The objective function used in trajectory optimization is often non-convex and can have an infinite set of local optima. In such cases, there are diverse solutions to perform a given task. Although there are a few methods to find multiple solutions for motion planning, they are limited to generating a finite set of solutions. To address this issue, we presents an optimization method that learns an infinite set of solutions in trajectory optimization. In our framework, diverse solutions are obtained by learning latent representations of solutions. Our approach can be interpreted as training a deep generative model of collision-free trajectories for motion planning. The experimental results indicate that the trained model represents an infinite set of homotopic solutions for motion planning problems.

翻译：轨迹优化中所使用的客观功能通常不是曲线,可以有无限的局部选择。 在这种情况下,可以有多种不同的解决方案来完成特定任务。 虽然有几种方法可以找到多种运动规划解决方案,但仅限于产生一套有限的解决方案。为了解决这一问题,我们提出了一个优化方法,在轨迹优化中学习一套无限的解决方案。在我们的框架里,通过学习潜在的解决方案的表达方式,可以获得多种解决方案。我们的方法可以被解释为培训一个不碰撞轨道的深度遗传模型,用于运动规划。实验结果显示,经过培训的模型代表了一套无限的关于运动规划问题的同质解决方案。