Abstract-Ensuring the safety of humans in a collaborative environment with industrial robots is a major concern of human-robot co-working. Most current approaches give no formal guarantee of safety; where such guarantees are given, accounting for the unpredictability of the human may limit robot efficiency. We therefore developed a novel trajectory planner for a robot arm, which formally guarantees the safety of humans from collision with the robot for every possible human behaviour, without restricting the robot more than necessary. To achieve this, the trajectory planner verifies online that the robot adheres to two separate safety criteria derived from ISO standards using reachable occupancies of surrounding humans and the robot. While one criterion anticipates all possible movements of the human and provides a reasonable safety guarantee, the other criterion additionally guarantees strict safety as long as the human behaves as expected according to ISO standards. We implemented the trajectory planner for a real robot arm and show some experimental results.