Impact of slope on dynamics of running and climbing

By combining biological studies and modeling work, the dynamics of running on horizontal terrain and climbing pure vertical surfaces have been distilled down to simple reduced order models. These models have inspired distinct control and design considerations for robots operating in each terrain. However, while the extremes are understood, the intermediate regions of moderate slopes have yet to be fully explored. In this paper, we examine how cockroaches vary their behavior as slope is changed from horizontal to vertical, with special care to examine individual leg forces when possible. The results are then compared with a lateral leg spring based (LLS, horizontal running) and Full-Goldman based (FG, vertical running) models. Overall, from the experimental data, there appears to be a continuous shift in the dynamics as slope varies, which is confirmed by similar behaviors exhibited by the LLS and FG models. Finally, by examining the stability and efficiency of the models, it is shown that there are stability limits related to the amount of energy added by the front versus rear legs. This corresponds to the shift in leg usage demonstrated by the biological experiments and may have significant implications for the design and control of multi-modal robotic systems.