We propose a constructive control design for stabilization of non-periodic trajectories of underactuated mechanical systems. An important example of such a system is an underactuated “dynamic walking” biped robot walking over rough terrain. The proposed technique is to compute a transverse linearization about the desired motion: a linear impulsive system which locally represents dynamics about ...

We consider a class of multi-link mechanical systems arising from the dynamics of multisegmental animal locomotion in a two dimensional plane. As revealed in the earlier paper, when the head link is constrained along a specified direction, the remaining links can be fully controlled by the corresponding joint torques to achieve an autonomous locomotion in natural oscillation. In this paper, we ...

This paper presents analysis and design results for control systems subject to oscillatory inputs, i.e., inputs of large amplitude and high frequency. The key analysis results are a series expansion characterizing the averaged system and various Lie-algebraic conditions that guarantee the series can be summed. Various example systems provide insight into the results. With regards to design, we ...

In this paper, a mechanical model for an underactuated multi-finger grasping device is presented. The device has single-tendon, three-phalanx fingers, all moved by only one actuator. By means of the model, both the kinematic and dynamical behaviour of the finger itself can be studied. The finger is part of a more complex mechanical system that consists of a four-finger grasping device for robot...

This paper presents motion planning algorithms for underactuated systems evolving on rigid rotation and displacement groups. Motion planning is transcribed into (low-dimensional) combinatorial selection and inversekinematic problems. We present a catalog of solutions for all underactuated systems on SE(2), SO(3) and SE(2) × R classified according to their controllability properties.

Recent developments in millimeter-scale fabrication processes have led to rapid progress towards creating airborne flapping wing robots based on Dipteran (two winged) insects. Previous work to regulate forces and torques generated by flapping wings has focused on controlling wing trajectory. An alternative approach uses underactuated mechanisms with tuned dynamics to passively regulate these fo...

We develop tools for studying the control of underactuated mechanical systems that evolve on a configuration space with a principal fiber bundle structure. Taking the viewpoint of affine connection control systems, we derive reduced formulations of the Levi-Civita and the nonholonomic affine connections, along with the symmetric product, in the presence of symmetries and nonholonomic constraint...

A companion paper has addressed the problem of designing controllers that induce exponentially stable, periodic walking motions at a given fixed walking rate for a planar, biped robot with one degree of underactuation in single support. This note provides two additional control features: (i) the ability to compose such controllers in order to obtain walking at several discrete walking rates wit...

We introduce the notion of kinematic controllability for second-order underactuated mechanical systems. For systems satisfying this property, the problem of planning fast collision-free trajectories between zero velocity states can be decoupled into the computationally simpler problems of path planning for a kinematic system followed by time-optimal time scaling. While this approach is well kno...

Explicit formulas of smooth time-varying state feedbacks, which make the origin of an underactuated surface vessel globally uniformly asymptotically stable, are proposed. The construction of the feedback extensively relies on the backstepping approach. The feedbacks constructed are time-periodic functions.