The Science of Off-Roading: Uncharted 4's 4x4

[Music] all right uh hello everyone welcome to the science of off-roading my name is Ed Pera I'm a programmer at nauy dog during this talk we'll be going uh bouncing between the high and lowlevel topics as we fa uh going uh as we go through the set of challenges we faced while developing the car that Drake drives around Madagascar in Uncharted 4 let me start with some of the goals we had in mind we set out to work on the 4x4 at its core we felt it needed to be fun to drive for as many people as possible un4 is an adventure game that we felt that anyone should be able to pick up and enjoy and since the 4x4 is a critical part of the story we need to make sure everyone enjoys driving it secondly we wanted a sense of realism to keep the player grounded in Drake's Adventure finally we needed to make sure whatever we designed would work on the rockier muddy terrain found when driving around the mountains of Madagascar to accomplish these goals we had to figure out what kind of simulation we wanted

when making a vehicle simulation you kind of have to figure out where in the Spectrum you want to fall you can choose the real side with a game like Gran Turismo the tagline is literally the real driving simulator in games like this you can have a very realistic Tire grip simulation maybe the rubber wears down and the tire loses friction your motor can be complex with details like how much power is generated with when each cylinder fires the shape of the chassis can change airf flow uh giving you a different handling and efficiency on the other end you have games like Super Mario Kart where simple fun is much more important there are aspects of racing introduced but they are largely game mechanics rather than simulation the best example is drifting where you end up hopping around so you don't take a penalty and play a can spinning out animation another aspect is the fairly simple motor uh with the ad mechanics of boosts like when you use a mushroom or rev the engine just right at the start of a race so where we end up with a 4x4 we end up somewhere in the middle in my opinion when you're dealing with an environment that's going for realism

it's actually easier to run simulation on the more real side if you try to model it as simple as possible the complexities of a realistic environment require you to add several hacks to get the simulation to look right with a more realistic simulation you can throw really varied terrain at it in it should remain stable you might still need to tweak some of the parameters to make it feel good but you won't need to fundamentally change the underlying physical model I'm going to be going over the physical model in three parts we're going to be talking about Collision detection so that's the chassis in the wheels and how that responds to Collision we'll quickly go over motor simulation and how it generates torque then we'll talk about how that torque is applied to the wheels and how that generates forces apply to the vehicle so let's go over how the Drake mobile stands on its feet stated simply the vehicle is built out of rigid bodies held together using constraints we start off with a single rigid body for the chassis a rigid body for each wheel and constraints that keep everything together we use Havoc as a solver for these constraints but Prov provide many

of our own inputs we turned off Collision on the wheels in favor of havoc's Point constraint system this system allows us to pass a point that we want the tires to stick to and it also generates a normal force based on the motion and mass of the chassis and the wheels later I'll go over how this normal force is used to compute friction in order to find the point of contact we use a ray cast for each wheel from what we call the hard point to the furthest point the suspension can extend the hard point is the point where the suspension is attached to the chassis and provides a nice reference point for the math we'll be doing on the wheels I turn off the tire display so you can get a better look at at the ray cast in this image the yellow sphere at the bottom is is the dedicated uh is the detected Collision point so let's take a look at how that all works driving on flat ground so this is a great start make we can make some turns start driving I'm a huge fan of getting something up and running as fast as possible first and add features as they go so so this is

flat ground how does it handle on our test track of rough terrain it's obviously not so good we seem to have hit an invisible wall I checked the level file the designer definitely didn't put one there so we need to break down the issues first and foremost the unpredict unpredictable Collision response here is a big problem second Collision response doesn't happen fast enough in the screenshot you can clearly see that the wheels P that the wheels penetrating the bumps and the that definitely does not meet our standards so how do we fix these issues first thing it's obvious that a ray cast just won't cut it we consider options like moving the ray cast forward if the car is moving but it just didn't seem accurate enough instead we replace the ray cast with the shape cast using using the tire Dimensions as a cylinder for our shape another tweak was to cast The Ray from above the hard point in this case well above the hard point there are cases where the nose of the vehicle would spend a frame already in collision and get stuck moving the start of the cast up made sure that never

happens this screenshot shows the first Collision Point detected by the shape cast on this round bump there are actually several points returned by the shape cast as a first step we take the closest return point which looks fairly accurate this is a vast Improvement we're getting much less visible penetration but it's not quite there yet as you can see under certain circumstances it can be very unstable response when where you see a lot of jittering this is caused by the fact that we're only taking the first Collision point so it's ping ponging between which plank to put the P the put to put the tire on top of we now need to take more Collision points and pass them to the point constraint system this allows us to have this uh this allows us to have the tire sit on multiple planks which stabilizes the response we limited the number of points we used to three per wheel since we felt more than that would have diminishing returns so this looks pretty good one thing we discovered we don't like is how rough the Collision response is to surfaces who's not uh whose normal is

not aligned with the suspension Direction you can see from the start of this that hitting that first bump you completely lose all momentum this is an implementation detail of Havoc that we wanted to work around so we fake it and tell Havoc that all normals are in the direction of the suspension smooth as butter we really liked how player favoring the response is here if you run into any situations like this we know the 4x4 will keep momentum nice and not frustrate the player this is obviously quite unrealistic but this is one of the many times we leaned away from realism to make for a more fun Driving Experience there's an unfortunate side effect though in that the wheels do not respond perfectly to Collision anymore you can kind of see the the wheels penetrating the bumps now our solution is to reimplement wheel Collision response ourselves using the highest point from before we place the wheel so that it tangents the point the first thing we need to do here is figure out where P1 and P2 are these represent two potential points furthest

penetrating into geometry because the wheel uh could be at an angle we have to consider either side as the deepest point to compute the points we take the wheels orientation vectors up and right and offset from the center point now we need to see which point is deepest we do this using D products there are two vectors one from C to P1 and one from C to P2 if we dot these within our surface's normal Vector we produce two scalers S1 and S2 S1 and S2 represent scalar distances meaning how far cp1 and cp2 travel in the direction of n you can see these scalers in their geometric sense in this image whichever these scalers is larger determines which of the associated points is deeper in this example P1 is deeper now we can't use S1 directly since that's the distance from the center to the corner we have to compute another scaler S3 that represents the distance from the contact point to the contact to the corner along the contact normal

we do this by taking the vector from the contact point to c to cp1 and dotting that with n this resultant scalar is the final distance we have to move the Wheel by in order to have the wheel's Corner rest on the surface now obviously if we just separate along the contact normal the wheel will be pulled out of alignment with a suspension so the next step is projecting the separation Vector onto the suspension Direction and moving along that Vector now let's let's take a look at how that math works out so responding to low penetration distances we have a stable and correct looking Collision response which is unfortunate for Drake he's probably asking if we can go around at this point unfortunately you quickly run into an issue when you have to spend when you have to move the wheel so far along the suspension direction that it goes past the hard point and into the 4x4's chassis to avoid clipping the wheel well we limit the distance the wheel can travel upwards though it never passes the hard point to counteract the fact that you would now see the wheel penetrating the ground we apply an

upward force on the hard point and it Nets us two benefits first it will get the 4x4 out of collision secondly when you slam it to the ground hard and it creates a nice jerk that the player can feel side note this force is then delivered to Nate sorry Nate by the way if you're interested in how our character animations are affected by physics and you didn't catch it this morning you can check out mikel's uh talk in the vault after the show so with the wheels colliding properly we ran into another issue as you can see we need to tweak what we consider valid points of contact because our cast will detect any Collision these walls count as points the place the tires on top of the limit we made was based on the angle of the surface the wheel probe detected taking the angle between the vertical vector and the normal of the surface we ignore surfaces whose angle exceeds a designer tuned maximum angle so what does that look like

with the wheel with the wall Collis safely ignored the 4x4 bumps the wall and continues on and now another case okay apparently sometimes you do want to drive on the wall to solve this we gave design the ability to turn off the angle check in script last issue regarding collision and Chassis movement is when you drive off of a cliff into a place that is still a drivable space we wanted to avoid flipping onto the 4x4 side or roof as this would disrupt the player's Driving Experience the quickest solution is to counter the Jeep's rotation using forces based on what direction the vehicle is currently rotating let's see what that looks like so as you can see it's a little unrealistic but it's very important to keep the player happily driving around in fact for fun we added some air control where we'd apply forces to the forit before if it's in the air and you're pushing on a direction of the steering stick constantly keeping the player feeling like they have some

control so now we now that we have Collision detection settled let's talk about powering the Beast with our motor simulation we decided to go with a manual transmission it ends up being a simp simpler simulation when you don't have to deal with the torque converter who wants to deal with viscosity anyway am I right simulium motor requires a differential equation because the speed of which you're traveling feeds back into the motor's power curve we implement this by breaking the problem into two parts the motor and the wheels so in this chart we're looking at how much power and torque are generated by Any Given RPM this curve is tuned by designers using the X Y coordinates based on the size of the space and how responsive they want the 4x4 to be basically the way this curve works is your power grows as your motor spins faster and faster up to a peak power at which point you start losing efficiency and the power starts dropping in the simulation the motor starts at a minimum idle RPM and how much gas pedal is pressed applies a similar percentage of uh torque generated at the current motor RPM it's

a big simplification of how gas is applied to a real motor but it's very effective so the second part as I mentioned is how torque is generated from the motor and transfers to the wheels to understand how that works I need to mention another aspect of our transmission this is a differential this allows the attached wheels to rotate at a different at different RS so if you slam on the gas and uh one of the wheels is stuck and locked in place the other wheel will spin freely and you won't flood or stall the engine during development with we took a look at a lot of different elements of a real car and considered which ones to simulate looking at the benefit of differentials this seemed like a good element to include the primary reason we wanted this is to improve handling when the wheels are free to turn at different rates you get more grip on the outside tires to understand this imagine one side of the car carving one Circle the yellow circle here and another side carving another Circle the blue circle these two circles are obviously have different circumferences so if the wheels were fixed to turn at the same rate there would be there would necessarily be sliding because the wheels are traveling different

distances the secondary benefit is we get big amounts of wheel spin so our FX and foreground team have plenty of opportunity to send mud and rocks flying now with a differential torque applied to the wheel torque uh now with a differential torque appli to it will be divided evenly between the wheels attached so assuming a forward and rear differential and a differential between these two we now have a system where torque is divided evenly among all four wheels since each wheel is allowed to sprin freely we then calculate the next frames RPM using the fastest Spinning Wheel because in a manual transmission with the clutch applied the wheels in the motor are directly linked with the motor generating torque I'm going to be talk about how that torque ends up putting a force on the vehicle to get it moving forward so let's talk about friction we have power transferred from the motor to the wheel now we need to transfer the power from the wheel to the ground so the 4x4 moves forward friction dictates how much force can be applied to before there is slip and how much slip there is since friction is between two surfaces

we have to define the friction for the tires and the friction for the geometric surfaces the tires will be driving on in order to accomplish the second part we break the environment up into several surface types each with a tuned amount of friction the the designers and artists work together to lay out all the friction types to make for a fun and interesting Driving Experience let's take a look at how that surface is blocked out we have our grass here with very high friction indicated by the yellow in this picture a money transition Point here with what would be an inet amount of friction then a very little friction in a muddy riverbed as you can see it's really broken up very roughly we didn't go into fine details of little bits of higher friction here and there and it still feels really good to drive across we spent a lot of time tuning friction on some of these surface types to make these money climbs challenging while still being fun you really have to keep throwing uh throwing at a plate tester with fresh eyes to see how difficult they find it

so let's get into some of the details about friction and torque the first thing we need is the normal force n applied to the tire this we get back out of Havoc for each wheel uh once we've applied the point of contact we let the solver give us this information because the pressure on the wheel is dependent on the downward momentum of the chassis and the forces gen generated by the suspension so doing this is needlessly gritty for the coefficient of friction we multiply the friction of the tire with the friction of the surface it's in contact with this coefficient is then multiplied with the four Force returned from Havoc to generate a maximum friction Force torque is then the rotational Force applied to the wheel with the friction resisting this rotation the opposite Force pushes the wheel forward our maximum friction force is split into two directions we take the torque applied to the wheel divided by the radius and that gives us a linear forward Force our lateral force is a little bit more complicated we create a lateral slip coefficient based on the lateral velocity divided by the forward velocity multiplying this by the normal force return from Havoc we get a nice

simulation where you regain control in a reasonable amount of time no matter how fast you're sliding combining the two directions we get a total Force Vector shown here the length of this Vector must be below the maximum friction Force we calculated earlier dividing the two gives us a scalar to apply to the input vectors so that our total Force Falls below the maximum we apply this scalar to both directions so the resultant total Force Falls below the max force so leral friction force is applied to the lateral velocity to slow the vehicle down when sliding side to side in the forward direction we apply up to the maximum friction to the wheel the leftover difference is then applied back to the wheel as extra rotational velocity because the tire is slipping in this case in the other direction however if the torque applied is less than the maximum friction Force we apply an opposite braking force on the angle of velocity of the wheel so it slows to meet the friction if the wheel is over spinning and slipping one final request from design was of course being able to power slide

tossing around some ideas most importantly we wanted to make it easy to use we decided to implement a big fake with a hint of realism when you hit the handbrake button we simply reduce the friction on the back tires this lets the rear kick out but in a way we can easily tune so that concludes the driving and physical aspects of the 4x4 design would give me a layout that they wanted the 4x4 to drive on and we'd work together to get the vehicle to feel and look right for the space now with that working nicely what do you do if a designer comes to you and says Hey it' be kind the car drove itself okay then that sounds like fun so the reason for this Tech is so that NPCs like Civ Elena can hop into the driver's seat and drive to Drake if he got too far from the 4x4 thankfully some of the AI work is already done for me I have to tweak some things but the nav search code used by NPCs can be converted over pretty easily so we have static paths generated almost immediately the interesting bit comes with we talk about how to make a car on

Four Wheels drive towards the nextnav Waypoint questions to answer how do you actually turn to face the point how fast should you be traveling what if the next W Waypoint is behind you how do you even know it's behind you how do you know if there's a physical object in front of you that you need to drive around how do you drive around it some basic principles cars have a defined turn radius like we talked about earlier this is the radius of the smallest circular turn the vehicle is capable of making the size of the Turning Circle changes based on half fast you're traveling because the wheels won't necessarily grip the ground hard enough to make the given turn the circle also expands the further the steering wheel gets from the furthest Edge understanding these aspects of your physical model lets you make decisions like how far do I have to turn the wheel to make the target let's go over how to calculate the turn radius based on the physical dimensions of the car I base my I based my math on the acan steering geometry in this image Theta is the maximum angle the wheel uh the wheels can rotate left to right W is the width of the 4x4 and L is the

length putting it all together gives us the radius of the Turning Circle I'm uncertain if this is the perfect calculation of a tightest turning Circle the fourway could drive along but it was close enough of an estimate that it worked well for our AI logic okay so now we're able to calculate if we can make a turn towards the Waypoint we obviously know the location of these circles since they are attached to the car assuming they're infinite cylinders we use 2D algebra to figure out if the way point is inside of either Circle if the way point is insided by the circle we turn uh we need to put the four4 into res into reverse turn the wheel in the opposite direction so now now our nose will turn towards the target once our nose is facing close enough to the Target that the target uh is outside of the Turning Circle we can switch back to drive and complete the turn this logic also applies to whether the target is behind us reverse until we make the turn and continue on now let's take a closer look at what following a path ends up looking like

nice next up let's talk about obstacle avoidance our navm search uh gives us a really good path to follow to avoid things like bolt buildings or big boulders but what do we do if another car is in the way and that car does not affect a nav mesh to detect this we need several Ray casts one per Corner forward and back whose length is based on the speed the for before is driving when one of the casts detected some detects something we simply push the steering wheel in the opposite direction based on how close the ray cast detected Collision we never forget that we eventually want to steer towards the target again but the probe tells us when we're clear to start that turn the direction the probe cast is tunable in these videos the probes are directly in front and behind but depending on the environment you're dealing with you might want these probes to shoot out at an angle to give more consideration to what's around the vehicle for Simplicity we assume that design is not caused some kind of traffic jam that we could we could never Ste around this is obviously wouldn't

work in a city full of cars but driving around the hills of Madagascar this is an effective simplification a small feature requested by Design was spline following for this we turn off nav M search and simply get a point on the spline curve some distance away from us based on how how fast we're traveling obstacle avoidance is still on in this case since other objects can get in the way we want to steer around the obstacle and continue to use the nearest point on this blind as our Target so with navigation steering and obstacle avoidance put together you've got a pretty good system for getting around most spaces so to wrap up first we went over Collision detection using rigid bodies constraints and our own implementation of wheel response we created a vehicle that moves around rough terrain smoothly our motor with a mix of realism some glass over details we created a nice balance between a tunal realistic motor and avoiding the grittiness of a deeper simulation our tire friction simulation allows us to actually drive the vehicle and make turns in an easy to use way that most players can grasp we took new requirements from design

where we had to add AI to the car and brought over navigation from existing systems and we layered on steering behaviors so the 4x4 can follow the generated navigation paths I want to give a quick thanks to some of the folks in na dog who helped put the 4x4 together but actually took quite a few people to put all the bells and whistles on it so these are just a few of the names Ino made the beautiful visual model that we all came to love Christof helped with some of the rigging Rob is an audio designer and Jonathan is an audio programmer and together they work to get things like the motor purring just right y Alis and Travis are programmers who helped with the simulation Curt and James are designers who helped on tuning and level layout so that's the 4x4 the development is really about problem solving we took a very design oriented approach to development and always Focus changes on the needs for making the game fun thanks for [Music] [Applause] [Music] listening so we have about five minutes for questions if anybody has anything

mention if you want to come to the microphone please uh uh sorry sorry uh you mentioned about the rigid body I imagine you're allow to using Unity right no we we use Havoc but it's our own game engine okay thank you mhm uh so I had a similar Simulator for driving okay and I found an issue was do you gloss over this real quick when you're falling down and you need to take that wheel and push it up so it doesn't go through the ground using Force now you don't want to do that instantly or you just suddenly pop up so you need to add force over time but if you're falling really far that's a lot of force and it would bounce my car up fairly high and I'm wondering how you guys handle that so CU it's a lot of force in a very short amount of time cuz that Collision when you just hit is very is

very quick so to like move that I just wondering how you guys handle that so the the question is well how did we handle uh the force applying to the vehicle to get it out of collision if it actually is already in um we I'm actually okay with it being in Collision for a little bit so we don't push so hard that it flies out of collision and so I actually have a a tuning where there's a maximum amount of force that it's actually allowed to be applied on it so that it doesn't ever get pushed out that far okay thank you over here hi uh did you have any trouble like if the vehicle bottoms out and then the Collision of the chassis gets snagged on some small rock or something like that uh it the the vehicle does bottom out a lot but um the Havoc rigid body system is pretty good at making sure the that ites doesn't cause a problem there are there are some cases and you can still see them in the shipped game though where you the like the the rocks and stuff will go like will go flying

because um because the chassis like hits that hits that rock in a bad way um that's not like it is something I looked into a little bit but it's not something we cared enough about to have to like fix is the 4x4 a one off or is naughty dog going to look into more vehicle play in the future oh we had the boat oh yeah uh yeah I mean we are we are definitely always exploring what other things we can do like having having the having the 4way 4 in there was was a starting off point for making the boat and so that's they share a lot of the same code so it's obviously a really good jumping off point for making any other vehicle simulation thanks MH uh uh I was developing like an VR truck simulator one of the problem I I got into is like when you got a trailer behind your car uh while you're trying like driving forward of course uh the like motor belongs to like a rear wheels

of the like the truck head but how do you manage to like balance those initial like uh uh you know the power when you're trying to do some color uh the power uh uh on inner tile and outer tile they are different how do you like balance that out I got a lot of problem with that uh uh I'm not what's what is the what's the problem you're having I'm not sure uh when you driving your car too fast yeah you know uh uh when doing color in fact the uh uh the friction on on your uh inner tile and the outer tire they are different okay uh that's where with my like uh simulator went not wrong a lot of ties I like uh the way I'm solving it is that we tuned a lot to make it feels better I wonder how you like a man solve

that and uh in Uncharted for the car is also running on like uneven uh uneven path sometimes it's like uh on the brink of like getting contact with the ground a lot how do you like try try to make them like in that like uh very B uh boundary moment to make the C still like getting the force moving forward like correctly yeah so the the question summarize is uh the all four tires are running on different friction most of the time um as you're going from the river bed to the grass one side is still slipping other side catches um the uh the differential actually helps in this case um because we we're splitting the the torque to all four tires that makes it so that um it it's actually a smoother transition um because you don't have a sudden like very hard grip on one of the tires and cause it to just like stop um and other than that like we

didn't really have any issues in that area I think may possibly because of how stable the point constraint system is in Havoc um we basically told it the lateral lateral friction we wanted um and how much force is being applied there and it would do a decent job of stabilizing okay thank you mhm um my question was just also about the the chase sequence and other cars in the Chas sequence and the Motorcycle do they use the same model um a lot of that is um faked with splines um there I think I think there's uh some of the same like the the way the tires work and detect Collision I think is the same but the actual driving and movement is on a spline and they didn't run like obstacle avoidance or anything no no okay thank you very much

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