November 13, 2019 Abstract Collision avoidance is one of the most primary problems in the decentralized multiagent navigation: while the agents are moving towards their own targets, attentions should be paid to avoid the collisions with the others. In this paper, we introduced the concept of the local action cell, which provides for each agent a set of velocities that are safe to perform. Consequently, as long as the local action cells are updated on time and each agent selects its motion within the corresponding cell, there should be no collision caused. Furthermore, we coupled the local action cell with an adaptive learning framework, in which the performance of selected motions are evaluated and used as the references for making decisions in the following updates. The efficiency of the proposed approaches were demonstrated through the experiments for three commonly considered scenarios, where the comparisons have been made with several well studied strategies. 1 Introduction Collision-free navigation is a fundamental and important problem in the design of the multiagent systems, which are widely applied in the fields such as robots control and traffic engineering.