Apprenticeship Learning for Robotic Control, with Applications to Quadruped Locomotion

and Autonomous Helicopter Flight

Pieter AbbeelPieter Abbeel

Stanford University

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

Winter/Spring 2008

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

Big picture and key challenges

Dynamics Model PPPPsasasasa

Reward Reinforcement Controller/

Probability distribution over next states given current state and actionDescribes desirability

of being in a state.

Reward Function RRRR

ReinforcementLearning /

Optimal Control

Controller/Policy ππππ

Prescribes action to take for each 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

Overview

� Sample complexity

� Performance of resulting controller

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

� Quadruped locomotion

� Autonomous helicopter flight

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 π*)

Problem setup

π

� Desired output:

� Policy , which (ideally) has performance guarantees, i.e.,

� Note: R* is unknown.

� 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), (s , a ), (s , a ), …

Prior work: behavioral cloning

(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

� Limitations:

� Fails to provide strong performance guarantees

� Underlying assumption: policy simplicity

Problem structure

Dynamics Model PPPPsasasasa Prescribes action to

take for each state: typically very complex

Often fairly succinct

Reward Function RRRR

ReinforcementLearning /

Optimal Control

Controller/Policy ππππ

Apprenticeship learning [Abbeel & Ng, 2004]

� Assume

� Initialize: pick some controller π0.

� Iterate for i = 1, 2, … :

� “Guess” the reward function:

Find a reward function such that the teacher maximally outperforms

Learning through reward functions rather than

directly learning policies.

Find a reward function such that the teacher maximally outperforms all previously found controllers.

� Find optimal control policy πifor the current guess of the reward

function Rw.

� If , exit the algorithm.

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 π*.

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 driving

Teacher 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 examplesDriving

demonstrationDriving

demonstrationLearned behavior

Learned behavior

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.

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

Experimental setup

� 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.

Learned reward weights

Learned controller

Quadruped

� Reward function trades off 25 features.

[Kolter, Abbeel & Ng, 2008]

� Demonstrate path across the “training terrain”

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

Experimental setup

of reward weights w.

� Receive “testing terrain”---height map.

� Find a policy for crossing the testing terrain.

Learned reward weights

Without learning

With learned reward function

Apprenticeship learning

Dynamics Model PPPPsasasasa

Teacher’s flight

Learn

R

Reward Function RRRR

ReinforcementLearning /

Optimal Control

Controller ππππ

(s0, a0, s1, a1, ….)

Apprenticeship learning

Dynamics Model PPPPsasasasa

Teacher’s flight

ReinforcementLearning /

Optimal Control

Learn

R

Reward Function RRRR

Controller ππππ

(s0, a0, s1, a1, ….)

Motivating example

•Textbook model

Collect

flight data.

•Textbook model� How to fly for data collection?

Accurate

dynamics

model Psa

•Textbook model

• Specification

Accurate

dynamics

model Psa

•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).

Desired properties

� Near-optimal performance (compared to teacher).

� Small number of teacher demonstrations.

� Small number of autonomous trials.

Learn Psa

Learn Psa

Apprenticeship learning of the model

Dynamics

Model PPPPsasasasa

Autonomous flight

(s0, a0, s1, a1, ….)

Teacher’s flight

(s0, a0, s1, a1, ….)

Reward Function RRRR

ReinforcementLearning /

Optimal Control

Controller ππππ

(s0, a0, s1, a1, ….)(s0, a0, s1, a1, ….)

Theoretical guarantees

No explicit exploration required.

[Abbeel & Ng, 2005]

Learn Psa

Learn Psa

Dynamics Model PPPPsasasasa

Autonomous flight

(s , a , s , a , ….)

Teacher’s flight

(s , a , s , a , ….)

Apprenticeship learning summary

Learn

R

Reward Function RRRR

ReinforcementLearning /

Optimal Control

Controller ππππ

(s0, a0, s1, a1, ….)(s0, a0, s1, a1, ….)

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� 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.

Experimental setup for helicopter

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.

AccuracyWhite: target trajectory. Black: autonomously flown trajectory.

Summary

� Apprenticeship learning algorithms

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

� Formal guarantees� 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%.

Current and future work

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.

Thank you.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 π*.

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

Model Learning: Proof Idea

capable of flying the helicopter well in our simulation.

� Thus, each time we solve for the optimal controller using the current model/simulator P

sa, 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 P

sapredicting 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.

� 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 π satisfies

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

Probabilistic graphical model for multiple demonstrations

Full model

� Step 1: find the time-warping, and the distributional parameters

We use EM, and dynamic time warping to

Learning algorithm

� We use EM, and dynamic time warping to alternatingly optimize over the different parameters.

� Step 2: find the intended trajectory

Teacher demonstration for quadruped

� Full teacher demonstration = sequence of footsteps.

� Much simpler to “teach hierarchically”:� 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)

Experimental setup

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.