  We present an optimization-based framework for multicopter trajectory
planning subject to geometrical configuration constraints and user-defined
dynamic constraints. The basis of the framework is a novel trajectory
representation built upon our novel optimality conditions for unconstrained
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 robustness 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 methods by orders of
magnitude. The source code of our framework is available at:
https://github.com/ZJU-FAST-Lab/GCOPTER
