Creating An "Autopilot" For Lander in Perl

Question

I'm using Perl to create a simple Lunar Lander game. All of the elements work (i.e. graphical interface, user implemented controls, etc), but I cannot seem to get the "AutoPilot" function to work. This function should fly the lander to a spot that it can land (or a spot designated as a target for landing), and then safely land there. The restrictions placed on landing are the slope of the place the lander lands and the velocity that the lander has when landing. The only file I can change is AutoPilot.pm. I will post the code I am allowed to work with:

package AutoPilot;
use strict;
use warnings;
# use diagnostics;

=head1 Lunar Lander Autopilot

The autopilot is called on every step of the lunar lander simulation.  
It is passed state information as an argument and returns a set of course 
correction commands.

The lander world takes the surface of the moon (a circle!)
and maps it onto a rectangular region. 
On the x-axis, the lander will wrap around when it hits either the
left or right edge of the region.  If the lander goes above the maximum
height of the world, it escapes into the space and thus fails. 
Similarly, if the lander's position goes below 0 without ever landing
on some solid surface, it "sinks" and thus fails again.

The simulation is simple in the respect that if the langer goes at a high speed
it may pass through the terrain boundary.  

The y-axis has normal gravitational physics.

The goal of the autopilot is to land the craft at (or near) the landing
zone without crashing it (or failing by leaving the world).

=head2 Interface in a nutshell

When the simulation is initialized, AutoPilot::Initialize() is called.
Every clock tick, AutoPilot::ComputeLanding() is called by the simulator.
For more explanation, see below.

=cut

# if you want to keep data between invocations of ComputeLanding, put
# the data in this part of the code.  Use Initialize() to handle simulation
# resets.

my  $call_count = 0;
my  $gravity;
my ($x_min, $y_min, $x_max, $y_max);
my ($lander_width, $lander_height, $center_x, $center_y);
my  $target_x; 
my ($thrust, $left_right_thrust); 
my ($max_rotation, $max_left_right_thrusters, $max_main_thruster);
my $ascend_height = 980;

=head1 AutoPilot::Initialize()

This method is called when a new simulation is started.
The following parameters are passed to initialize:

 $gravity, a number, describing the gravity in the world

 $space_boundaries, a reference to an array with 4 numerical
        elements, ($x_min, $y_min, $x_max, $y_max), describing 
        the world boundaries

 $target_x, a number representing the target landing position

 $lander_capabilities, a reference to an array with
   5 elements,

    ($thrust, $left_right_thrust, $max_rotation, $max_left_right_thrusters, $max_main_thruster),

   describing the capabilities of the lander.

 $lander_dimensions, a reference to an array with    
   4 elements,

    ($lander_width, $lander_height, $center_x, $center_y),

   describing the dimensions of the lander.

=head2 Details
=head3 Dimensions
The dimensions are given in 'units' (you can think of 'units' as meters).
The actual numbers can take any real value, not only integers.

=head4 World dimensions

The lander world is a square region with  a lower left corner at 
($x_min,$y_min)  and an upper right corner at ($x_max, $y_max).
The measurement units of these dimensions will just be called units
(think about units as meters). By definition, $x_max>$x_min and
$y_max>$y_min.

The default values for the lower left and upper right corners
are (-800,0), and (800,1600), respectively.

=head4 Lander dimensions 

The lander is $lander_width units wide and $lander_height high.
The coordinates of the lander are always specified with respect to its center.
The center of the lander relative to the lower left corner of the lander bounding box
is given by $center_x, $center_y. Thus, if ($x,$y) are the coordinates of the lander,
($x-$center_x,$y-$center_y) and ($x-$center_x+$lander_width,$y-$center_y+$lander_height)
specify the corners of the bounding box of the lander. (Think of the lander as completely
filling this box.) The significance of the bounding box of the lander is that a collision 
occurs if the bounding box intersects with the terrain or the upper/lower edges of the world.
If a collision occurs, as described earlier, the lander might have just landed,
crashed or 'escaped' (and thus the lander failed).
The constraints on these values are: $lander_width>0, $lander_height>0,
$center_x>0, $center_y>0. 

The default value for the width is 60 units, for the height it is 50,
for $center_x it is 30, for $center_y it is 25. 

=head4 Forces

The gravitational force is:

    $g

The thrust exerted by the engine when fired is:

    $thrust

The thrust exerted by the left/right thrusters when fired is:

    $left_right_thrust    

=head4 Limits to the controls

Within a single timestep there are limits to how many degrees the 
lander may rotate in a timestep, and how many times the side thrusters, 
and main thruster, can fire. These are stored in:

    $max_rotation, $max_left_right_thrusters, $max_main_thruster

=head4 Target

The target landing zone that the lander is supposed to land at:

    $target_x

which returns

    the string "any" if any safe landing site will do, or

    a number giving the x-coordinate of the desired landing site.
    Note: there is no guarantee that this is actually a safe spot to land!

For more details about how the lander is controlled, see AutoPilot::ComputeLanding.

=cut

sub Initialize {
    my ($space_boundaries, $lander_capabilities,$lander_dimensions);
    ($gravity,  $space_boundaries, $target_x, $lander_capabilities, $lander_dimensions) = @_;
    ($x_min, $y_min, $x_max, $y_max) = @{$space_boundaries};
    ( $thrust, $left_right_thrust, $max_rotation,
      $max_left_right_thrusters, $max_main_thruster) = @{$lander_capabilities};
    ($lander_width, $lander_height, $center_x, $center_y) = @{$lander_dimensions};

    $call_count = 0;
}

=head1 AutoPilot::ComputeLanding()

This method is called for every clock tick of the simulation.
It is passed the necessary information about the current state
and it must return an array with elements, describing the
actions that the lander should execute in the current tick.

The parameters passed to the method describe the actual state
 of the lander, the current terrain below the lander and some
 extra information. In particular, the parameters are:

  $fuel, a nonnegative integer describing the remaining amount of fuel.
        When the fuel runs out, the lander becomes uncontrolled.

  $terrain_info, an array describing the terrain below the lander (see below).

  $lander_state, an array which contains information about the lander's state.
        For more information, see below.

  $debug, an integer encoding whether the autopilot should output any debug information.
        Effectively, the value supplied on the command line after "-D",
        or if this value is not supplied, the value of the variable $autopilot_debug
        in the main program. 

  $time, the time elapsed from the beginning of the simulation.
        If the simulation is reset, time is also reset to 0.

=head2 Details of the parameters

=head3 The terrain information

The array referred to by $terrain_info is either empty, or
it describes the terrain element which is just (vertically) below the lander.
It is empty, when there is no terrain element below the lander.
When it is non-empty, it has the following elements:

 ($x0, $y0, $x1, $y1, $slope, $crashSpeed, $crashSlope)

where

    ($x0, $y0)  is the left coordinate of the terrain segment,
    ($x1, $y1)  is the right coordinate of the terrain segment,
    $slope      is the left to right slope of the segment (rise/run),
    $crashSpeed is the maximum landing speed to avoid a crash,
    $crashSlope is the maximum ground slope to avoid a crash.

=head3 The state of the lander

The array referred to by $lander_state contains
 the current position, attitude, and velocity of the lander:

 ($px, $py, $attitude, $vx, $vy, $speed)

where

    $px is its x position in the world, in the range [-800, 800],
    $py is its y position in the world, in the range [0, 1600],
    $attitude is its current attitude angle in unit degrees, 
    from y axis, where
        0 is vertical,
        > 0 is to the left (counter clockwise),
        < 0 is to the right (clockwise),
    $vx is the x velocity in m/s  (< 0 is to left, > 0 is to right),
    $vy is the y velocity in m/s  (< 0 is down, > 0 is up),
    $speed is the speed in m/s, where $speed == sqrt($vx*$vx + $vy*$vy)

=head2 The array to be returned

To control the lander you must return an array with 3 values:

 ($rotation, $left_right_thruster, $main_thruster)

$rotation instructs the lander to rotate the given number of degrees. 
A value of 5 will cause the lander to rotate 5 degrees counter clockwise, 
-5 will rotate 5 degrees clockwise.

$left_right_thruster instructs the lander to fire either the left or 
right thruster. Negative value fire the right thruster, pushing the 
lander to the left, positive fire the left thruster, pushing to the right. 
The absolute value of the value given is the number of pushes, 
so a value of -5 will fire the right thruster 5 times.

$main_thruster instructs the lander to fire the main engine, 
a value of 5 will fire the main engine 5 times.

Each firing of either the main engine or a side engine consumes 
one unit of fuel.
When the fuel runs out, the lander becomes uncontrolled.

Note that your instructions will only be executed up until the 
limits denoted in $max_rotation, $max_side_thrusters, and $max_main_thruster. 
If you return a value larger than one of these maximums than the 
lander will only execute the value of the maximum.

=cut


sub ComputeLanding {
    my ($fuel, $terrain_info, $lander_state, $debug, $time)  = @_;

    my $rotation = 0;
    my $left_right_thruster = 0;
    my $main_thruster = 0;
    # fetch and update historical information
    $call_count++;

    if ( ! $terrain_info ) {
        # hmm, we are not above any terrain!  So do nothing.
        return;
    }

    my ($x0, $y0, $x1, $y1, $slope, $crashSpeed, $crashSlope) =
        @{$terrain_info};

    my ($px, $py, $attitude, $vx, $vy, $speed) =
        @{$lander_state};

    if ( $debug ) {
        printf "%5d ", $call_count;
        printf "%5s ", $target_x;
        printf "%4d, (%6.1f, %6.1f), %4d, ",
            $fuel, $px, $py, $attitude;
        printf "(%5.2f, %5.2f), %5.2f, ",
            $vx, $vy, $speed;
        printf "(%d %d %d %d, %5.2f), %5.2f, %5.2f\n",
          $x0, $y0, $x1, $y1, $slope, $crashSpeed, $crashSlope;
    }

    # reduce horizontal velocity
    if ( $vx < -1 && $attitude > -90 ) {
        # going to the left, rotate clockwise, but not past -90!
        $rotation = -1;
    } 
    elsif ( 1 < $vx && $attitude < 90 ) {
        # going to the right, rotate counterclockwise, but not past 90
        $rotation = +1;
    } 
    else {
        # we're stable horizontally so make sure we are vertical
        $rotation = -$attitude;
    }

    # reduce vertical velocity


    if ($target_x eq "any"){
    if (abs($slope) < $crashSlope){
        if ($vy < -$crashSpeed + 6){
        $main_thruster = 1;
        if (int($vx) < 1 && int ($vx) > -1){
            $left_right_thruster = 0;
        }
        if (int($vx) < -1){
            $left_right_thruster = 1;
        }
        if (int($vx) > 1){
            $left_right_thruster = -1;
        }
        }
    }
     else{
        if ( $py < $ascend_height) {
        if ($vy < 5){
        $main_thruster=2;
        }
        }   
        if ($py > $ascend_height){
        $left_right_thruster = 1;
        if ($vx > 18){
            $left_right_thruster = 0;
        }
        }
    }
    }

    if ($target_x ne "any"){

    if ($target_x < $px + 5 && $target_x > $px - 5){
        print "I made it here";
        if (abs($slope) < $crashSlope){
        if ($vy < -$crashSpeed + 1){
        $main_thruster = 1;
        if (int($vx) < 1 && int ($vx) > -1){
            $left_right_thruster = 0;
        }
        if (int($vx) < -1){
            $left_right_thruster = 1;
        }
        if (int($vx) > 1){
            $left_right_thruster = -1;
        }
        }
    }

    }
    if ($target_x != $px){
        if ( $py < $ascend_height) {
            if ($vy < 5){
            $main_thruster=2;
            }
        }
        if ($py > $ascend_height){
        $left_right_thruster = 1;
        if ($vx > 10){
            $left_right_thruster = 0;
        }
        }
    }

    }

    return ($rotation, $left_right_thruster, $main_thruster);
}

1; # package ends

Sorry about the length of the code...

So, there are a few things I want this autopilot program to do. In order they are:

1. Stabilize the lander (reduce attitude and horizontal drift to zero if they are nonzero). Once stabilized:
2. If above a target and the target's segment is safe to land on then descend on it.
3. Otherwise ascend to the safe height, which is above 1200 units. You can safely assume that there are no objects at this height or higher and also that during straight ascends from its initial position, the lander will not hit anything.
4. Once at the safe height, the lander can start going horizontally towards to its target, if a target is given, otherwise it should target the first safe landing spot that is can sense by scanning the terrain in one direction. It is important that the lander maintains its altitude while it moves horizontally, because it cannot sense objects next to it and there could be objects anywhere below this height.
5. Once the target x coordinate is reached and is found to be safe to land on, start a descend.
6. If the target x coordinate is is reached, but the terrain is unsafe, if a good spot has been seen while moving towards the target, go back to it, otherwise continue searching for a good spot.
7. Once a good spot is seen, just land on it nice and safe.

Ok, so, I've updated the code. My code is now able to land the lander in all tests (except one, got fed up, the code works close enough) where there is no target. However, I am having huge troubles figuring out how to get the lander to land at a target. Any ideas with my code so far? (actual used code is found in the ComputeLanding subroutine)

Answer 1

Here's a hint: try approaching the problem from the other end.

• Landing is almost equivalent to takeoff with time reversed. The only thing that doesn't get reversed is fuel consumption. (Whether that matters depends on whether the simulation counts fuel as part of the lander's mass. In a realistic sim, it should, but at a glance, it looks like yours might not.)
• The optimal way (in terms of fuel efficiency) to take off in a rocket is to fire the engines at maximum power until you're going fast enough, then turn them off. The slower you climb, the more fuel you waste hovering.

Thus, the optimal way to land a rocket is to freefall (after a possible initial burn to correct heading) until the last possible instant, and then fire the engines at full power so that you come to a stop just above the landing pad (or hit the pad at whatever velocity you consider acceptable, if that's greater than zero).

Can you calculate what the right moment to turn on the engines would be? (Even if you can't do it directly, you could always approximate it by binary search. Just pick a point and simulate what happens: if you crash, start the burn earlier; if you stop before hitting the surface, start it later.)

(Ps. This seems like a rather silly exercise for a Perl programming course. Yes, you can certainly solve this in Perl, but there's nothing about Perl that would be particularly well suited for this exercise. Indeed, this isn't even fundamentally a programming problem, but a mathematical one — the only programming aspect to it is translating the mathematical solution, once found, into a working program.)