Apprenticeship Learning for Robotic Control, with Applications to Quadruped Locomotion and Autonomous Helicopter

Flight

Pieter AbbeelStanford University

(Variation hereof) presented at Cornell/USC/UCSD/Michigan/UNC/Duke/UCLA/UW/EPFL/Berkeley/CM

UWinter/Spring 2008

In collaboration with: Andrew Y. Ng, Adam Coates, J. Zico Kolter, Morgan Quigley, Dmitri Dolgov, Sebastian Thrun.

Big picture and key challengesDynamics Model

Psa

Reward Function R

ReinforcementLearning /

Optimal Control

Controller/Policy p

Prescribes action to take for each

state

Probability distribution over next states given current state and

actionDescribes

desirability of being in a state.

Key challenges Providing a formal specification of the control

task. Building a good dynamics model. Finding closed-loop controllers.

Apprenticeship learning algorithms Leverage expert demonstrations to learn to perform a

desired task.

Formal guarantees Running time Sample complexity Performance of resulting controller

Enabled us to solve highly challenging, previously unsolved, real-world control problems in

Quadruped locomotion Autonomous helicopter flight

Overview

Example task: driving

Input: Dynamics model / Simulator Psa(st+1 | st, at) No reward function Teacher’s demonstration: s0, a0, s1, a1, s2, a2, …

(= trace of the teacher’s policy p*)

Desired output: Policy , which (ideally) has

performance guarantees, i.e.,

Note: R* is unknown.

Problem setup

Formulate as standard machine learning problem Fix a policy class

E.g., support vector machine, neural network, decision tree, deep belief net, …

Estimate a policy from the training examples (s0, a0), (s1, a1), (s2, a2), …

E.g., Pomerleau, 1989; Sammut et al., 1992; Kuniyoshi et al., 1994; Demiris & Hayes, 1994; Amit & Mataric, 2002.

Prior work: behavioral cloning

Prior work: behavioral cloning

Limitations: Fails to provide strong performance

guarantees Underlying assumption: policy simplicity

Problem structureDynamics Model

Psa

Reward Function R

ReinforcementLearning /

Optimal Control

Controller/Policy p

Prescribes action to take for each state: typically very complex

Often fairly succinct

Apprenticeship learning [Abbeel & Ng, 2004]

Assume Initialize: pick some controller p0. Iterate for i = 1, 2, … :

“Guess” the reward function: Find a reward function such that the teacher maximally outperforms all previously found controllers.

Find optimal control policy pi for the current guess of the reward function Rw.

If , exit the algorithm.

Learning through reward functions rather than

directly learning policies.

There is no reward function for which the teacher significantly

outperforms thus-far found policies.

Theoretical guarantees

Guarantee w.r.t. unrecoverable reward function of teacher.

Sample complexity does not depend on complexity of teacher’s policy p*.

Related work Prior work:

Behavioral cloning. (covered earlier) Utility elicitation / Inverse reinforcement

learning, Ng & Russell, 2000. No strong performance guarantees.

Closely related later work: Ratliff et al., 2006, 2007; Neu & Szepesvari,

2007;Syed & Schapire, 2008.

Work on specialized reward function: trajectories. E.g., Atkeson & Schaal, 1997.

Highway drivingTeacher in Training World Learned Policy in Testing World

Input: Dynamics model / Simulator Psa(st+1 | st, at) Teacher’s demonstration: 1 minute in “training world” Note: R* is unknown. Reward features: 5 features corresponding to lanes/shoulders; 10

features corresponding to presence of other car in current lane at different distances

More driving examples

In each video, the left sub-panel shows a demonstration of a different driving “style”, and the right sub-panel shows the behavior learned from watching the demonstration.

Driving demonstratio

n

Driving demonstrati

on

Learned behavior

Learned behavior

Parking lot navigation

[Abbeel et al., submitted]

Reward function trades off: curvature smoothness, distance to obstacles, alignment with principal directions.

Demonstrate parking lot navigation on “train parking lot.”

Run our apprenticeship learning algorithm to find a set of reward weights w.

Receive “test parking lot” map + starting point and destination.

Find a policy for navigating the test parking lot.

Experimental setup

Learned reward weights

Learned controller

Reward function trades off 25 features.

Quadruped

[Kolter, Abbeel & Ng, 2008]

Demonstrate path across the “training terrain”

Run our apprenticeship learning algorithm to find a set of reward weights w.

Receive “testing terrain”---height map.

Find a policy for crossing the testing terrain.

Experimental setup

Learned reward weights

Without learning

With learned reward function

LearnR

Apprenticeship learning

Dynamics Model

Psa

Reward Function R

ReinforcementLearning /

Optimal Control

Controller p

Teacher’s flight

(s0, a0, s1, a1, ….)

ReinforcementLearning /

Optimal Control

LearnR

Apprenticeship learning

Dynamics Model

Psa

Reward Function R

Controller p

Teacher’s flight

(s0, a0, s1, a1, ….)

Accurate dynamics model Psa

Motivating example

• Textbook model• Specification

Accurate dynamics model Psa

Collect flight data.

• Textbook model• Specification

Learn model from data.

How to fly for data collection?

How to ensure that the entire flight envelope is covered?

Aggressive (manual) exploration

Never any explicit exploration (neither manual nor autonomous).

Near-optimal performance (compared to teacher).

Small number of teacher demonstrations.

Small number of autonomous trials.

Desired properties

Learn Psa Learn Psa

Apprenticeship learning of the model

Dynamics Model

Psa

Reward Function R

ReinforcementLearning /

Optimal Control

Controller p

Autonomous flight

(s0, a0, s1, a1, ….)

Teacher’s flight

(s0, a0, s1, a1, ….)

No explicit exploration required.

Theoretical guarantees

[Abbeel & Ng, 2005]

LearnR

Learn Psa

Learn Psa Dynamics

Model Psa

Reward Function R

ReinforcementLearning /

Optimal Control

Controller p

Autonomous flight

(s0, a0, s1, a1, ….)

Teacher’s flight

(s0, a0, s1, a1, ….)

Apprenticeship learning summary

Other relevant parts of the story

Learning the dynamics model from data Locally weighted models Exploiting structure from physics Simulation accuracy at time-scales relevant for

control

Reinforcement learning / Optimal control Model predictive control Receding horizon differential dynamic

programming[Abbeel et al. 2005, 2006a, 2006b, 2007]

Related work Bagnell & Schneider, 2001; LaCivita, Papageorgiou,

Messner & Kanade, 2002; Ng, Kim, Jordan & Sastry 2004a (2001);

Roberts, Corke & Buskey, 2003; Saripalli, Montgomery & Sukhatme, 2003; Shim, Chung, Kim & Sastry, 2003; Doherty et al., 2004.

Gavrilets, Martinos, Mettler and Feron, 2002; Ng et al., 2004b.

Maneuvers presented here are significantly more challenging than those flown by any other autonomous helicopter.

Autonomous aerobatic flips (attempt) before apprenticeship learning

Task description: meticulously hand-engineeredModel: learned from (commonly used) frequency sweeps data

1. Our expert pilot demonstrates the airshow several times.

Experimental setup for helicopter

Demonstrations

1. Our expert pilot demonstrates the airshow several times.

2. Learn a reward function---trajectory.3. Learn a dynamics model.

Experimental setup for helicopter

Learned reward (trajectory)

1. Our expert pilot demonstrates the airshow several times.

2. Learn a reward function---trajectory.3. Learn a dynamics model.4. Find the optimal control policy for learned reward

and dynamics model.5. Autonomously fly the airshow

6. Learn an improved dynamics model. Go back to step 4.

Experimental setup for helicopter

Accuracy White: target trajectory. Black: autonomously flown trajectory.

Summary Apprenticeship learning algorithms

Learn to perform a task from observing expert demonstrations of the task.

Formal guarantees Running time. Sample complexity. Performance of resulting controller.

Enabled us to solve highly challenging, previously unsolved, real-world control problems.

Applications: Autonomous helicopters to assist in

in wildland fire fighting. Fixed-wing formation flight:

Estimated fuel savings for three aircraft formation: 20%.

Learning from demonstrations only scratches surface of the potential impact of work at intersection machine learning/control on robotics.

Safe autonomous learning. More general advice taking.

Current and future work

Thank you.

Chaos (short)

Chaos (long)

Flips

Auto-rotation descent

Tic-toc

Autonomous nose-in funnel

From initial pilot demonstrations, our model/simulator Psa will be accurate for the part of the state space (s,a) visited by the pilot.

Our model/simulator will correctly predict the helicopter’s behavior under the pilot’s controller p*.

Consequently, there is at least one controller (namely p*) that looks capable of flying the helicopter well in our simulation.

Thus, each time we solve for the optimal controller using the current model/simulator Psa, we will find a controller that successfully flies the helicopter according to Psa.

If, on the actual helicopter, this controller fails to fly the helicopter---despite the model Psa predicting that it should---then it must be visiting parts of the state space that are inaccurately modeled.

Hence, we get useful training data to improve the model. This can happen only a small number of times.

Model Learning: Proof Idea

Apprenticeship Learning via Inverse Reinforcement Learning, Pieter Abbeel and Andrew Y. Ng. In Proc. ICML, 2004.

Learning First Order Markov Models for Control, Pieter Abbeel and Andrew Y. Ng. In NIPS 17, 2005.

Exploration and Apprenticeship Learning in Reinforcement Learning, Pieter Abbeel and Andrew Y. Ng. In Proc. ICML, 2005.

Modeling Vehicular Dynamics, with Application to Modeling Helicopters, Pieter Abbeel, Varun Ganapathi and Andrew Y. Ng. In NIPS 18, 2006.

Using Inaccurate Models in Reinforcement Learning, Pieter Abbeel, Morgan Quigley and Andrew Y. Ng. In Proc. ICML, 2006.

An Application of Reinforcement Learning to Aerobatic Helicopter Flight, Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng. In NIPS 19, 2007.

Hierarchical Apprenticeship Learning with Application to Quadruped Locomotion,

J. Zico Kolter, Pieter Abbeel and Andrew Y. Ng. In NIPS 20, 2008.

Helicopter dynamics model in auto

Performance guarantee intuition

Intuition by example: Let

If the returned controller p satisfies

Then no matter what the values of and are, the controller p performs as well as the teacher’s controller p*.

Probabilistic graphical model for multiple demonstrations

Teacher demonstration for quadruped

Full teacher demonstration = sequence of footsteps.

Much simpler to “teach hierarchically”: Specify a body path. Specify best footstep in a small area.

Hierarchical inverse RL

Quadratic programming problem (QP): quadratic objective, linear constraints.

Constraint generation for path constraints.

Training: Have quadruped walk straight across a fairly

simple board with fixed-spaced foot placements.

Around each foot placement: label the best foot placement. (about 20 labels)

Label the best body-path for the training board.

Use our hierarchical inverse RL algorithm to learn a reward function from the footstep and path labels.

Test on hold-out terrains: Plan a path across the test-board.

Experimental setup