Robots are integrating more huge-size models to enrich functions and improve accuracy, which leads to out-of-control computing pressure. And thus robots are encountering bottlenecks in computing power and battery capacity. Fog or cloud robotics is one of the most anticipated theories to address these issues. Approaches of cloud robotics have developed from system-level to node-level. However, the present node-level systems are not flexible enough to dynamically adapt to changing conditions. To address this, we present ElasticROS, which evolves the present node-level systems into an algorithm-level one. ElasticROS is based on ROS and ROS2. For fog and cloud robotics, it is the first robot operating system with algorithm-level collaborative computing. ElasticROS develops elastic collaborative computing to achieve adaptability to dynamic conditions. The collaborative computing algorithm is the core and challenge of ElasticROS. We abstract the problem and then propose an algorithm named ElasAction to address. It is a dynamic action decision algorithm based on online learning, which determines how robots and servers cooperate. The algorithm dynamically updates parameters to adapt to changes of conditions where the robot is currently in. It achieves elastically distributing of computing tasks to robots and servers according to configurations. In addition, we prove that the regret upper bound of the ElasAction is sublinear, which guarantees its convergence and thus enables ElasticROS to be stable in its elasticity. Finally, we conducted experiments with ElasticROS on common tasks of robotics, including SLAM, grasping and human-robot dialogue, and then measured its performances in latency, CPU usage and power consumption. The algorithm-level ElasticROS performs significantly better than the present node-level system.