![]() For the self-balancing robot the pivot point is the axle. The pendulum’s mass is located a distance from the pivot point. Starting with the x-axis and, we can consider the self-balancing robot consisting of a cart (the wheels and motors) with mass M and a pendulum (everything else free to rotate in respect to the wheel and motors) with mass m. In this example, the equations of motion for the x and y directions will be derived using the free body diagram of a pendulum on a cart. With Newton’s law and the self-balancing robot’s free body diagram we can go ahead and write the equations of motion for the system. Inverted pendulums usual take one of three forms, either an inverted pendulum on a linear track, inverted pendulum on a cart or a self-balancing robot. Α = the angular acceleration of the body, rad/s 2įree body diagram Free body diagram of inverted pendulum on cartįree body diagram of self-balancing robot I = the body’s mass moment of inertia about it’s centre of mass, kg.m 2 M = the sum of all external moments about the centre of mass of a body, N.m The application of Newton’s law to one-dimensional rotational systems requires the equation to be modified to The cornerstone for obtaining a mathematical model, or the equations of motion for any mechanical system is Newton’s law į = the vector sum of all forces applied to each body in the system, newtons Ī = vector acceleration of each body with respect to an inertial reference frame, m/s 2 Personal goal: refresh basic understanding of modelling and control. Dertermining the centre of gravity for a self-balancing robotĪccurately model an inverted pendulum to use for control algorithms development for physical implementation.This is part of a series of posts covering the development of a self-balancing robot: ![]()
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May 2023
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