Gravity powered locomotion and active control of a family tree of robotic mechanisms

This dissertation presents several novel approaches to identify and control the locomotion modes of a collection of energetically efficient robots that can produce stable gait. One cannot ignore the promise of robots that can walk by using very little energy. Gravity powered bipeds provide ample proof that this is possible. It is conceivable that mechanisms that are much simpler than legged robots can also produce gravity powered locomotion. It is also plausible that one can gain deeper understanding of the dynamics of such simple mechanisms.;Evolutionary biology tells us that one can learn a great deal by studying the hereditary traits of organisms that evolve over generations. Thus, we foresee great benefits in analyzing a chain of mechanisms that span from the very simple to the progressively more complicated. We have generated a family of five generations of planar mechanisms, with members that can be as simple as a bouncing particle or as complex as a five link biped. In this dissertation we have studied the gravity powered locomotion (passive gaits) of the first three generations by placing them on inclined planes. The elements of the first three generations are: bounding ball, baton, and three-mass two-link system. We demonstrated that not only each system inherits all the passive gait patterns of its ancestors but also it can create its own.;We discovered three types of passive gait patterns, each including various gait modes, for the first three generations of our systems: Hopping, Tapping, and Walking. The bouncing particle can generate a passive hopping gait. The baton inherits the hopping gait and generates quasi-periodic hopping modes and a new tapping gait with three modes. The three-mass system inherits all gaits and modes of the baton and generates two additional tapping modes (crawling and flapping). In addition, this last system generates bipedal locomotion. All gaits of our passive systems are structurally unstable. The passive hopping and tapping gaits require that the coefficient of restitution of the masses that periodically collide with the ground to be equal to one (e = 1). Bipedal locomotion requires e = 0. A minimum surface friction coefficient is another necessary physical condition for the passive gaits. Hopping and tapping gaits are significantly less susceptible to changes in locomotion surface slope angle than is the bipedal locomotion of the three-mass system.;We used the impulsive control and nonlinear control theories to actively maintain the passive gaits of our systems. We have shown that the hopping, tapping, and walking gaits are controllable with impulsive actuation. For all the systems, a Lyapunov based impulsive controller is sufficient to produce energetically efficient and asymptotically stable hopping and tapping gaits on arbitrary ground slope angles. For the three-mass system, a Lyapunov based impulsive controller is sufficient to produce non-scuffing, energetically efficient, and asymptotically stable walking on flat surfaces. A potential energy shaping continuous controller in addition to the Lyapunov based impulsive controller is sufficient to produce non-scuffing, energetically efficient, and asymptotically stable walking on arbitrary ground slope angles.;We have developed a preliminary contact based rule of passive gait patterns that seems to work well for the first three generations of the family. We think that this rule can be extended to the more complex, last two generations of the family. The use of this rule will make it possible to catalogue the majority of the passive gait patterns of the systems we consider. In addition, as we have seen in our study, it will pave the way to develop an impulsive active control scheme.;Having a catalogue of gait patterns for robotic locomotion systems, that are progressively related in structure, can be the best road map to design reconfigurable locomotors. Such reconfigurable robots would become potentially capable to separate or cluster into specialized forms, depending on the tasks they are about to perform.