Inspired by natural swarming and flocking behaviors, in this paper we study a series of problems concerning motion control for autonomous multiagent formations moving in a two dimensional space and avoiding collision with each other as well as obstacles. We give a hierarchical task map and argue that if the formation is kept rigid via implementation of certain distance maintenance constraints, then no inter-agent collision can happen. We outline recently developed procedures based on graph theory for achieving this. We then take the study further by investigating and discussing two strategies for obstacle avoidance by the entire formation. We present some simulation results for the motion of an asymmetrically controlled formation with no global leader, in presence of multiple obstacles on the plane of interest.