Massachusetts Institute of Technology
Sign in

Dynamic Walking 2010. Ian Manchester. Regions of Attraction to Limit Cycles of Nonlinear Hybrid Systems

This talk will present a method for computing estimates of regions of attraction to limit cycles of quite a general class of nonlinear hybrid systems. Such limit cycles typically represent the "nominal" motion of a walking robot, with alternating phases of continuous motion and distinct impacts upon footfall. The problems of stabilizing such motions and characterizing the regions of stability are central in dynamic walking, and this talk will present contributions on both problems. It is well-known that limit cycles cannot be asymptotically stable in the standard sense, since perturbations in phase are persistent. The more relevant concept is orbital stability, which can be analyzed via a lower-dimensional coordinate system transversal to the target orbit. A new analytical construction is given which is applicable to general nonlinear systems with impacts. This coordinate system is then used for both control via transverse linearization, and computing estimates of regions of attraction via Lyapunov's direct method and the sum-of-squares relaxation of polynomial boundedness. Both impacts (switching surfaces) and the need for well-posedness of dynamics present interesting issues in the selection of transversal coordinate system, which will be discussed. The method will be illustrated with examples including the van der Pol oscillator, the rimless wheel, and the compass-gait walker.

Comments (0)

It looks like no one has posted a comment yet. You can be the first!

You need to log in, in order to post comments.

Dynamic Walking 2010

Dynamic Walking 2010

Category: Education | Updated 7 years ago

August 05, 2010 13:33
All Rights Reserved (What is this?)
Additional Files

9251 times

More from Dynamic Walking 2010

Dynamic Walking 2010. Shuuji Kajita. Development of Cybernetic Human HRP-4C - struggle to realize human walking

Dynamic Walking 2010. Shuuji Kajita...

Added 7 years ago | 00:47:15 | 5557 views

Dynamic Walking 2010. Jessy Grizzle. Feedback Control of the Bipedal Robot MABEL

Dynamic Walking 2010. Jessy Grizzle...

Added 7 years ago | 00:56:13 | 8549 views

Dynamic Walking 2010. Emanuel Todorov. Linearly-solvable optimal control: Theory and applications

Dynamic Walking 2010. Emanuel Todor...

Added 7 years ago | 00:33:38 | 3875 views

Dynamic Walking 2010. Anton Shiriaev. VHC Tools for Gait Analysis and Control.

Dynamic Walking 2010. Anton Shiriae...

Added 7 years ago | 00:34:00 | 5690 views

Dynamic Walking 2010. Robert Gregg. Control and Planning with Asymptotically Stable Gait Primitives: 3D Dynamic Walking to Locomotor Rehabilitation.

Dynamic Walking 2010. Robert Gregg....

Added 7 years ago | 00:33:35 | 6978 views

Dynamic Walking 2010. Tomomichi Sugihara. Dynamics Morphing Toward Globally Stable Bipedalism

Dynamic Walking 2010. Tomomichi Sug...

Added 7 years ago | 00:27:34 | 5508 views