PDF《Parameterized Maneuver Learning for》

Parameterized Maneuver Learning for Autonomous Helicopter Flight Jie Tang, Arjun Singh, Nimbus Goehausen, and Pieter Abbeel Abstract― Many robotic control tasks involve complex dy- namics that are hard to model.

Hand-specifying trajectories that satisfy a system'

s dynamics can be very time-consuming and often exceedingly dif?cult. We present an algorithm for automatically generating large classes of trajectories for dif?cult control tasks by learning parameterized versions of desired maneuvers from multiple expert demonstrations. Our algorithm has enabled the successful execution of several parameterized aerobatic maneuvers by our autonomous helicopter. I. INTRODUCTION Trajectory following is a fundamental building block for many robotics tasks. By reducing the control problem to trajectory following, one can often suffer less from the curse of dimensionality as it becomes suf?cient to consider a relatively small part of the state space during control policy design. Unfortunately, specifying the desired trajectory and building an appropriate model for the robot dynamics along that trajectory are often highly non-trivial, tightly coupled tasks. For the control design to bene?t from being reduced to a trajectory following task, it typically requires that the target trajectory is at least approximately physically feasible. Specifying such a target trajectory can be highly challenging. In the apprenticeship learning setting, where we have access to an expert who can provide demonstrations, it is natural to request a demonstration of the desired trajectory as the speci?cation of the target trajectory. However, rarely will an expert be able to demonstrate exactly the trajectory we desire to execute autonomously. Repeated expert demon- strations together can often capture a desired maneuver, as different demonstrations deviate from the intent in different ways. Abbeel et al. [1] and Coates et al. [7] describe a generative probabilistic model that enabled them to extract an expert helicopter pilot'

s intended trajectory from multiple suboptimal demonstrations. They also show how multiple demonstrations can be leveraged to obtain a high accuracy dynamics model, which is speci?cally tuned to the particular maneuver in consideration. Unfortunately, most robotics tasks require us to adapt our learned maneuvers to account for a changing environment: consider ?ying aerobatic helicopter maneuvers while avoid- ing trees and other obstacles. We may need to perform stall The authors are with the Department of Electrical Engi- neering and Computer Sciences, UC Berkeley, CA 94720, U.S.A. Email: jietang@eecs.berkeley.edu, arjun@hkn.eecs.berkeley.edu, nimbus@berkeley.edu, pabbeel@cs.berkeley.edu. turns1 of any altitude between

10 and

50 meters. An approach based on the work presented in [1] and [7] would require us to anticipate every possible stall turn altitude and gather expert demonstrations for each one in advance. This seems wasteful, as the different stall turn trajectories will share many properties. In this paper, we present a probabilistic model-based algo- rithm (building upon [1], [7]), which makes ef?cient use of expert demonstrations by learning parameterized maneuvers rather than a discrete set of maneuvers. We ?rst collect a wide range of executions of the maneuver of interest. When asked for a particular execution of the maneuver, such as a stall turn of a particular altitude, our algorithm generates the appropriate target trajectory. We tested our algorithm on three aggressive helicopter maneuvers: stall turns, loops, and tic-tocs. Our algorithm successfully generates ?yable parameterized maneuvers from a relatively small number of demonstrations. The generated trajectories closely match held-out trajectories. Our heli- copter can perform these interpolated trajectories with an accuracy comparable to that of a human expert. Fig. 1. Our Synergy N9 autonomous helicopter. Videos of our autonomous helicopter ?ight results are available at the following page: http://rll.eecs.berkeley.edu/heli/icra10 II. OVERVIEW In many trajectory-following problems, the trajectories can be categorized into distinct maneuver classes. Furthermore, for many maneuver classes, a particular execution of a 1During a stall turn a forward ?ying helicopter pitches