2.47 Bio-Inspired Robotics Final Project

Presentation

• Link to the google slides presentation.

Proposal

• Link to the google docs.

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

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

Updates and Results

5 December

2 December

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?)

• change bezier to lower dimensions to allow for sudden changes

• check if angle calculation is correct

• from last to to first

• adding springs