Amira Abdel-Rahman
2.47 Final Project

Repository



2.47 Bio-Inspired Robotics Final Project
Proposal link.


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 \\
-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

First objective: maximize height h'
 to push it to go up, got the max x'

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


Updates and Results

November 23

having trouble finding a gait
Added starting \dot{q_1}^{start}
,\dot{q_2}^{start}
,\dot{x}^{start}
,\dot{y}^{start}
 to the optimization variables
added  q_1^{start}
 and q_2^{start}
 to the optimization variables
recently added tf as it changed the dynamics
Moving to casadi instead of fmincon (maybe the derivatives will help)

lots has to be changed as it does not support branching statements they have discontinuous derivatives, that affect the two functions discrete_impact_contact and joint_limit_constraint in simulate_leg.m

first the angle constraints has to be added as constraints
second the simulation has to be divided into three stages: stance flight and stance again. The tf of each of these stages will be come an optimization variable as well


November 12: First Hop


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?)