How Do You Verify Equations for a Balancing Robot?

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SUMMARY

The discussion focuses on verifying the mechanical equations for a balancing robot, specifically one that maintains its upright position by controlling motors based on the center of mass. The user has derived equations for both the body and wheels but is uncertain about their accuracy. The request for validation highlights the importance of correct mathematical modeling in robotics, particularly in applications involving dynamic stability.

PREREQUISITES
  • Understanding of Newtonian mechanics
  • Familiarity with control systems in robotics
  • Knowledge of kinematics and dynamics
  • Basic proficiency in mathematical modeling
NEXT STEPS
  • Review the principles of dynamic stability in robotics
  • Study the derivation of equations of motion for robotic systems
  • Explore control algorithms for balancing robots, such as PID control
  • Examine case studies of similar balancing robots for practical insights
USEFUL FOR

Robotics engineers, mechanical engineers, students in robotics courses, and hobbyists building balancing robots will benefit from this discussion.

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Homework Statement


I am building a balancing robot like the one here:
http://www.geology.smu.edu/~dpa-www/robo/nbot/

It's basically a body mounted on two wheels and its purpose is to control the motors as to keep the wheels under the center of mass and therefore keep the body in an upward position.

I wrote the mechanical equations for the body and for the wheels separately, but I am not sure if they are correct. I need someone to check them, please.

Homework Equations


Are the equations in the attached photos correct?

The Attempt at a Solution


<see the attached photos>
 

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Last edited:
Physics news on Phys.org
Scraping the J x Theta derived twice x ...
from the first two equations in the first pic.

Those were wrong.



Are there any other mistakes?
 

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