  Trajectory planning is a key piece in the algorithmic architecture of a
robot. Trajectory planners typically use iterative optimization schemes for
generating smooth trajectories that avoid collisions and are optimal for
tracking given the robot's physical specifications. Starting from an initial
estimate, the planners iteratively refine the solution so as to satisfy the
desired constraints. In this paper, we show that such iterative optimization
based planners can be vulnerable to adversarial attacks that force the planner
either to fail completely, or significantly increase the time required to find
a solution. The key insight here is that an adversary in the environment can
directly affect the optimization cost function of a planner. We demonstrate how
the adversary can adjust its own state configurations to result in poorly
conditioned eigenstructure of the objective leading to failures. We apply our
method against two state of the art trajectory planners and demonstrate that an
adversary can consistently exploit certain weaknesses of an iterative
optimization scheme.
