  We present a novel continuous time trajectory representation based on a
Chebyshev polynomial basis, which when governed by known dynamics models,
allows for full trajectory and robot dynamics estimation, particularly useful
for high-performance robotics applications such as unmanned aerial vehicles. We
show that we can gracefully incorporate model dynamics to our trajectory
representation, within a factor-graph based framework, and leverage ideas from
pseudo-spectral optimal control to parameterize the state and the control
trajectories as interpolating polynomials. This allows us to perform efficient
optimization at specifically chosen points derived from the theory, while
recovering full trajectory estimates. Through simulated experiments we
demonstrate the applicability of our representation for accurate flight
dynamics estimation for multirotor aerial vehicles. The representation
framework is general and can thus be applied to a multitude of high-performance
applications beyond multirotor platforms.
