Design of oscillatory movement for ground-based locomotion and synchronized movement in bioinspired robotics

Animals in nature move through the rhythmic oscillation of their appendages and bodies. Similar oscillatory motion is a hallmark of bioinspired robots, which seek to embed biological principles into the design, sensing, and control of robots. While there is a robust theory of nonlinear oscillatory systems, there still exist fundamental gaps in knowledge when considering robotic locomotion. For example, ground-based robots make intermittent contact with the ground to propel themselves forward or to turn, and such ``making and breaking'' of contact between the oscillatory actuation source and the environment can lead to novel locomotion challenges. Additionally, when multiple robots are moving together the coordination of rhythmic gaits (such as through synchronization) may lead to beneficial group movement. However, the methods to design such synchronized locomotion are not altogether straightforward especially when considering potential communication limitations between robots. This dissertation addresses specific problems in oscillatory locomotion of bioinspired robots. In the first study the author developed a inch-worm inspired robot that can push and pull against the ground with simple ``feet'' to propel itself. The author studied how basic feedforward oscillatory actuation of the ``feet'' leads to non-trivial locomotion dynamics through foot slipping and stochastic foot-ground contact mechanics. In follow up work the author demonstrated enhanced capabilities of this robot such as turning, that was achieved through incorporation of soft materials in the design process. In the third study the author studied the collective behavior of simple three-link ``swimming'' robots that are controlled through feedforward oscillatory actuation. Oscillatory phase differences between neighboring robots lead to intermittent collisions that drive the group into a stable spatial configuration by lateral and longitudinal movement. We derive conditions for group spacing and density based on phase variation, examine the effective interaction potential between neighboring robots, and identify a compatibility condition for robots to safely swim in close proximity without collisions. In the last study the author enables the oscillatory motion of robot's in a collective to be generated through nonlinear, limit-cycle dynamics. The author finds that intermittent contact between robots leads to overall group synchronization of oscillatory swimming gaits which reduces contact forces between robots and enables high density configurations. A phase oscillator model of this process is developed and the author derives the theoretical conditions for group synchronization, observing good agreement between experiments and the theoretical model. This work enables the author to demonstrate in experiment the swimming synchronization of four three-link robots that do not communicate with each other, but instead leverage the nonlinear dynamics of the nonlinear oscillator control system. Ultimately, the work the author presents in this thesis leads to new understanding of how oscillatory motion is influenced by intermittent, nonlinear, interactions with the environment and between robots