This paper is concerned with the collective behaviors of robots beyond the nearest neighbor rules, i.e., dispersion and flocking, when robots interact with others by applying an acute angle test (AAT)-based interaction rule. Different from a conventional nearest neighbor rule or its variations, the AAT-based interaction rule allows interactions with some far-neighbors and excludes unnecessary nearest neighbors. The resulting dispersion and flocking hold the advantages of scalability, connectivity, robustness, and effective area coverage. For the dispersion, a spring-like controller is proposed to achieve collision-free coordination. With switching topology, a new fixed-time consensus-based energy function is developed to guarantee the system stability. An upper bound of settling time for energy consensus is obtained, and a uniform time interval is accordingly set so that energy distribution is conducted in a fair manner. For the flocking, based on a class of generalized potential functions taking nonsmooth switching into account, a new controller is proposed to ensure that the same velocity for all robots is eventually reached. A co-optimizing problem is further investigated to accomplish additional tasks, such as enhancing communication performance, while maintaining the collective behaviors of mobile robots. Simulation results are presented to show the effectiveness of the theoretical results.