Commit 62c6cd4f authored by Amira Abdel-Rahman's avatar Amira Abdel-Rahman
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# 2.47 Final Project
# 2.47 Bio-Inspired Robotics Final Project
2.47 Bio-Inspired Robotics Final Project
Proposal [link.](https://docs.google.com/document/d/1dNlEJe5-szEFqpwIeSgpptBZx4WYQ4iAs7nnBplzilc/edit)
<img src="./img/leg.png" width="50%" /><br></br>
---
## Simulation
$$
q = [\theta_1 ; \theta_2; x; y]; \\
\dot{q} = [\dot{\theta}_1 ; \dot{\theta}_2; \dot{x}; \dot{y}];
$$
---
## 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)
---
## Optimization
### Variables
Two Bezier curves for torques:
$$
ctrl_1=[T_1,T_2,..T_n] \\
ctrl_2=[T_1,T_2,..T_n] \\
n=6 \\
2<T_i<2
$$
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
---
## Results
###First Hop
<img src="./img/first_hop.gif" width="80%" /><br></br>
<img src="./img/6.1_cntrl.png" width="80%" /><br></br>
<img src="./img/6.3_cntrl.png" width="80%" /><br></br>
---
## TODO and Questions
- [ ] script to calculate before and after adding spring
- [ ] Optimize with springs
- [ ] get real physical variables
- [ ] angle limits
- [ ] masses
- [ ] torques limits
- [ ] the friction coefficients
- [ ] try other starting conditions
- [ ] is velocity calculation correct?
- [ ] what if it torque not enough
- [ ] for the control should $T_1 = T_n$ (cyclical control?)
---
Proposal: https://docs.google.com/document/d/1dNlEJe5-szEFqpwIeSgpptBZx4WYQ4iAs7nnBplzilc/edit
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