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Optimization-Based Collision Avoidance. (arXiv:1711.03449v1 [math.OC])
来源于:arXiv
This paper presents a novel method for reformulating non-differentiable
collision avoidance constraints into smooth nonlinear constraints using strong
duality of convex optimization. We focus on a controlled object whose goal is
to avoid obstacles while moving in an n-dimensional space. The proposed
reformulation does not introduce approximations, and applies to general
obstacles and controlled objects that can be represented in an n-dimensional
space as the finite union of convex sets. Furthermore, we connect our results
with the notion of signed distance, which is widely used in traditional
trajectory generation algorithms. Our method can be used in generic navigation
and trajectory planning tasks, and the smoothness property allows the use of
general-purpose gradient- and Hessian-based optimization algorithms. Finally,
in case a collision cannot be avoided, our framework allows us to find
"least-intrusive" trajectories, measured in terms of penetration. We
demonstrate the efficacy o 查看全文>>