Mini Cheetah improves its 'cat-like skills' with nickel coin boots
As quadruped robots learn to perform more and more dynamic tasks, they will likely spend a lot of time not standing on their feet. Falling is not necessarily inevitable (although it certainly is, since these are still robots on legs), because one can be in flight one way or another. The most dangerous phase of flight will be falling from a significant height, since that will almost certainly break your very expensive robot and any payload it may be carrying.
A bad fall is a problem not only for robots, so it is no surprise that quadrupeds in nature have already solved it. Or at least, it has been solved by cats, which can reliably land on their paws to reduce the impact of a fall. To teach quadruped robots this trick, robotics researchers at the University of Notre Dame taught Mini Cheetah some self-righting skills in mid-air using boots full of coins.
Mini Cheetah's legs (like those of many robots) were specifically designed to be light, because they must move quickly, and for that the mass that moves back and forth with each step must be minimized. This makes the robot as efficient as possible. But for the bot to reorient itself in the air, it must, on the contrary, start swinging as much mass as possible.
Each Mini Cheetah leg was modified with 3D-printed boots packed with two rolls of American five-cent coins (nickels), which add about 500 g to each foot, enough for the robot to move as needed. The reason the nickel boots matter is that the only way Mini Cheetah can change its orientation while falling is by swinging its legs. When its legs move in one direction, the body moves in the other, and the heavier the legs, the greater the force they can exert on the body.
As in any robotics work, getting the hardware to do what you want is only half the battle. And sometimes far less than half. The problem with Mini Cheetah was that it has very, very little time to figure out how to do everything right. It must detect that it is falling, work out its orientation, plan how to come down, and then successfully execute that plan. The bot does not have time to think all this through once it starts plummeting, which is why the method devised by the researchers is called a 'reflex' approach.
“Although trajectory optimization algorithms keep getting better, they are still not fast enough to find a solution from scratch in the fraction of a second between the moment the robot detects a fall and the moment it needs to start the recovery movement. We got around this problem by repeatedly dropping the robot in simulation, where we can spend as much time as we need to find a solution, and training a neural network to imitate the trajectory optimizer. The trained neural network maps initial orientations to trajectories along which the robot lands on its feet. We call this a 'reflex' approach because the neural network has essentially learned an automatic response that can be executed when the robot detects that it is falling”

This method works fairly well, but there are some limitations, most of which would not seem so bad if quadruped robots were not compared with quadruped animals. Cats are simply supercompetent at what they do, and the ability to imitate their skill of quickly rotating into a favorable landing configuration from any initial orientation will be very hard for a robot to achieve.
“The more I work in robotics, the more I realize how amazing nature is, and this project is a great example of that. Cats can make a full 180-degree turn when falling from shoulder height. Our robot ran into torque limits when turning 90 degrees from a height of about 3 m off the ground. Using full three-dimensional motion would be a huge improvement (sideways rotation should be easier, because the robot's moment of inertia is smaller in that direction), although I would be surprised if that alone brought us to cat-level performance”
The biggest challenge scientists faced when moving from 2D to 3D is self-collisions. It seems that keeping the robot from colliding should be simple, but the collisions themselves impose quite unpleasant constraints that make it numerically difficult to find high-quality solutions for trajectory optimization algorithms.

There are flexible actuated vertebrae for quadruped robots that have many advantages but are quite complex in themselves. According to Kurtz, in the case of the falling cat problem, a flexible spine could help both by providing a naturally flexible mass distribution and in terms of controller design, since one could directly imitate the cat's 'bend and twist' motion. Similarly, a flexible spine could help in tasks with long flight phases, such as space jumping problems.
“That said, reorienting in the air is not the main task for most quadruped robots, and it is not obvious to me that a flexible spine would help much with walking, running or climbing over uneven terrain. Moreover, existing rigid-backed hardware platforms such as Mini Cheetah are quite capable, and I think we have not yet unlocked the full potential of these robots. Control algorithms remain the main limiting factor for today's legged devices, and adding a flexible spine would likely lead to even more complex control problems”