# hw3 - ECE 594D Robot Locomotion Homework 3 Winter 2010 (due...

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ECE 594D Robot Locomotion Winter 2010 Homework 3 (due 5pm 2/5, in HFH 5115) 3.1 Non-collocated Partial Feedback Linearization (PFL) control for the acrobot. In class, we looked at MATLAB simulation results for collocated PFL control of the acrobot (Figure 1), as outlined in Spong [3]. Download two m-ﬁles from the course homework website: ac- robot_collocated_linearization.m , which solves the equations of motion (EOMs) for the system with collocated PFL control , and acrobot_animate.m , which will allow you to ani- mate the motion. You can then run a simulation using the following MATLAB commands: X0 = [-pi/2+.1;0;0;0]; % set an initial condition [t,y] = ode45(@acrobot_collocated_linearization,[0 20],X0); % to simulate gure(1) acrobot_animate(t,y) % to animate a) Modify acrobot_collocated_linearization.m to implement non-collocated PFL control, as outlined in [3]. (It is probably best to begin by copying this m-ﬁle to a new ﬁle called ac- robot_noncollocated_linearization.m , so you have the old code to look at if you need to debug anything as you edit. In addition to [3], you may wish to reference the PFL class notes, handed out in class and also available for download from the class handouts website.) (i) Include a print-out of your code in your homework. (ii) Include a print-out of a plot of the states over time, e.g., from: plot(t,y) Figure 1: The acrobot (image taken from [2]; torque input τ at elbow not shown). (Last revised January 30, 2010) 1 Homework 3

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ECE 594D Robot Locomotion Winter 2010 3.2 Underpowered actuators. The torque required to achieve PFL control was not an issue ad- dressed in [3] nor in class so far. Separate from the issue of being “underactuated” (where we cannot independently control every degree of freedom), the system dynamics may be notice- ably “underpowered”. Motors, for example, generally provide much lower torque and higher velocity than desired (which is why they are often geared down). However, gearing down a motor changes the actuator dynamics, making it challenging (if not impossible) to provide a pure “torque” output. So, we wish to use either a “direct drive” motor or very low transmission ratio (e.g., a belt drive increasing torque by a factor of 2-3 or so). All of which is to say: it is
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## This note was uploaded on 12/29/2011 for the course ECE 594d taught by Professor Teel,a during the Fall '08 term at UCSB.

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hw3 - ECE 594D Robot Locomotion Homework 3 Winter 2010 (due...

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