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Underactuated Robotics MIT 6.832
Saul Field edited this page Nov 6, 2020
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Schedule: http://underactuated.csail.mit.edu/Spring2020/schedule.html
Text: http://underactuated.csail.mit.edu/index.html
Lectures (2020): https://www.youtube.com/playlist?list=PLkx8KyIQkMfX1WpWYqtep7TOmboZeDtev
Lectures (2019): https://www.youtube.com/playlist?list=PLkx8KyIQkMfVG-tWyV3CcQbon0Mh5zYaj
Lecture: https://youtu.be/lMhs3TbjMl0
Text: http://underactuated.mit.edu/acrobot.html
- deriving equations of motion for 3 "canonically underactuated systems" (acrobot, cart-pole, quadroter)
- can we linearize the nonlinear dynamics at a fixed point and use LQR?
- controllability: A control system is called controllable if it is possible to construct an unconstrained input signal which will move the system from any initial state to any final state in a finite interval of time
- underactuated does not mean non-controllable!
- eigenvalue analysis of the linearization for the pendulum
- phase portrait of the linear system approximates the true phase portrait extremely well (locally)
- demo: simulations using LQR on the cart-pole and the quadrotor; stabilizes the system very well
- half of the problem still remains: how do we get the system to the area around the fixed point if we don't start there?
Good overview of linear systems and eigenvalue analysis:
Lecture: https://youtu.be/sL5KRBjrk6I
Text: http://underactuated.mit.edu/acrobot.html
- energy shaping controller for the simple pendulum
- controller is attractive but not stable
- intuition: E will be less than E_desired until it gets to the upright fixed point, u will be proportional to theta_dot. This means it will swing to one side until it reaches theta_dot = 0, then will pump energy through the control torque in the direction of increasing theta_dot as it swings down.
- after it reaches the fixed point, if it is perturbed it will swing all the way down and around the other side to get back to the fixed point. This is not the desired behaviour of a stable system, so we need LQR to balance when we're in the vicinity of the fixed point
- use collocated partial feedback linearization for the cart-pole to simplify the dynamics. Then, design an energy shaping controller to stabilize the pendulum, with added PD terms to stabilize the cart itself (still switch to LQR at the top)