Modeling, simulation, and optimization of a monopod hopping on yielding terrain

Legged locomotion on deformable terrain is a challenging and open robo-physics problem since the uncertainty in terrain dynamics introduced by ground deformation complicates the dynamical modelling and control methods. Moreover, learning how (e.g. what controls and mechanisms) to move efficiently and stably on soft ground is a bigger issue. This work seeks to control a 1D monopod hopper to jump to desired height. To achieve this goal, I first set up and validate a discrete element method (DEM) based soft ground simulation environment of a spherical granular material. With this simulation environment, I generate resistive force theory (RFT) based models of the ground reaction force. Then I use the RFT model to develop a feedforward force control for this robot. In the DEM simulation, I use feedback control to compensate for variations in the ground reaction force from the RFT model predictions. With the feedback control, the robot tracks the desired trajectories well and reaches the desired height after five hops. It reduces the apex position errors a lot more than a pure feedforward control. I also change the area of the robots square foot from 1cm^2 to 49cm^2. The feedback controller is able to deal with the ground reaction force fluctuations even when the foot dimensions are on the order of a grain diameter.