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Introduction

Method

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Example Trajectory

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A visualization of how the polynomial zonotope trajectory representation is used to construct the polynomial zonotope forward occupancy for a two link arm in 2D. +

A visualization of how the polynomial zonotope trajectory representation is used to construct the polynomial zonotope forward occupancy for a two link arm in 2D. A desired trajectory for each joint is shown in black in the top two rows. The same desired trajectory is depicted in each column. The planning time horizon is represented as a finite set of polynomial zonotopes (Sec. VIII-A1). @@ -276,6 +267,15 @@

Example Trajectory

The third column depicts a family of desired trajectories buffered by the ultimate bound that are overapproximated by a finite set of polynomial zonotopes and the corresponding forward occupancy of the robot over this entire set. The fourth column depicts a subset of the sets illustrated in the third column generated by slicing in a specific trajectory parameter (Sec. VIII-A4). Note that the desired trajectory always remains within polynomial zonotopes.

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Example Trajectory

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