A comparison of dynamics interpolation methods for speeding up trajectory optimisation

Abstract

Trajectory optimisation methods for robotic motion planning often require the use of first order derivatives of the dynamics of the system with respect to the states and controls of the system. Particularly when multi-contact dynamics are present, these derivatives are often numerically approximated by a method such as finite-differencing. Finite-differencing whilst using an expensive physics simulator is usually the bottleneck in these trajectory optimisation algorithms. Since these dynamics derivatives do not change substantially over certain time intervals, we reason that trajectory optimisers can compute the dynamics derivatives less often and then interpolate approximations to the derivatives in between calculated derivatives without losing too much accuracy whilst gaining a significant speed up for overall optimisation time. We investigate multiple different methods to detect such time intervals and to interpolate between them.