The context of service robotics is characterized by the presence of humans in the vicinity of the robot. The movements of these robots should not disturb the safety of humans or their comfort. From the motion planning point of view, the planner must both avoid hitting humans or colliding with the environment and also adapt the robot's kinematic limits depending on the proximity of humans. At each level of the system (Planning and execution / Control), the robot must ensure the safety and the comfort of humans. We propose an approach of motion planning and motion control based on polynomial trajectories. In the first part, we present a trajectory generator which limits the speed, the acceleration and the jerk (derivative of the acceleration)...