In this extended abstract, we report on ongoing work towards an approximate multimodal optimization algorithm with asymptotic guarantees. Multimodal optimization is the problem of finding all local optimal solutions (modes) to a path optimization problem. This is important to compress path databases, as contingencies for replanning and as source of symbolic representations. Following ideas from Morse theory, we define modes as paths invariant under optimization of a cost functional. We develop a multi-mode estimation algorithm which approximately finds all modes of a given motion optimization problem and asymptotically converges. This is made possible by integrating sparse roadmaps with an existing single-mode optimization algorithm. Initial evaluation results show the multi-mode estimation algorithm as a promising direction to study path spaces from a topological point of view.
翻译:在这一扩展的抽象中,我们报告了当前为建立具有无症状保证的近似多式联运优化算法而正在进行的工作。多模式优化是找到所有当地最佳解决方案(模式)解决路径优化问题的问题。这对于压缩路径数据库十分重要,作为重新规划的意外事件和象征性表述的来源。根据莫尔斯理论的想法,我们将模式定义为在成本功能优化情况下的无变化路径。我们开发了多模式估算算法,它大致可以找到特定运动优化问题的所有模式,也可以找到零散路径与现有单一模式优化算法相结合。初步评估结果显示多模式估算算法是从顶层角度研究路径空间的有希望的方向。