Robot stability

Tip angle and the acceleration a robot can take before it tips, from its centre of gravity.

Inputs

Centre of gravity height

From the floor. Raise it for an extended elevator or arm.

Horizontal distance to tipping edge

From the CG to the wheel contact line in the direction of tipping.

Result

Tip angle

55.3

Maximum acceleration before tipping: 1.444

How it’s calculated

Formula

\theta_\text{tip} = \arctan\frac{b}{h}

a_\text{max} = g \, \frac{b}{h}

With your numbers (converted to SI units)

\theta_\text{tip} = \arctan\frac{0.3302}{0.2286} = 55.3^\circ

a_\text{max} = 9.807 \times \frac{0.3302}{0.2286} = 14.17\,\text{m/s}^2

What it means

A robot tips when the line from its centre of gravity through the tipping edge goes past vertical. Tilting it by θ_tip (on a ramp, or hit from the side) brings it to that edge. Accelerating or braking harder than a_max also tips it, because the inertial force acts at the CG. A low CG and a wide base are what make a robot hard to tip.

Assumptions

A rigid robot on a flat floor; bumpers and suspension flex are ignored.
Quasi-static: ignores momentum from a hit.

Learn the concepts behind this on resources.simbotics.org · All formulas