Estimate the Pulling Force of Boston Dynamics' Robo-Dog Army 估计波士顿动力公司机器狗大军的拉力
Rhett Allain 雷特 阿兰
When Boston Dynamics shares a new robot video，my robophobia levels increase just a little bit. I don't know why. There is something about these robots that get into the uncanny valley for me. This particular video is both fascinating and disturbing. It's fascinating because here are a bunch of robots pulling a truck （not a pickup truck a real truck）. It's disturbing because it shows a BUNCH of robots. That's the beginning of a robot army.
Perhaps the best way to calm myself is to consider the physics. Analyzing situations such as this is exactly what I like to do. If I combine something I like （physics） with something disturbing （robot army） maybe I will be OK.
So， just how difficult is it to pull a truck like this？ Is this something that only a robot can do， or could a small bunny rabbit also do it？ The physics is mostly about friction. If you want to pull this massive truck， you both need high friction and you need low friction yes， at the same time.
What is friction？ In a situation like this， there are actually two types of friction. There is the static friction between the pet robots' feet （maybe they aren't pets） and then there is the rolling friction between the tires of the truck and the road.
OK， the less-than-or-equal part makes it pretty tough to deal with friction. But since we are looking at the extreme cases， we can say that the robots are at the maximum friction （or close to it）. Let me draw a force diagram for the lead dogbot while it is pulling on the rope.
Yes， all of those forces should add up to zero vector force. That's what you need to move at a constant velocity. Then why do you need to pull that truck at all？ If you want it to move at a constant velocity， it shouldn't need any pulling force？ Right？ Yes， in an ideal situation you wouldn't need to pull the truck at all （once you got it moving）. However， in this case there is also a frictional force on the truck. Also， this is not on flat ground （but I will get to that shortly）.
Let's estimate this maximum pulling force from one SpotMini robot （that's what they are called）. According to Boston Dynamics， the robot has a mass of 25 kg. This means the weight and the normal force （since it's on flat ground） would be equal to 245 Newtons. Assuming a coefficient of 0.7 for the interaction between rubber and asphalt，the maximum frictional force would be 171.5 Newtons per bot. For 10 robot dogs， this would be 1715 Newtons. That's fairly significant.
But why do you need to pull with any force？ It's not because the truck is heavy; it's because there is also a frictional force on the truck. The truck isn't sliding， it's rolling. So we call this rolling friction. It basically works the same way as normal friction， but it's actually due to the deformation in the tires and the friction in the wheel bearings as the truck rolls. It's pretty tough to estimate the coefficients （because it depends on lots of things），but I can do it anyway. A site lists the rolling coefficient of friction at around 0.02 for a tire on asphalt. Notice that this coefficient is much lower than the static coefficient for the robots.
OK， I could draw the same diagram for the truck that I did for the robot. The only difference would the replacement of legs with wheels and the directions of the forces. In this case the frictional force is to the left and the tension in the rope is to the right. If you look at the video very carefully， you will see the GVW （gross vehicle weight） right there on the side of the truck. It lists a value of 26，000 （pounds） which is equivalent to 11793 kilograms. With this mass and rolling friction coefficient，you would have to pull with a force of 2311 Newtons. That's pretty close to the estimated friction from the robot dogs.
What about pulling a truck uphill？ Yes， that is much harder.
Hold on. Why am I helping the robots figure out this physics stuff？ Shouldn't the robots be helping me？ Is this just the first step of the robopocalypse？！