A real-time collision-avoidance algorithm for human-symbiotic robots that are required to avoid multiple pedestrians was developed. An algorithm to predict the likelihood of a collision with obstacles was based on the relative velocities between a moving robot and multiple obstacles. An algorithm that can generate the optimum path sequence to a goal in real time was also developed. The collision-avoidance path is generated by repeating an operation to select two tangent paths that connect a via-point on a path to a collision circle of each obstacle that exists in the relative space. A robot - called EMIEW" - using these algorithms with a system for avoiding collisions with many obstacles moves at a speed of 0.8 m/s in a cluster of five people walking at 1.2 m/s. The repeat period for generating a new avoidance path is 0.5s, and the processing time for the developed algorithm in the each period is a maximum of 4 ms.