I am creating a Multiplayer game using socket io in javascript. The game works perfectly at the moment aside from the client interpolation. Right now, when I get a packet from the server, I simply set the clients position to the position sent by the server. Here is what I have tried to do:

getServerInfo(packet) {
     var otherPlayer = players[packet.id]; // GET PLAYER
     otherPlayer.setTarget(packet.x, packet.y); // SET TARGET TO MOVE TO
     ...
}

So I set the players Target position. And then in the Players Update method I simply did this:

var update = function(delta) {
    if (x != target.x || y != target.y){
        var direction = Math.atan2((target.y - y), (target.x - x));
        x += (delta* speed) * Math.cos(direction);
        y += (delta* speed) * Math.sin(direction);
        var dist = Math.sqrt((x - target.x) * (x - target.x) + (y - target.y)
                * (y - target.y));
        if (dist < treshhold){
            x = target.x;
            y = target.y;
        }
    }   
}

This basically moves the player in the direction of the target at a fixed speed. The issue is that the player arrives at the target either before or after the next information arrives from the server.

Edit: I have just read Gabriel Bambettas Article on this subject, and he mentions this:

Say you receive position data at t = 1000. You already had received data at t = 900, so you know where the player was at t = 900 and t = 1000. So, from t = 1000 and t = 1100, you show what the other player did from t = 900 to t = 1000. This way you’re always showing the user actual movement data, except you’re showing it 100 ms “late”.

This again assumed that it is exactly 100ms late. If your ping varies a lot, this will not work.

Would you be able to provide some pseudo code so I can get an Idea of how to do this?

I have found this question online here. But none of the answers provide an example of how to do it, only suggestions.

I am creating a Multiplayer game using socket io in javascript. The game works perfectly at the moment aside from the client interpolation. Right now, when I get a packet from the server, I simply set the clients position to the position sent by the server. Here is what I have tried to do:

getServerInfo(packet) {
     var otherPlayer = players[packet.id]; // GET PLAYER
     otherPlayer.setTarget(packet.x, packet.y); // SET TARGET TO MOVE TO
     ...
}

So I set the players Target position. And then in the Players Update method I simply did this:

var update = function(delta) {
    if (x != target.x || y != target.y){
        var direction = Math.atan2((target.y - y), (target.x - x));
        x += (delta* speed) * Math.cos(direction);
        y += (delta* speed) * Math.sin(direction);
        var dist = Math.sqrt((x - target.x) * (x - target.x) + (y - target.y)
                * (y - target.y));
        if (dist < treshhold){
            x = target.x;
            y = target.y;
        }
    }   
}

This basically moves the player in the direction of the target at a fixed speed. The issue is that the player arrives at the target either before or after the next information arrives from the server.

Edit: I have just read Gabriel Bambettas Article on this subject, and he mentions this:

Say you receive position data at t = 1000. You already had received data at t = 900, so you know where the player was at t = 900 and t = 1000. So, from t = 1000 and t = 1100, you show what the other player did from t = 900 to t = 1000. This way you’re always showing the user actual movement data, except you’re showing it 100 ms “late”.

This again assumed that it is exactly 100ms late. If your ping varies a lot, this will not work.

Would you be able to provide some pseudo code so I can get an Idea of how to do this?

I have found this question online here. But none of the answers provide an example of how to do it, only suggestions.

• javascript
• algorithm
• multiplayer

• I am running into this issue as well, with jitter in my game. Were you able to solve this using the answer with the checkmark? Or were there other factors at play that helped you solve this problem? If so, could you please provide some sort of example implementation? Thank you. – daniel metlitski Commented Apr 21, 2017 at 11:34

3 Answers 3

I'm completely fresh to multiplayer game client/server architecture and algorithms, however in reading this question the first thing that came to mind was implementing second-order (or higher) Kalman filters on the relevant variables for each player.

Specifically, the Kalman prediction steps which are much better than simple dead-reckoning. Also the fact that Kalman prediction and update steps work somewhat as weighted or optimal interpolators. And futhermore, the dynamics of players could be encoded directly rather than playing around with abstracted parameterizations used in other methods.

Meanwhile, a quick search led me to this:

An improvement of dead reckoning algorithm using kalman filter for minimizing network traffic of 3d on-line games

The abstract:

Online 3D games require efficient and fast user interaction support over network, and the networking support is usually implemented using network game engine. The network game engine should minimize the network delay and mitigate the network traffic congestion. To minimize the network traffic between game users, a client-based prediction (dead reckoning algorithm) is used. Each game entity uses the algorithm to estimates its own movement (also other entities' movement), and when the estimation error is over threshold, the entity sends the UPDATE (including position, velocity, etc) packet to other entities. As the estimation accuracy is increased, each entity can minimize the transmission of the UPDATE packet. To improve the prediction accuracy of dead reckoning algorithm, we propose the Kalman filter based dead reckoning approach. To show real demonstration, we use a popular network game (BZFlag), and improve the game optimized dead reckoning algorithm using Kalman filter. We improve the prediction accuracy and reduce the network traffic by 12 percents.

Might seem wordy and like a whole new problem to learn what it's all about... and discrete state-space for that matter.

Briefly, I'd say a Kalman filter is a filter that takes into account uncertainty, which is what you've got here. It normally works on measurement uncertainty at a known sample rate, but it could be re-tooled to work with uncertainty in measurement period/phase.

The idea being that in lieu of a proper measurement, you'd simply update with the kalman predictions. The tactic is similar to target tracking applications.

I was recommended them on stackexchange myself - took about a week to figure out how they were relevant but I've since implemented them successfully in vision processing work.

(...it's making me want to experiment with your problem now !)

As I wanted more direct control over the filter, I copied someone else's roll-your-own implementation of a Kalman filter in matlab into openCV (in C++):

void Marker::kalmanPredict(){

    //Prediction for state vector 
    Xx = A * Xx;
    Xy = A * Xy;
    //and covariance
    Px = A * Px * A.t() + Q;
    Py = A * Py * A.t() + Q;
}

void Marker::kalmanUpdate(Point2d& measuredPosition){

    //Kalman gain K:
    Mat tempINVx = Mat(2, 2, CV_64F);
    Mat tempINVy = Mat(2, 2, CV_64F);
    tempINVx = C*Px*C.t() + R;
    tempINVy = C*Py*C.t() + R;
    Kx = Px*C.t() * tempINVx.inv(DECOMP_CHOLESKY);
    Ky = Py*C.t() * tempINVy.inv(DECOMP_CHOLESKY);

    //Estimate of velocity
    //units are pixels.s^-1
    Point2d measuredVelocity = Point2d(measuredPosition.x - Xx.at<double>(0), measuredPosition.y - Xy.at<double>(0));  
    Mat zx = (Mat_<double>(2,1) << measuredPosition.x, measuredVelocity.x);
    Mat zy = (Mat_<double>(2,1) << measuredPosition.y, measuredVelocity.y);

    //kalman correction based on position measurement and velocity estimate:
    Xx = Xx + Kx*(zx - C*Xx);
    Xy = Xy + Ky*(zy - C*Xy);
    //and covariance again
    Px = Px - Kx*C*Px;
    Py = Py - Ky*C*Py;
}

I don't expect you to be able to use this directly though, but if anyone comes across it and understand what 'A', 'P', 'Q' and 'C' are in state-space (hint hint, state-space understanding is a pre-req here) they'll likely see how connect the dots.

(both matlab and openCV have their own Kalman filter implementations included by the way...)

This question is being left open with a request for more detail, so I’ll try to fill in the gaps of Patrick Klug’s answer. He suggested, reasonably, that you transmit both the current position and the current velocity at each time point.

Since two position and two velocity measurements give a system of four equations, it enables us to solve for a system of four unknowns, namely a cubic spline (which has four coefficients, a, b, c and d). In order for this spline to be smooth, the first and second derivatives (velocity and acceleration) should be equal at the endpoints. There are two standard, equivalent ways of calculating this: Hermite splines (https://en.wikipedia.org/wiki/Cubic_Hermite_spline) and Bézier splines (http://mathfaculty.fullerton.edu/mathews/n2003/BezierCurveMod.html). For a two-dimensional problem such as this, I suggested separating variables and finding splines for both x and y based on the tangent data in the updates, which is called a clamped piecewise cubic Hermite spline. This has several advantages over the splines in the link above, such as cardinal splines, which do not take advantage of that information. The locations and velocities at the control points will match, you can interpolate up to the last update rather than the one before, and you can apply this method just as easily to polar coordinates if the game world is inherently polar like Space wars. (Another approach sometimes used for periodic data is to perform a FFT and do trigonometric interpolation in the frequency domain, but that doesn’t sound applicable here.)

What originally appeared here was a derivation of the Hermite spline using linear algebra in a somewhat unusual way that (unless I made a mistake entering it) would have worked. However, the comments convinced me it would be more helpful to give the standard names for what I was talking about. If you are interested in the mathematical details of how and why this works, this is a better explanation: https://math.stackexchange.com/questions/62360/natural-cubic-splines-vs-piecewise-hermite-splines

A better algorithm than the one I gave is to represent the sample points and first derivatives as a tridiagonal matrix that, multiplied by a column vector of coefficients, produces the boundary conditions, and solve for the coefficients. An alternative is to add control points to a Bézier curve where the tangent lines at the sampled points intersect and on the tangent lines at the endpoints. Both methods produce the same, unique, smooth cubic spline.

One situation you might be able to avoid if you were choosing the points rather than receiving updates is if you get a bad sample of points. You can’t, for example, intersect parallel tangent lines, or tell what happened if it’s back in the same place with a nonzero first derivative. You’d never choose those points for a piecewise spline, but you might get them if an object made a swerve between updates.

If my computer weren’t broken right now, here is where I would put fancy graphics like the ones I posted to TeX.SX. Unfortunately, I have to bow out of those for now.

Is this better than straight linear interpolation? Definitely: linear interpolation will get you straight- line paths, quadratic splines won't be smooth, and higher-order polynomials will likely be overfitted. Cubic splines are the standard way to solve that problem.

Are they better for extrapolation, where you try to predict where a game object will go? Possibly not: this way, you’re assuming that a player who’s accelerating will keep accelerating, rather than that they will immediately stop accelerating, and that could put you much further off. However, the time between updates should be short, so you shouldn’t get too far off.

Finally, you might make things a lot easier on yourself by programming in a bit more conservation of momentum. If there’s a limit to how quickly objects can turn, accelerate or decelerate, their paths will not be able to diverge as much from where you predict based on their last positions and velocities.

Depending on your game you might want to prefer smooth player movement over super-precise location. If so, then I'd suggest to aim for 'eventual consistency'. I think your idea of keeping 'real' and 'simulated' data-points is a good one. Just make sure that from time to time you force the simulated to converge with the real, otherwise the gap will get too big.

Regarding your concern about different movement speed I'd suggest you include the current velocity and direction of the player in addition to the current position in your packet. This will enable you to more smoothly predict where the player would be based on your own framerate/update timing.

Essentially you would calculate the current simulated velocity and direction taking into account the last simulated location and velocity as well as last known location and velocity (put more emphasis on the second) and then simulate new position based on that.

If the gap between simulated and known gets too big, just put more emphasis on the known location and the otherPlayer will catch up quicker.