with an onboard controller as a second-order system with polytopic uncertainty in the gains. In addition, we consider bounded attitude tracking errors and additive input disturbances. Using linear matrix inequalities (LMIs), we compute small ellipsoidal robust PI sets and large ellipsoidal inflated safe PI sets around positional setpoints where collision avoidance and input constraints are satisfied. We use the sets to construct a graph where the nodes are associated to position setpoints, and the edges are included if it is possible to transition from one node setpoint to the next one while satisfying constraints and avoiding collisions. The motion plan is obtained by selecting the sequence of active setpoints based on set membership conditions. The construction of the graph can be performed offline, while the online computation of the motion plan is simple and fast, as demonstrated by a Monte-Carlo simulation study in a cluttered indoor environment.