8 replies to this topic

[Phaesphoros]

Disclaimer: I'm neither an animator nor an expert for bipedal movement.

For "What has this to do with gameplay balance?", see the end of the post.


I've decided to look into how bipeds move, i.e. things that use two legs like 'Mechs and humans, to see what Real Life™ says about climbing a slope.

A step of a biped.

Spoiler

First, a step on a plane. Not very interesting, but it help for some principles, like how the centre of mass moves. The centre of mass is located slightly over the hip for humans. Note how this point is in constant forward motion:


Now, climbing a slope is bit different. It's not just the same walk rotated



Rather than that, the vertical movement is not constant, it only occurs at the end of a step. Also note how the feet (and toes, not displayed) are used both to gain height and stability:

Now, why does a biped slow down when it tries to climb a hill? I think there are two main reasons.

First

Spoiler

It might have something to do with the muscles, and how they work. Muscles can only "create" a force by contracting (they either contract or relax), that's why they come in pairs:


To move to the second position, this biped can use both the muscles of the thigh and lower leg. If it makes a bigger step, it can only make use of the thigh's muscles:



Additionally, the contraction might be less efficient if the thigh is in this position (angle). That is, the biped has to contract the muscle harder to get the same force to move its body.

Therefore, you'll normally make smaller steps while climbing a hill. The same goes for stairs: the more you climb at once, the more exhausting it is.

This mechanism interestingly seems not to impose a limit to the angle of a slope the biped CAN climb; it just has to make it steps smaller.

The second reason why a biped walks slower uphill...

Spoiler

... has to do with friction. Yeah, some physics, bear with me for a moment.

If you stand on a slope, you might note that there's friction between your feet and the slope, and that's what keeps you from sliding down.



If the biped stands still, the only force acting is the gravitational force. It can be applied (to model gravity) at the centre of mass of a body. As the biped doesn't move, a force equal in amount and opposite in the direction has to be applied by the biped to cancel the gravitational force. No resulting force => no movement. This force comes from standing on the ground, you could say the ground applies this force to your feet.

But the biped stands still on a slope, the gravitational force cannot be directly cancelled by the force coming from the ground as the latter is always normal to the surface of the ground; hence it's called normal force. The friction between the ground and the feet therefore has to cancel the rest of the gravitational force.

Also note that in the picture above, the biped has both feet on the ground. The friction therefore acts on both feet, which have twice the area.

The biped now climbs the hill. In order to do so, it needs to accelerate. This acceleration introduces another force, and the biped needs to lift one foot. In the picture below, I've depicted the force it needs to impose to the ground in order to accelerate.



Note how the forces compare to the situation before:
The friction at one foot needs to be much higher, because it's only one foot and there's this additional force to accelerate.

The crux is that there's a maximum friction. If this blue arrow becomes to large, the foot will slide off. That does not yet mean it's impossible to climb the hill. Only when the acceleration from sliding down the slope (due to gravity) is as big as acceleration to climb the slope, then the biped cannot climb the slope, it'll run on the same spot.

The maximum friction is dependent on the biped's feet (surface area, material, etc.) as well as the material of the slope.

The amount of friction required to make a step also depends on the angle of the slope (just imagine a vertical wall), therefore there's also a maximum to the steepness of a slope a biped can climb. It also depends on the weight of the biped, or in other terms the magnitude of the gravitational force.

Conclusion
Yes, there is a maximum speed with which a biped can climb a slope, and there's a maximum angle. But they're dependent on the material of the slope, and it's rather unlikely that BT 'Mechs precisely know it. It's more likely (and realistic) if they make smaller steps to climb, and eventually their feet slide off such that they run on the spot.

There's also an effect leading to slow-down while climbing, but it doesn't impose a limit on the angle of a slope a biped is able to climb.


Two other things need to be considered.

Spoiler

1) There are slopes that are infinitely steep, such as this (in the red circle):


Yet, a biped is able to climb this particular slope. Using the steepness alone to slow the biped down isn't enough to take these cases into account (and it looks like there are quite a few of them in the maps, to a lesser degree than infinite, but with the same effect).

2) A heavy biped will make its own stairs with its feet:


And for stairs, there's no problem of friction (actually, there is, but as much as for walking on a plane).

What has this to do with gameplay balance?

• Every 'Mech has different feet, and the ability to climb hills could be different not only for the weight of the 'Mech, but also for each type.
  
• Different ground materials on different maps could have different maximum climbing angles.
  
• 'Mech tonnage could/should affect the maximum angle the 'Mech is able to climb.
  
• This is new the GD but feel free to find a better (sub)forum.

Edited by Phaesphoros, 04 July 2013 - 06:33 PM.

[skullman86]

I think your second to last animation highlights the biggest problem with the system at the moment.

[Phaesphoros]

skullman86, on 04 July 2013 - 09:18 PM, said:

I think your second to last animation highlights the biggest problem with the system at the moment.

Yes, I agree. I can only guess a solution to this (as depicted) is more troublesome to implement and requires more computations on the server (server load = expensive = bad). You need foresight to move your leg on a slope that doesn't have a constant angle.

One could maybe have a less expensive solution for the server if the client requested to move the leg to a certain position, and the server checks if that movement is possible. Then only the client would need to have foresight.

Edited by Phaesphoros, 04 July 2013 - 09:36 PM.

[Kiiyor]

Nice write up. It's worth noting however that Battletech physics laugh at real physics in a degrading manner.

I'm all for heavier mechs making their own stairs, that actually sounds awesome. Imagine if terrain was deformable like that - a few assaults could churn up a hill to make an impromptu ramp.

I'm sure it's a complete and utter coding nightmare, but in the spirit of these forums, i'm going to demand it like an entitled tool who thinks it's the easiest thing in the world anyway.

PGI, make me deformable terrain. And buildings I can crush.

[Phaesphoros]

Kiiyor, on 04 July 2013 - 09:33 PM, said:

It's worth noting however that Battletech physics laugh at real physics in a degrading manner.

yeah... but I think importing some "real" physics here would make it feel more realistic, and less like a game / artificially restricted. We humans (assuming you're one of us, too) are experts in bipedal movement, and literally know how a biped climbs a hill. You don't just stop, especially not if the slope ends in less than a step.

[Kiiyor]

Phaesphoros, on 04 July 2013 - 10:07 PM, said:

yeah... but I think importing some "real" physics here would make it feel more realistic, and less like a game / artificially restricted. We humans (assuming you're one of us, too) are experts in bipedal movement, and literally know how a biped climbs a hill. You don't just stop, especially not if the slope ends in less than a step.

Yep. The coders have quite the job on their hands to get that all under control though.

Maybe instead of stopping, the mech could slow (to 1KPH or so) and wobble dramatically as the gyro struggles to keep things upright.

At the very least, it could lead to some comical arm flailing on the edges of cliffs.

[Phaesphoros]

I think a very simple first improvement would be not to stop the 'Mech, but to make it run on the spot. Doesn't help with movement, but should be more realistic.

A second improvement to that would be to make the 'Mech slide down the slope a bit (until it gets less steep) in the case you run on a spot and EITHER decrease the throttle OR turn away from the slope (to walk serpentinely).

[PanzerMagier]

Another triple A+ special from Phos. Keep up the good work man. Dunno why PGI hasn't hired you yet.

[jakucha]

Kiiyor, on 04 July 2013 - 09:33 PM, said:

Nice write up. It's worth noting however that Battletech physics laugh at real physics in a degrading manner.

I'm all for heavier mechs making their own stairs, that actually sounds awesome. Imagine if terrain was deformable like that - a few assaults could churn up a hill to make an impromptu ramp.

I'm sure it's a complete and utter coding nightmare, but in the spirit of these forums, i'm going to demand it like an entitled tool who thinks it's the easiest thing in the world anyway.

PGI, make me deformable terrain. And buildings I can crush.

Are you an actor? You've captured the spirit of Gameplay Balance perfectly.