learning parameterized maneuvers for autonomous helicopter flight jie tang, arjun singh, nimbus...
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Learning Parameterized Maneuvers for Autonomous Helicopter FlightJie Tang, Arjun Singh, Nimbus Goehausen,
Pieter AbbeelUC Berkeley
Dynamics Model
Optimal Control
Overview
Target Trajectory
Controller
Problem
• Robotics tasks involve complex trajectories– Stall turn
• Challenging, nonlinear dynamics
Dynamics Model
Optimal Control
Overview
Target Trajectory
Controller
Demonstrations
Learning Target Trajectory From Demonstration
Height
Problem: Demonstrations are suboptimal– Use multiple demonstrations– Current state of the art in helicopter
aerobatics (Coates, Abbeel, and Ng, ICML 2008)
– Our work: learn parameterized maneuver classes
Problem: Demonstrations will be different from desired target trajectory
Example Data
Learning Trajectory
• HMM-like generative model– Dynamics model used as HMM transition model– Synthetic observations enforce parameterization– Demos are observations of hidden trajectory
• Problem: how do we align observations to hidden trajectory?
Demo 1
Demo 2
Hidden
Height 50m
Learning Trajectory
• Dynamic Time Warping• Extended Kalman filter / smoother• Repeat
Demo 1
Demo 2
Hidden
Height 50m
Smoothed Dynamic Time Warping• Potential outcome of dynamic time warping:
• More desirable outcome:
• Introduce smoothing penalty – Extra dimension in dynamic program
• Some demonstrations should contribute more to target trajectory than others– Difficult to tune these observation covariances
• Learn optimal observation covariances using EM
Weighting Demonstrations
Targ
et H
eigh
t
Learned TrajectoryTa
rget
Hei
ght
Dynamics Model
Optimal Control
Overview
Target Trajectory
Controller
Demonstrations
Frequency Sweeps and Step
Responses
Learning dynamics• Standard helicopter dynamics model estimated from data
– Has relatively large errors in aggressive flight regimes• After learning target trajectory, we obtain aligned demonstrations
– Errors in model are consistent for executions of the same maneuver class• Many hidden variables are not modeled explicitly
– Airflow, rotor speed, actuator latency• Learn corrections to dynamics model along each target trajectory
2G error
Dynamics Model
Optimal Control
Overview
Target Trajectory
Controller
Standard Dynamics Model+Trajectory-Specific
Corrections
Frequency Sweeps and Step
Responses
Optimal ControlReceding Horizon
Differential Dynamic Programming
Demonstrations
Experimental Setup
Onboard IMU @333Hz
Offboard Cameras 1280x960@20HzExtended Kalman FilterRHDDP controller
Controls @ 20Hz
“Position”
3-axis magnetometer, accelerometer,
gyroscope (“Orientation”)
Results: Stall Turn
Max speed: 57 mph
Results: Loops
Results: Tic-Tocs
Typical Flight Performance: Stall Turn
Quantitative Evaluation
• Flight conditions: wind up to 15mph• Similar accuracy is maintained for queries very
different from our demonstrations– e.g., can learn 60m stall turns from 40m, 80m
demonstrations• Four or five demonstrations sufficient to cover a
wide range of stall turns, loops, and tic-tocs– e.g., four stall turns at 20m, 40m, 60m, 80m sufficient
to generate any stall turn between 20m and 80m
Conclusions
• Presented an algorithm for learning parameterized target trajectories and accurate dynamics models from demonstrations
• With few demonstrations, can generate a wide variety of novel trajectories
• Validated on a variety of parameterized aerobatic helicopter maneuvers
Thank you
Thank you