Abstract
Locomotion systems with variant constraints are familiar in real world applications, but the dynamics and control issues of variant constraint systems have not been sufficiently discussed to date. From the viewpoint of Lagrange–d’Alembert equations with additional variable constraints, this paper investigates the modeling approaches of a class of hybrid dynamical systems (HDS) with instantaneously variant constraints and the switching control techniques of stabilizing the HDS to given periodic orbits. It is shown that under certain conditions there possibly exist zero impact periodic orbits in the HDS, and the HDS can be stabilized to the period-one orbits by a linear controller with only partial state feedback, even though the HDS are generally underactuated nonholonomic systems. As an example, a one-legged planar hopping robot is employed to demonstrate the main results of modeling and control of a class of HDS.
Highlights
Variant constraint systems, such as structurally reconfigurable systems, soft body locomotion systems, and contact or collision systems and so on, are familiar in real world applications
Theorems 2 and 4, it is not difficult to find that the hybrid dynamical system (21), (22), (23) or (24) could be stabilized to a smooth periodic orbit that is governed by the nature dynamics of the system while the periodic orbit satisfies the zero impulse condition Equation (27)
From the viewpoint of Lagrange–d’Alembert equations with additional constraints, this paper investigates the modeling approaches of a class of variant constraint systems (VCS) with instantaneously variant constraints, and the switching control techniques of stabilizing the VCS to given periodic orbits
Summary
Variant constraint systems, such as structurally reconfigurable systems, soft body locomotion systems, and contact or collision systems and so on, are familiar in real world applications. Introduced the impact model of several kinds of dynamical legged robots in brief and the main contents of the monograph are motion planning and hybrid control issues of the HDS. It is interesting that many theoretical or experimental investigations, such as the legged running robot systems [4,5,9], have shown that the underactuated nonholonomic systems [19] could be stabilized to certain time varying trajectories by switched linear controllers. VCS can be stabilized to certain periodic orbits by simple switched linear controllers with only partial state feedback in a time-sharing manner. This point is appealing in practice and supports the innovations of the VCS in a broader field well.
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