Train DDPG Agent to Control Sliding Robot

This example shows how to train a deep deterministic policy gradient (DDPG) agent to generate trajectories for a robot sliding without friction over a 2-D plane, modeled in Simulink®. For more information on DDPG agents, see Deep Deterministic Policy Gradient (DDPG) Agent (Reinforcement Learning Toolbox).

The example code may involve computation of random numbers at various stages such as initialization of the agent, creation of the actor and critic, resetting the environment during simulations, generating observations (for stochastic environments), generating exploration actions, and sampling min-batches of experiences for learning. Fixing the random number stream preserves the sequence of the random numbers every time you run the code and improves reproducibility of results. You will fix the random number stream at various locations in the example.

Fix the random number stream with the seed 0 and random number algorithm Mersenne Twister. For more information on random number generation see rng.

previousRngState = rng(0,"twister")
previousRngState = struct with fields:
Type: 'twister'
Seed: 0
State: [625x1 uint32]

The output previousRngState is a structure that contains information about the previous state of the stream. You will restore the state at the end of the example.

Sliding Robot Model

The reinforcement learning environment for this example is a sliding robot with its initial condition randomized around a ring having a radius of 15 m. The orientation of the robot is also randomized. The robot has two thrusters mounted on the side of the body that are used to propel and steer the robot. The training goal is to drive the robot from its initial condition to the origin facing east.

Open the model.

mdl = "rlSlidingRobotEnv";
open_system(mdl)

Set the initial model state variables.

theta0 = 0;
x0 = -15;
y0 = 0;

Define the sample time Ts and the simulation duration Tf.

Ts = 0.4;
Tf = 30;

For this model:

• The goal orientation is 0 rad (robot facing east).

• The thrust from each actuator is bounded from -1 to 1 N

• The observations from the environment are the position, orientation (sine and cosine of orientation), velocity, and angular velocity of the robot.

• The reward ${\mathit{r}}_{\mathit{t}}$ provided at every time step is

${\mathit{r}}_{1}=10\left(\left({{\mathit{x}}_{\mathit{t}}}^{2}+{{\mathit{y}}_{\mathit{t}}}^{2}+{\theta }_{\mathit{t}}{\text{\hspace{0.17em}}}^{2}\right)<0.5\right)$

${\mathit{r}}_{2}=-100\left(|{\mathit{x}}_{\mathit{t}}|\ge 20\text{\hspace{0.17em}}||\text{\hspace{0.17em}}|{\mathit{y}}_{\mathit{t}}|\ge 20\right)$

${\mathit{r}}_{3}=-\left(0.2{\left({\mathit{R}}_{\mathit{t}-1}+{\mathit{L}}_{\mathit{t}-1}\right)}^{2\text{\hspace{0.17em}}}+0.3{\left({\mathit{R}}_{\mathit{t}-1}-{\mathit{L}}_{\mathit{t}-1}\right)}^{2}+0.03{{\mathit{x}}_{\mathit{t}}}^{2}+0.03{{\mathit{y}}_{\mathit{t}}}^{2}+0.02{\theta }_{\mathit{t}}{\text{\hspace{0.17em}}}^{2}\right)$

${\mathit{r}}_{\mathit{t}}={\mathit{r}}_{1}+{\mathit{r}}_{2}+{\mathit{r}}_{3}$

where:

• ${\mathit{x}}_{\mathit{t}}$ is the position of the robot along the x-axis.

• ${\mathit{y}}_{\mathit{t}}$ is the position of the robot along the y-axis.

• $\theta {\text{\hspace{0.17em}}}_{\mathit{t}}$ is the orientation of the robot.

• ${\mathit{L}}_{\mathit{t}-1}$ is the control effort from the left thruster.

• ${\mathit{R}}_{\mathit{t}-1}$ is the control effort from the right thruster.

• ${\mathit{r}}_{1}$ is the reward when the robot is close to the goal.

• ${\mathit{r}}_{2}$ is the penalty when the robot drives beyond 20 m in either the x or y direction. The simulation is terminated when ${\mathit{r}}_{2}<0$.

• ${\mathit{r}}_{3}$ is a QR penalty that penalizes distance from the goal and control effort.

Create Integrated Model

To train an agent for the SlidingRobotEnv model, use the createIntegratedEnv function to automatically generate a Simulink model containing an RL Agent block that is ready for training.

integratedMdl = "IntegratedSlidingRobot";
[~,agentBlk,obsInfo,actInfo] = ...
createIntegratedEnv(mdl,integratedMdl);

Actions and Observations

Before creating the environment object, specify names for the observation and action specifications, and bound the thrust actions between -1 and 1.

The observation vector for this environment is ${\left[\begin{array}{ccccccc}\mathit{x}& \mathit{y}& \stackrel{˙}{\mathit{x}}& \stackrel{˙}{\mathit{y}}& \mathrm{sin}\left(\theta \text{\hspace{0.17em}}\right)& \mathrm{cos}\left(\theta \right)& \stackrel{˙}{\theta \text{\hspace{0.17em}}}\end{array}\right]}^{\mathit{T}}$. Assign a name to the environment observation channel.

obsInfo.Name = "observations";

The action vector for this environment is ${\left[\begin{array}{cc}{\mathit{T}}_{\mathit{R}}& {\mathit{T}}_{\mathit{L}}\end{array}\right]}^{\mathit{T}}$. Assign a name, as well as upper and lower limits, to the environment action channel.

actInfo.Name = "thrusts";
actInfo.LowerLimit = -ones(prod(actInfo.Dimension),1);
actInfo.UpperLimit =  ones(prod(actInfo.Dimension),1);

Note that prod(obsInfo.Dimension) and prod(actInfo.Dimension) return the number of dimensions of the observation and action spaces, respectively, regardless of whether they are arranged as row vectors, column vectors, or matrices.

Create Environment Object

Create an environment object using the integrated Simulink model.

integratedMdl, ...
agentBlk, ...
obsInfo, ...
actInfo);

Reset Function

Create a custom reset function that randomizes the initial position of the robot along a ring of radius 15 m and the initial orientation. For details on the reset function, see slidingRobotResetFcn.

env.ResetFcn = @(in) slidingRobotResetFcn(in);

Create DDPG agent

DDPG agents use a parametrized Q-value function approximator to estimate the value of the policy. A Q-value function critic takes the current observation and an action as inputs and returns a single scalar as output (the estimated discounted cumulative long-term reward given the action from the state corresponding to the current observation, and following the policy thereafter).

When you create the agent, the initial parameters of the critic network are initialized with random values. Fix the random number stream so that the agent is always initialized with the same parameter values.

rng(0,"twister");

To model the parametrized Q-value function within the critic, use a neural network with two input layers (one for the observation channel, as specified by obsInfo, and the other for the action channel, as specified by actInfo) and one output layer (which returns the scalar value).

Define each network path as an array of layer objects. Assign names to the input and output layers of each path. These names allow you to connect the paths and then later explicitly associate the network input and output layers with the appropriate environment channel.

% Specify the number of outputs for the hidden layers.
hiddenLayerSize = 128;

% Define observation path layers
observationPath = [
featureInputLayer(prod(obsInfo.Dimension),Name="obsInLyr")
concatenationLayer(1,2,Name="cat")
fullyConnectedLayer(hiddenLayerSize)
reluLayer
fullyConnectedLayer(hiddenLayerSize)
reluLayer
fullyConnectedLayer(hiddenLayerSize)
reluLayer
fullyConnectedLayer(1,Name="fc4")
];

% Define action path layers
actionPath = featureInputLayer( ...
prod(actInfo.Dimension), ...
Name="actInLyr");

Assemble a dlnetwork object.

criticNetwork = dlnetwork();

Connect actionPath to observationPath.

criticNetwork = connectLayers(criticNetwork,"actInLyr","cat/in2");

Initialize network and display the number of parameters.

criticNetwork = initialize(criticNetwork);
summary(criticNetwork)
Initialized: true

Number of learnables: 34.4k

Inputs:
1   'obsInLyr'   7 features
2   'actInLyr'   2 features

Create the critic using criticNetwork, the environment specifications, and the names of the network input layers to be connected to the observation and action channels. For more information see rlQValueFunction (Reinforcement Learning Toolbox).

critic = rlQValueFunction(criticNetwork,obsInfo,actInfo,...
ObservationInputNames="obsInLyr",ActionInputNames="actInLyr");

DDPG agents use a parametrized deterministic policy over continuous action spaces, which is learned by a continuous deterministic actor. This actor takes the current observation as input and returns as output an action that is a deterministic function of the observation.

To model the parametrized policy within the actor, use a neural network with one input layer (which receives the content of the environment observation channel, as specified by obsInfo) and one output layer (which returns the action to the environment action channel, as specified by actInfo).

Define the network as an array of layer objects.

actorNetwork = [
featureInputLayer(prod(obsInfo.Dimension))
fullyConnectedLayer(hiddenLayerSize)
reluLayer
fullyConnectedLayer(hiddenLayerSize)
reluLayer
fullyConnectedLayer(hiddenLayerSize)
reluLayer
fullyConnectedLayer(prod(actInfo.Dimension))
tanhLayer
];

Convert the array of layer object to a dlnetwork object, initialize the network, and display the number of parameters.

actorNetwork = dlnetwork(actorNetwork);
actorNetwork = initialize(actorNetwork);
summary(actorNetwork)
Initialized: true

Number of learnables: 34.3k

Inputs:
1   'input'   7 features

Define the actor using actorNetwork, and the specifications for the action and observation channels. For more information, see rlContinuousDeterministicActor (Reinforcement Learning Toolbox).

actor = rlContinuousDeterministicActor(actorNetwork,obsInfo,actInfo);

Specify options for the critic and the actor using rlOptimizerOptions (Reinforcement Learning Toolbox).

criticOptions = rlOptimizerOptions( ...
LearnRate=1e-03, ...

actorOptions = rlOptimizerOptions( ...
LearnRate=1e-03, ...

Specify the DDPG agent options using rlDDPGAgentOptions (Reinforcement Learning Toolbox), include the training options for the actor and critic.

agentOptions = rlDDPGAgentOptions(...
SampleTime=Ts,...
ActorOptimizerOptions=actorOptions,...
CriticOptimizerOptions=criticOptions,...
ExperienceBufferLength=1e6 ,...
TargetSmoothFactor=1e-3,...
MiniBatchSize=512,...
MaxMiniBatchPerEpoch=50);

% Gaussian noise
agentOptions.NoiseOptions.MeanAttractionConstant = 1/Ts;
agentOptions.NoiseOptions.StandardDeviation = 1e-1;
agentOptions.NoiseOptions.StandardDeviationMin = 1e-2;
agentOptions.NoiseOptions.StandardDeviationDecayRate = 1e-6;

Then, create the agent using the actor, the critic and the agent options. For more information, see rlDDPGAgent (Reinforcement Learning Toolbox).

agent = rlDDPGAgent(actor,critic,agentOptions);

Alternatively, you can create the agent first, and then access its option object and modify the options using dot notation.

Train Agent

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

• Run each training for at most 10000 episodes, with each episode lasting at most ceil(Tf/Ts) time steps.

• Display the training progress in the Reinforcement Learning Training Monitor (set the Plots option) and disable the command line display (set the Verbose option to false).

• Evaluate the trained greedy policy every 50 training episodes by averaging the cumulative reward over 5 simulations.

• Stop training the agent when the average cumulative reward obtained during the evaluation episodes equals of exceeds 425. At this point, the agent can drive the sliding robot to the goal position.

maxepisodes = 10000;
maxsteps = ceil(Tf/Ts);
trainingOptions = rlTrainingOptions(...
MaxEpisodes=maxepisodes,...
MaxStepsPerEpisode=maxsteps,...
StopOnError="on",...
Verbose=false,...
Plots="training-progress",...
StopTrainingCriteria="EvaluationStatistic",...
StopTrainingValue=425,...
ScoreAveragingWindowLength=10);

% agent evaluator
evl = rlEvaluator(EvaluationFrequency=50,NumEpisodes=5);

Fix the random stream for reproducibility.

rng(0,"twister");

Train the agent using the train (Reinforcement Learning Toolbox) function. Training 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,trainingOptions,Evaluator=evl);
else
% Load the pretrained agent for the example.
end

Simulate DDPG Agent

Fix the random stream for reproducibility.

rng(0,"twister");

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

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

Restore the random number stream using the information stored in previousRngState.

rng(previousRngState);