Abstract : 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). The motion planner generates trajectories consisting of series of segments of cubic polynomial curves. The mono-dimensional case is first introduced and then extended to the multi-dimensional one. In the second part, we propose to approximate the trajectories by sequences of triplets of segments of cubic curves. This method allows to find trajectories that respect a given maximum error. These trajectory generators are integrated into the path planner and produce directly executable motion. An original application of the trajectory approximation is the approximation of a trajectory defined in Cartesian space by a trajectory defined in the joint space. This approach simplifies the structure of the robot controller. The presence of humans in the workspace of the robot requires also an adaptation of the trajectories during the execution. We propose a method to adapt the motion law of the multidimensional path at runtime. This work, conducted as part of the European project DEXMART and the ANR project ASSIST, has been integrated and validated on the Jido and PR2 platforms of LAAS-CNRS.