Autonomous navigation in cluttered, unknown environments necessitates precise and safe maneuvering. Our work develops efficient trajectory planning techniques for differentially flat systems (e.g., multi-rotor and car-like robots) that account for the system's attitude and dynamics and guarantee global (sub)optimality. Differential flatness allows converting time-parameterized flat output (e.g., position and yaw) trajectories into control inputs. To plan time-parameterized trajectories, we consider a linear quadratic minimum time (LQMT) optimal control problem. Our idea is to generate short-duration dynamically feasible motion primitives by discretizing the input space (e.g., acceleration or jerk), which reduces the LQMT problem to graph search. A key insight is that, if the obstacle and input constraints are relaxed, the LQMT problem can be solved in closed form. This allows us to design an accurate and consistent heuristic function that enables extremely efficient search-based planning in the discretized control space. The desired vehicle orientation can also be computed from the motion primitives allowing us to check collisions for robots with complex shape.
@article{Liu_AttitudePlanning_RAL18,
author = {Liu, Sikang and Mohta, Kartik and Atanasov, Nikolay and Kumar, Vijay},
title = {Search-based Motion Planning for Aggressive Flight in SE(3)},
journal = {IEEE Robotics and Automation Letters (RAL)},
year = {2018},
volume = {3},
number = {3},
pages = {2439-2446},
doi = {http://www.doi.org/10.1109/LRA.2018.2795654}
}
@inproceedings{Liu_DynamicTrajectoryPlanning_IROS17,
author = {S. Liu and N. Atanasov and K. Mohta and V. Kumar},
title = {Search-based Motion Planning for Quadrotors using Linear Quadratic Minimum Time Control},
booktitle = {IEEE/RSJ Int. Conf. on Intelligent Robots and Systems (IROS)},
year = {2017},
doi = {http://www.doi.org/10.1109/IROS.2017.8206119}
}