controllability.pdf - Controllability and Walking Robots ME...

Info icon This preview shows pages 1–14. Sign up to view the full content.

View Full Document Right Arrow Icon
Controllability and Walking Robots ME 6401, Fall 2016
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Why study Controllability? Controllability is an important aspect of robot walking control design
Image of page 2
Underactuation: # Degrees of Freedom > # of Actuators corresponds to Locally Uncontrollable Nonlinear Dynamics What Makes Walking Control Difficult?
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
My Ph.D. Research In the event a robot encounters uncontrollable dynamics, manipulate the remaining controllable dynamics to stabilize the walking (hybrid system) [1] Powell, Ma, Ambrose and Ames. Mechanics-Based Design of Underactuated Robotic Walking Gaits: Initial Experimental Realization. Humanoids 2016
Image of page 4
Uncontrollable Dynamics [1] Powell, Ma, Ambrose and Ames. Mechanics-Based Design of Underactuated Robotic Walking Gaits: Initial Experimental Realization. Humanoids 2016
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Finishing the Controllability Lecture Remaining Topics to Cover: Controllable Subspace If you can’t control the whole system, what can you control? Two Tank Example Flow-rate Model (see lecture 2) Apply controllability rank test Compute the controllable subspace
Image of page 6
Previous Lecture Definition [Controllability]. A dynamical system is controllable on [t 0 , t 1 ] if there exists an input function u(t) that transfers any initial state x(t 0 ) to any final state x(t 1 ).
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Previous Lecture Definition [Controllability]. A dynamical system is controllable on [t 0 , t 1 ] if there exists an input function u(t) that transfers any initial state x(t 0 ) to any final state x(t 1 ). Theorem [LTI Controllability]. A system of the form is completely controllable iff rank(P) = n , where is the Controllability Matrix
Image of page 8
Previous Lecture Definition [Controllability]. A dynamical system is controllable on [t 0 , t 1 ] if there exists an input function u(t) that transfers any initial state x(t 0 ) to any final state x(t 1 ). Theorem [LTI Controllability]. A system of the form is completely controllable iff rank(P) = n , where is the Controllability Matrix what if rank(P) < n ?
Image of page 9

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Controllable Subspace Consider a 3-Dimensional System
Image of page 10
Controllable Subspace Consider a 3-Dimensional System the system can be steered from the origin to an arbitrary point in space Controllable
Image of page 11

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Controllable Subspace Consider a 3-Dimensional System the system can be steered from the origin to an arbitrary point in space Controllable Not controllable the system can only be steered from the origin to a subset of the space
Image of page 12
Controllable Subspace
Image of page 13

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 14
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern