Geometrically Constrained Trajectory Optimization for Multicopters

In this article, we present an optimization-based framework for multicopter trajectory planning subject to ge- ometrical configuration constraints and user-defined dynamic constraints. The basis of the framework is a novel trajectory rep- resentation built upon our novel optimality conditions for uncon- strained control effort minimization. We design linear-complexity operations on this representation to conduct spatial-temporal deformation under various planning requirements. Smooth maps are utilized to exactly eliminate geometrical constraints in a lightweight fashion. A variety of state-input constraints are supported by the decoupling of dense constraint evaluation from sparse parameterization, and backward differentiation of flatness map. As a result, this framework transforms a generally constrained multicopter planning problem into an unconstrained optimization that can be solved reliably and efficiently. Our framework bridges the gaps among solution quality, planning efficiency, and constraint fidelity for a multicopter with limited resources and maneuvering capability. Its generality and robust- ness are both demonstrated by applications to different flight tasks. Extensive simulations and benchmarks are also conducted to show its capability of generating high-quality solutions while retaining the computation speed against other specialized meth- ods by orders of magnitude. The source code of our framework is available at: https://github.com/ZJU-FAST-Lab/GCOPTER.