README.md

2.47 Bio-Inspired Robotics Final Project

Presentation

• Link to the google slides presentation.

Proposal

• Link to the google docs.

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Simulation

q   = [\theta_1  ; \theta_2; x; y]; \\
\dot{q}   = [\dot{\theta}_1  ; \dot{\theta}_2; \dot{x}; \dot{y}];

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Control

simulation/optimization

All torque control with bezier curves

hardware control

Get Bezier curve path of the leg from simulation/optimization and have an Impedance control (flight stage) and torque control (stance phase)

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Optimization

Variables

Two Bezier curves for torques:

ctrl_1=[T_1,T_2,..T_n] \\
ctrl_2=[T_1,T_2,..T_n] \\
n=6 \\
-0.85<T_i<085

Starting Conditions:

ground \ height = -0.164; \\
\theta_1=-36*\pi/180; \\
\theta_2=90*\pi/180;\\
x=y=0\\
\dot{\theta}_1=\dot{\theta}_2= 0\\
\dot{x}=\dot{y}= 0\\

Constraints

x^{end}>=x^{start} \\
q_1^{end}=q_1^{start} \\
q_2^{end}=q_2^{start} \\
y^{end}=y^{start} \\

\dot{q}_1^{end}=\dot{q}_1^{start} \\
\dot{q}_2^{end}=\dot{q}_2^{start} \\
\dot{x}^{end}=\dot{x}^{start} \\
\dot{y}^{end}=\dot{y}^{start} \\

Objective Function

1. First objective: maximize height h' to push it to go up, got the max x'
2. Then I added to the constraints:

   apex \ height = h' \\
   x_{end}=x' \\

   and minimized cost of transport by minimizing:

   E/(m*g*d)

   which is the similar as minimizing sum of torque squared as m, g and d is fixed

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Updates and Results

5 December

2 December