static vs dynamic stability

These are the two fundamentally different ways a robot can keep from falling over. A statically stable robot stays upright even if you froze it in place: at every instant its weight is balanced over a wide enough base of support that gravity cannot tip it, like a table or a person standing with feet apart. A dynamically stable robot, by contrast, only stays up because it keeps moving; freeze it and it would topple, the way a bicycle stays up while rolling but falls the moment it stops, or the way you can balance a broom on your palm only by constantly shuffling your hand.

The idea that ties this together is the support polygon: draw a line connecting all the points where the robot touches the ground (its feet), and the area enclosed is the safe zone. As long as the robot's center of mass — the average point where its weight acts — hangs directly above somewhere inside that polygon, gravity pulls it down onto its feet and it stays put. That is static stability. The wider the feet are spread, the bigger the polygon, the more margin for error. A four-legged robot standing still or a tripod is rock-solid this way.

Dynamic stability throws that safety net away on purpose. A walking or running robot spends much of its time with its center of mass outside the support polygon — during a stride it is literally tipping over — and it stays upright only by using momentum and quick, well-timed steps to catch itself before it falls, again and again. This is harder and riskier to control, but it is the price of speed and agility: fast running, two-legged walking, and balancing on a single point are all dynamic. Slow, careful, wide-stanced motion tends to be static; fast, narrow, momentum-driven motion tends to be dynamic.