Adaptive approximation of dynamics gradients via interpolation to speed up trajectory optimisation

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 inter-vals, we propose that trajectory optimisers can compute the dy-namics derivatives less often and then interpolate approximations to the derivatives in between calculated derivatives, gaining a sig-nificant speed up for overall optimisation time with no observable degradation in the generated behaviour. We investigate different methods of interpolating approximations as well as propose an adaptive method to detect when to compute the derivatives with finite-differencing. We find a speed-up of planning times on average by 60% in a contact-based manipulation task.