CS545_Lecture_13

# CS545_Lecture_13 - CS545-Contents XIII Trajectory Planning...

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CS545—Contents XIII Trajectory Planning Control Policies Desired Trajectories Optimization Methods Dynamical Systems Reading Assignment for Next Class See http://www-clmc.usc.edu/~cs545

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Learning Policies is the Goal of Learning Control Policy: u t ( ) = p x t ( ) , t , α ( )
Dynamic Programming & Reinforcement Learning Movement System Nonlinear Controller (Policy) Desired Behavior u x Dynamic Programming requires a model of the movement system Reinforcement Learning can work without models of the movement system Essentials both techniques require to learn a high-dimensional “value function” that assesses the quality of an action u in a state x learning the value function is a complex nonstationary, nonlinear learning process both methods die the curse of dimensionality V = max u r x , u ( ) + τ V x ( ) x f x , u ( ) (HJB-Eqn.)

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Desired Trajectories Essentials prescribe a desired trajectory convert desired trajectory into a (time-dependent) control policy, e.g., by PD- controller Problems Where do desired trajectories come from How to accomplish reactive control How to generalize to new tasks or new situations θ , θ ( ) desired = f ξ initial , ξ target , t ( ) u = p x , t , α ( ) = k θ θ t ( ) desired θ ( ) + k θ θ t ( ) desired θ ( )
Desired Trajectories (cont’d) There is a difference between PATH and TRAJECTORY planning A trajectory involves geometry AND time A path involves only geometry Planning can happen either in joint or operational space There is usually an infinity of possible desired trajectories How is the desired trajectory represented? Every point in time? Only start & final point? Via points? Movement Primitives x d = g t , α ( ) or θ d = f t , α ( )

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Joint Space Planning What could one plan? Arbitrary trajectories from start to end Trapizoidal (or any aother kind of) velocity profiles Polynomials: 1.order: straight lines 2.order: parabolas 3.order: cubic splines 5 order: quintic splines Interesting: Analyze the shape of the trajectories in position, velocity, acceleration, and jerk space.
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