FRC Drivetrain Heun

acceleration_heun.coffee

class HeunSimulation

  constructor: (args) ->
    @processing = false

    #robot properties
    @rolling_resistance = args['rolling_resistance'] * 4.448222
    @rolling_resistance_prime = args['rolling_resistance_prime'] * 0.2248089*0.3048
    @drivetrain_efficiency = args['drivetrain_efficiency']

    #motor properties
    @motor_stall_torque = args['motor_stall_torque'] * 0.00706155
    @motor_free_speed = args['motor_free_speed']/60*2*3.1415926536

    #mechanical properties
    @number_of_motors = args['number_of_motors']
    @gear_ratio = args['gear_ratio']
    @wheel_radius = args['wheel_radius']*2.54/100
    @mass = args['mass']*0.4535924
    @uk = args['uk']
    @us = args['us']

    #simulation properties
    @dt = args['dt']
    @duration = args['duration']

    @Vfree = @motor_free_speed*@wheel_radius/@gear_ratio
    @mass_in_newtons = @mass*9.80665
    @velocity = 0
    @position = 0
    @slipping = false
    @acceleration = 0
    @data = []
  accel: (vel) =>
    @motor_torque = @motor_stall_torque*(1-vel/@Vfree)
    wheel_torque = @drivetrain_efficiency * @motor_torque * @gear_ratio
    rolling_resistance_losses = @rolling_resistance + @rolling_resistance_prime * vel
    @vehicle_force = wheel_torque/@wheel_radius * @number_of_motors - rolling_resistance_losses
    if @vehicle_force < 0
      @vehicle_force = 0
    if @vehicle_force > @mass_in_newtons * @us
      @slipping = true
    else if @vehicle_force < @mass_in_newtons * @uk
      @slipping = false
    if @slipping
      @vehicle_force = @mass_in_newtons*@uk
    @vehicle_force/@mass

  heun: () =>
    for t in [@dt..@duration] by @dt
      @processing = true
      @temp_velocity = @velocity+@acceleration*@dt
      @temp_acceleration = @.accel(@temp_velocity)
      @temp_velocity = @velocity+(@acceleration+@temp_acceleration)/2*@dt
      @acceleration = @.accel(@temp_velocity)
      @position+=(@velocity+@temp_velocity)/2*@dt
      @velocity = @temp_velocity
      @data.push({t:t, position:@position*3.28083, velocity:@velocity*3.28083, acceleration:@acceleration*3.28083, slipping:@slipping, temp_acceleration:@temp_acceleration, temp_velocity:@temp_velocity, motor_torque:@motor_torque })
      @max_position = @position

@onmessage = (event) ->
  sim = new HeunSimulation(event.data)
  sim.heun()
  postMessage(JSON.stringify(sim))

acceleration_heun.js

// Generated by CoffeeScript 1.6.3
(function() {
  var HeunSimulation,
    __bind = function(fn, me){ return function(){ return fn.apply(me, arguments); }; };

  HeunSimulation = (function() {
    function HeunSimulation(args) {
      this.heun = __bind(this.heun, this);
      this.accel = __bind(this.accel, this);
      this.processing = false;
      this.rolling_resistance = args['rolling_resistance'] * 4.448222;
      this.rolling_resistance_prime = args['rolling_resistance_prime'] * 0.2248089 * 0.3048;
      this.drivetrain_efficiency = args['drivetrain_efficiency'];
      this.motor_stall_torque = args['motor_stall_torque'] * 0.00706155;
      this.motor_free_speed = args['motor_free_speed'] / 60 * 2 * 3.1415926536;
      this.number_of_motors = args['number_of_motors'];
      this.gear_ratio = args['gear_ratio'];
      this.wheel_radius = args['wheel_radius'] * 2.54 / 100;
      this.mass = args['mass'] * 0.4535924;
      this.uk = args['uk'];
      this.us = args['us'];
      this.dt = args['dt'];
      this.duration = args['duration'];
      this.Vfree = this.motor_free_speed * this.wheel_radius / this.gear_ratio;
      this.mass_in_newtons = this.mass * 9.80665;
      this.velocity = 0;
      this.position = 0;
      this.slipping = false;
      this.acceleration = 0;
      this.data = [];
    }

    HeunSimulation.prototype.accel = function(vel) {
      var rolling_resistance_losses, wheel_torque;
      this.motor_torque = this.motor_stall_torque * (1 - vel / this.Vfree);
      wheel_torque = this.drivetrain_efficiency * this.motor_torque * this.gear_ratio;
      rolling_resistance_losses = this.rolling_resistance + this.rolling_resistance_prime * vel;
      this.vehicle_force = wheel_torque / this.wheel_radius * this.number_of_motors - rolling_resistance_losses;
      if (this.vehicle_force < 0) {
        this.vehicle_force = 0;
      }
      if (this.vehicle_force > this.mass_in_newtons * this.us) {
        this.slipping = true;
      } else if (this.vehicle_force < this.mass_in_newtons * this.uk) {
        this.slipping = false;
      }
      if (this.slipping) {
        this.vehicle_force = this.mass_in_newtons * this.uk;
      }
      return this.vehicle_force / this.mass;
    };

    HeunSimulation.prototype.heun = function() {
      var t, _i, _ref, _ref1, _ref2, _results;
      _results = [];
      for (t = _i = _ref = this.dt, _ref1 = this.duration, _ref2 = this.dt; _ref2 > 0 ? _i <= _ref1 : _i >= _ref1; t = _i += _ref2) {
        this.processing = true;
        this.temp_velocity = this.velocity + this.acceleration * this.dt;
        this.temp_acceleration = this.accel(this.temp_velocity);
        this.temp_velocity = this.velocity + (this.acceleration + this.temp_acceleration) / 2 * this.dt;
        this.acceleration = this.accel(this.temp_velocity);
        this.position += (this.velocity + this.temp_velocity) / 2 * this.dt;
        this.velocity = this.temp_velocity;
        this.data.push({
          t: t,
          position: this.position * 3.28083,
          velocity: this.velocity * 3.28083,
          acceleration: this.acceleration * 3.28083,
          slipping: this.slipping,
          temp_acceleration: this.temp_acceleration,
          temp_velocity: this.temp_velocity,
          motor_torque: this.motor_torque
        });
        _results.push(this.max_position = this.position);
      }
      return _results;
    };

    return HeunSimulation;

  })();

  this.onmessage = function(event) {
    var sim;
    sim = new HeunSimulation(event.data);
    sim.heun();
    return postMessage(JSON.stringify(sim));
  };

}).call(this);

index.html

<html>
<head>
    <script src="http://ajax.googleapis.com/ajax/libs/jquery/1.4.2/jquery.min.js"></script>
<script src="http://cdnjs.cloudflare.com/ajax/libs/d3/3.3.3/d3.min.js" > </script>
<script src="http://jashkenas.github.com/coffee-script/extras/coffee-script.js"> </script>
    <script type="text/coffeescript" src="simulation.coffee"></script>
<link href="//netdna.bootstrapcdn.com/bootstrap/3.0.0/css/bootstrap.min.css" rel="stylesheet">
<style type="text/css">

  line{
    shape-rendering: crispEdges;
  }
  .acceleration{
    stroke:red;
    fill:none;
  }
  .velocity{
    stroke:green;
    fill:none;
  }
  .position{
    stroke:steelblue;
    fill:none;
  }
  .axis{
    font-size: 9px;
  }
  .axis path,
.axis line {
  fill: none;
  stroke: #000;
  shape-rendering: crispEdges;
}

.x.axis path {
  display: none;
}
</style>
</head>
<body>
  <div class="row">
   <div id="canvas" class="col-md-6">

   </div>
   <div class="col-md-2">
     <h2>Data</h2>
     <form class="" roll="form">
      <div class="form-group">
        <label for="wheel_radius" class="control-label">Wheel Radius (inches)</label>
        <input type="wheel_radius" class="form-control input-sm" id="wheel_radius" placeholder="Wheel Radius (inches)" value="3">
      </div>
      <div class="form-group">
        <label for="number_of_motors" class="control-label">Number of Motors</label>
        <input type="number_of_motors" class="form-control input-sm" id="number_of_motors" placeholder="Number of Motors" value="4">
      </div>
      <div class="form-group">
        <label for="gear_reduction" class="control-label">Gear Reduction</label>
        <input type="gear_reduction" class="form-control input-sm" id="gear_reduction" placeholder="Gear Reduction" value="12.75">
      </div>
      <div class="form-group">
        <label for="duration" class="control-label">Duration</label>
        <input type="duration" class="form-control input-sm" id="duration" placeholder="Duration" value="1.0">
      </div>
      <button type="button" class="btn btn-primary" onclick="window.recompute()">Recompute</button>

     </form>
   </div>
 </div>
</body>
</html>

simulation.coffee

width = 550
height = 350
window.acceleration_scale = d3.scale.linear()
  .range([height,50])
  .domain([0,23])
window.velocity_scale = d3.scale.linear()
  .range([height,50])
  .domain([0,12])
window.position_scale = d3.scale.linear()
  .range([height,50])
  .domain([0,8])
window.time_scale = d3.scale.linear()
  .range([50,width])
  .domain([0,1])
svg = d3.selectAll("#canvas").append("svg")
  .attr("width", width+50)
  .attr("height", height+50)
window.values = []

time_axis = d3.svg.axis()
  .scale(time_scale)
  .orient("bottom")
position_axis = d3.svg.axis()
  .scale(time_scale)
  .orient("left")
svg.append("g")
  .attr("class", "x axis")
  .attr("transform", "translate(0," + height + ")")
  .attr("id", "time_axis")
  .call(time_axis);
# svg.append("g")
#   .attr("class", "y axis position_axis")
#   .attr("id", "position_axis")
#   .attr("transform", "translate(50,0)")
#   .call(position_axis);


window.update = () =>

  svg.selectAll("path").remove()
  window.acceleration_scale.domain([0, d3.max(window.values, (d)->d.acceleration)])
  window.velocity_scale.domain([0, d3.max(window.values, (d)->d.velocity)])
  window.position_scale.domain([0, d3.max(window.values, (d)->d.position)])
  window.time_scale.domain([0, d3.max(window.values, (d)->d.t)])




  acceleration_line = d3.svg.line()
    .y((d)=> acceleration_scale(d.acceleration))
    .x((d)=> time_scale(d.t))
  velocity_line =d3.svg.line()
    .y((d)=> velocity_scale(d.velocity))
    .x((d)=> time_scale(d.t))
  position_line =d3.svg.line()
    .y((d)=> position_scale(d.position))
    .x((d)=> time_scale(d.t))


  t = svg.transition().duration(500)
  t.select("#time_axis").call(time_axis)
  t.select("#position_axis").call(position_axis)



  svg.append("path")
    .datum(window.values)
    .attr("class", "acceleration")
    .attr("d", acceleration_line)
  svg.append("path")
    .datum(window.values)
    .attr("class", "velocity")
    .attr("d", velocity_line)
  svg.append("path")
    .datum(window.values)
    .attr("class", "position")
    .attr("d", position_line)

window.heun =new Worker("acceleration_heun.js")
window.default_params =
  rolling_resistance: 10
  rolling_resistance_prime: 1
  drivetrain_efficiency: 0.9
  motor_stall_torque: 343.4
  motor_free_speed: 5310
  number_of_motors: 4
  gear_ratio: 12.75
  wheel_radius: 3
  mass: 150
  us: 1
  uk: .7
  dt: .001
  duration: 1.0

window.heun.postMessage(window.default_params)


window.recompute = () =>
  window.heun.postMessage({
    rolling_resistance:10,
    rolling_resistance_prime:1,
    drivetrain_efficiency:0.9,
    motor_stall_torque: 343.4,
    motor_free_speed: 5310,
    number_of_motors: parseInt($('#number_of_motors').val()),
    gear_ratio: parseFloat($('#gear_reduction').val()),
    wheel_radius: parseFloat($('#wheel_radius').val()),
    mass: 150,
    us: 1,
    uk: .7,
    dt: .001,
    duration: parseFloat($('#duration').val())
  })




window.heun.onmessage = (event) =>
  console.log event.data
  window.values = JSON.parse(event.data).data
  window.update()