Pendulum Swing-Up with Image MATLAB Environment

The reinforcement learning environment for this example is a simple frictionless pendulum that initially hangs in a downward position. The training goal is to make the pendulum stand upright without falling over using minimal control effort.

For this environment:

Here:

For more information on this model, see Train DDPG Agent to Swing Up and Balance Pendulum with Image Observation (Reinforcement Learning Toolbox).

Create Environment Interface

Create a predefined environment interface for the pendulum.

env = rlPredefinedEnv('SimplePendulumWithImage-Discrete');

The interface has two observations. The first observation, named "pendImage", is a 50-by-50 grayscale image.

obsInfo = getObservationInfo(env);
obsInfo(1)

ans = 
  rlNumericSpec with properties:

     LowerLimit: 0
     UpperLimit: 1
           Name: "pendImage"
    Description: [0x0 string]
      Dimension: [50 50]
       DataType: "double"

The second observation, named "angularRate", is the angular velocity of the pendulum.

obsInfo(2)

ans = 
  rlNumericSpec with properties:

     LowerLimit: -Inf
     UpperLimit: Inf
           Name: "angularRate"
    Description: [0x0 string]
      Dimension: [1 1]
       DataType: "double"

The interface has a discrete action space where the agent can apply one of five possible torque values to the pendulum: -2, -1, 0, 1, or 2 N·m.

actInfo = getActionInfo(env)

actInfo = 
  rlFiniteSetSpec with properties:

       Elements: [-2 -1 0 1 2]
           Name: "torque"
    Description: [0x0 string]
      Dimension: [1 1]
       DataType: "double"

Fix the random generator seed for reproducibility.

rng(0)

Construct Critic Network Using Deep Network Designer

A DQN agent approximates the long-term reward, given observations and actions, using a critic value function representation. For this environment, the critic is a deep neural network with three inputs (two observations and one action), and one output. For more information on creating a deep neural network value function representation, see Create Policy and Value Function Representations (Reinforcement Learning Toolbox).

You can construct the critic network interactively by using the Deep Network Designer app. To do so, you first create separate input paths for each observation and action. These paths learn lower level features from their respective inputs. You then create a common output path that combines the outputs from the input paths.

Create Image Observation Path

To create the image observation path, first drag an ImageInputLayer from the Layer Library pane to the canvas. Set the layer InputSize to 50,50,1 for the image observation, and set Normalization to none.

Second, drag a Convolution2DLayer to the canvas and connect the input of this layer to the output of the ImageInputLayer. Create a convolution layer with 2 filters (NumFilters property) that have a height and width of 10 (FilterSize property), and use a stride of 5 in the horizontal and vertical directions (Stride property).

Finally, complete the image path network with two sets of ReLULayer and FullyConnectedLayer layers. The output sizes of the first and second FullyConnectedLayer layers are 400 and 300, respectively.

Create All Input Paths and Output Path

Construct the other input paths and output path in a similar manner. For this example, use the following options.

Angular velocity path (scalar input):

Action path (scalar input):

Output path:

Export Network from Deep Network Designer

To export the network to the MATLAB workspace, in Deep Network Designer, click Export. Deep Network Designer exports the network as a new variable containing the network layers. You can create the critic representation using this layer network variable.

Alternatively, to generate equivalent MATLAB code for the network, click Export > Generate Code.

The generated code is as follows.

lgraph = layerGraph();
layers = [
    imageInputLayer([1 1 1],"Name","torque","Normalization","none")
    fullyConnectedLayer(300,"Name","torque_fc1")];
lgraph = addLayers(lgraph,layers);
layers = [
    imageInputLayer([1 1 1],"Name","angularRate","Normalization","none")
    fullyConnectedLayer(400,"Name","dtheta_fc1")
    reluLayer("Name","dtheta_relu1")
    fullyConnectedLayer(300,"Name","dtheta_fc2")];
lgraph = addLayers(lgraph,layers);
layers = [
    imageInputLayer([50 50 1],"Name","pendImage","Normalization","none")
    convolution2dLayer([10 10],2,"Name","img_conv1","Stride",[5 5])
    reluLayer("Name","img_relu")
    fullyConnectedLayer(400,"Name","theta_fc1")
    reluLayer("Name","theta_relu1")
    fullyConnectedLayer(300,"Name","theta_fc2")];
lgraph = addLayers(lgraph,layers);
layers = [
    additionLayer(3,"Name","addition")
    reluLayer("Name","relu")
    fullyConnectedLayer(1,"Name","stateValue")];
lgraph = addLayers(lgraph,layers);
lgraph = connectLayers(lgraph,"torque_fc1","addition/in3");
lgraph = connectLayers(lgraph,"theta_fc2","addition/in1");
lgraph = connectLayers(lgraph,"dtheta_fc2","addition/in2");

View the critic network configuration.

figure
plot(lgraph)

Specify options for the critic representation using rlRepresentationOptions (Reinforcement Learning Toolbox).

criticOpts = rlRepresentationOptions('LearnRate',1e-03,'GradientThreshold',1);

Create the critic representation using the specified deep neural network lgraph and options. You must also specify the action and observation info for the critic, which you obtain from the environment interface. For more information, see rlQValueRepresentation (Reinforcement Learning Toolbox).

critic = rlQValueRepresentation(lgraph,obsInfo,actInfo,...
    'Observation',{'pendImage','angularRate'},'Action',{'torque'},criticOpts);

To create the DQN agent, first specify the DQN agent options using rlDQNAgentOptions (Reinforcement Learning Toolbox).

agentOpts = rlDQNAgentOptions(...
    'UseDoubleDQN',false,...    
    'TargetUpdateMethod',"smoothing",...
    'TargetSmoothFactor',1e-3,... 
    'ExperienceBufferLength',1e6,... 
    'DiscountFactor',0.99,...
    'SampleTime',env.Ts,...
    'MiniBatchSize',64);
agentOpts.EpsilonGreedyExploration.EpsilonDecay = 1e-5;

Then, create the DQN agent using the specified critic representation and agent options. For more information, see rlDQNAgent (Reinforcement Learning Toolbox).

agent = rlDQNAgent(critic,agentOpts);

Train Agent

To train the agent, first specify the training options. For this example, use the following options.

For more information, see rlTrainingOptions (Reinforcement Learning Toolbox).

trainOpts = rlTrainingOptions(...
    'MaxEpisodes',5000,...
    'MaxStepsPerEpisode',500,...
    'Verbose',false,...
    'Plots','training-progress',...
    'StopTrainingCriteria','AverageReward',...
    'StopTrainingValue',-1000);

You can visualize the pendulum system during training or simulation by using the plot function.

plot(env)

Train the agent using the train (Reinforcement Learning Toolbox) function. This is a computationally intensive process that takes several hours to complete. To save time while running this example, load a pretrained agent by setting doTraining to false. To train the agent yourself, set doTraining to true.

doTraining = false;

if doTraining
    % Train the agent.
    trainingStats = train(agent,env,trainOpts);
else
    % Load pretrained agent for the example.
    load('MATLABPendImageDQN.mat','agent');
end

Simulate DQN Agent

To validate the performance of the trained agent, simulate it within the pendulum environment. For more information on agent simulation, see rlSimulationOptions (Reinforcement Learning Toolbox) and sim (Reinforcement Learning Toolbox).

simOptions = rlSimulationOptions('MaxSteps',500);
experience = sim(env,agent,simOptions);

totalReward = sum(experience.Reward)

totalReward = -888.9802