an application of reinforcement learning to autonomous helicopter flight pieter abbeel, adam coates,...
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An Application of Reinforcement Learning
to Autonomous Helicopter Flight
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y.
NgStanford University
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng
Overview
Autonomous helicopter flight is widely accepted to be a highly challenging control/reinforcement learning (RL) problem.
Human expert pilots significantly outperform autonomous helicopters.
Apprenticeship learning algorithms use expert demonstrations to obtain good controllers.
Our experimental results significantly extend the state of the art in autonomous helicopter aerobatics.
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng
Apprenticeship learning: uses an expert demonstration to help select the model and the reward function.
Apprenticeship learning and RL
Reward Function R
ReinforcementLearning
Control policy )(...)(Emax 0 TsRsR
Unknown dynamics:
flight data is required to obtain an accurate model.
Hard to specify the reward function for
complex tasks such as
helicopter aerobatics.
Dynamics Model
Psa
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng
Learning the dynamical model
State-of-the-art: E3 algorithm, Kearns and Singh (2002). (And its variants/extensions: Kearns and Koller, 1999; Kakade, Kearns and Langford, 2003; Brafman and Tennenholtz, 2002.)
Have goodmodel of dynamics?
NO
“Explore”
YES
“Exploit”
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng
Learning the dynamical model
State-of-the-art: E3 algorithm, Kearns and Singh (2002). (And its variants/extensions: Kearns and Koller, 1999; Kakade, Kearns and Langford, 2003; Brafman and Tennenholtz, 2002.)
Have goodmodel of dynamics?
NO
“Explore”
YES
“Exploit”
Exploration policies are impractical: they do not even try
to perform well.Can we avoid explicit exploration and just
exploit?
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng
Aggressive manual exploration
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng
Apprenticeship learning of the model
Expert human pilot flight
(a1, s1, a2, s2, a3, s3, ….)
Learn P sa
(a1, s1, a2, s2, a3, s3, ….)
Autonomous flight
Learn Psa
Dynamics Model
Psa
Reward Function R
ReinforcementLearning )(...)(Emax 0 TsRsR
Control policy
[Abbeel & Ng, 2005]Theorem. The described procedure will return policy as good as the expert’s policy in a polynomial number of iterations.
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng
Learning the dynamics model
Details of algorithm for learning dynamics model: Gravity subtraction [Abbeel, Ganapathi & Ng,
2005] Lagged criterion [Abbeel & Ng, 2004]
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng
Autonomous nose-in funnel
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng
Autonomous tail-in funnel
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng
Apprenticeship learning: reward
Reward Function R
ReinforcementLearning
Control policy )(...)(Emax 0 TsRsR
Dynamics Model
Psa
Hard to specify the reward function for
complex tasks such as
helicopter aerobatics.
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng
Example task: flip
Ideal flip: rotate 360 degrees around horizontal axis going right to left through the helicopter.1
5
2 3 4
76 8
g
g g
gg
gg
g g
T
T
T
T
TT
T T
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng
Example task: flip (2)
Specify flip task as: Idealized trajectory
Reward function that penalizes for deviation. Reward function
+
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng
Example of a bad reward function
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng
Apprenticeship learning for the reward function
Our approach: Observe expert’s demonstration of task. Infer reward function from demonstration. [see also Ng &
Russell, 2000]
Algorithm: Iterate for t = 1, 2, … Inverse RL step:
Estimate expert’s reward function R(s)= wT(s) such that under R(s) the expert outperforms all previously found policies {i}.
RL step: Compute optimal policy t for the estimated
reward function.
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng
Theoretical Results: Convergence
Theorem. After a number of iterations polynomial in the number of features and the horizon, the algorithm outputs a policy that performs nearly as well as the expert, as evaluated on the unknown reward function R*(s)=w*T(s).
[Abbeel & Ng, 2004]
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng
Overview
Reward Function R
ReinforcementLearning
Control policy )(...)(Emax 0 TsRsR
Dynamics Model
Psa
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng
Optimal control algorithm
Differential dynamic programming [Jacobson & Mayne, 1970; Anderson & Moore, 1989] An efficient algorithm to (locally) optimize a
policy for continuous state/action spaces.
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng
DDP design choices and lessons learned
Simplest reward function: penalize for deviation from the target states for each time.
Penalize for high frequency control inputs significantly improves the controllers.
To allow aggressive maneuvering, we use a two-step procedure:
Make a plan off-line. Penalize for high frequency deviations from the planned inputs.
Penalize for integrated orientation error. [See paper for details.]
Process noise has little influence on controllers’ performance.
Observation noise and delay in observations greatly affect the controllers’ performance.
Insufficient: resulting controllers perform very poorly.
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng
Autonomous stationary flips
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng
Autonomous stationary rolls
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng
Related work
Bagnell & Schneider, 2001; LaCivita et al., 2006; Ng et al., 2004a; Roberts et al., 2003; Saripalli et al., 2003.; Ng et al., 2004b; Gavrilets, Martinos, Mettler and Feron, 2002.
Maneuvers presented here are significantly more difficult than those flown by any other autonomous helicopter.
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng
Conclusion
Apprenticeship learning for the dynamics model avoids explicit exploration in our experiments.
Procedure based on inverse RL for the reward function gives performance similar to human pilots.
Our results significantly extend state of the art in autonomous helicopter flight: first autonomous completion of stationary flips and rolls, tail-in funnels and nose-in funnels.
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng
Acknowledgments
Ben Tse, Garett Oku, Antonio Genova. Mark Woodward, Tim Worley.
Pieter Abbeel, Adam Coates, Morgan Quigley and Andrew Y. Ng
Continuous flips