Toward a Simple Model for Friction Dominated Multi-legged Locomotion

Legged locomotion is often modeled with non-slip contacts, in part due to the complexity associated with the number of possible Coulomb friction states that could arise. We have previously shown that multi-legged animals and robots almost inevitably slip a great deal, and that an alternative, non-Coulomb friction anzats provided promising simulation results with far less complexity. Here we report on advances in this model, where we have removed pitch and roll as dynamic parameters, thereby making the results dependent only on the ratios of leg stiffnesses and the ratios of friction coefficients, but not their absolute values. The new Python code takes 274+/-13 ms on a PC to simulate 500 time steps, running at x50 or more faster than real-time on one PC core. The error for predicting travelled distance per cycle (72 cycles, 14 trials, 7000 data points) is 7.3% (RMS). Per-cycle heading error was 0.13 rad (RMS). After finding and removing a systematic error in turning rates, per-cycle heading error reduced to 0.02 rad (RMS). We further illustrate the problems that arise solving for the Coulomb friction case. Overall, We hope this new simplified model will help us get a better understanding of multi-legged locomotion and multi-contact mechanics.