The SLIP model consists of a point mass attached to a massless spring leg. Its trajectory is divided into two phases. The flight phase, where the body follows a ballistic trajectory; and the stance phase, where the mass dynamics are affected by the compression and decompression of the spring. Despite its simple structure, the SLIP model dynamics are described by non-integrable equations of motion. Therefore, it is in general not possible to predict the trajectory of mass, and consequently it is not trivial to implement control strategies for successful hopping in the presence of noise.
In the considered model, the only control action we have access to consists of the angle at which the leg touches the ground. Our goal is to implement a strategy for leg positioning, to ensure that the model can perform successful jumps on rough terrain, even in the presence of faulty measurements of the terrain height. This study is being conducted with a series of Matlab simulations in order to obtain a lookup-table of feasible leg positions for a set of mass position and velocity (apex state). A region of desired apex states is detected, and a control strategy to maximize the probability of performing successful jumps and remain in the desired region is implemented .