The problem of performing complex maneuvers in challenging terrains is crucial to the advancement of legged robots and assistive devices, yet little progress has been made in exploring practical solutions to operate in these environments. In this thesis, we tackle the problem by developing strategies to predict a robot's center of mass (CoM) behavior based on contact constraints, and any arbitrary CoM path for situations in which the system has single or multiple points of contact through which external reaction forces may be applied. Our method consists of first leveraging previous work on multi-contact dynamics to derive reaction force behavior from internal tension force profiles and kinematic CoM trajectories. We then study the nonlinear dynamics of single contact phases along arbitrary paths and employ numerical integration to derive state-space approximations of CoM behavior. We use this theoretical framework to synthesize complex maneuvers in various terrains by means of a motion planner in which we determine step transition sequences for continuous motions involving contact profiles which vary with time. Furthermore, we validate our strategy through several comparative case studies, examining the motion of a human subject performing a difficult maneuver in an aggressive terrain. We then seed our motion planning algorithm with a limited set of parameters chosen to match those of a human subject and predict CoM behavior for the same motion pattern. These case studies show that the estimated CoM behaviors generated from our planning algorithm closely resemble the behavior of the human subject and therefore validate our methods. / text

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