In this paper, we plan robotic multi-contact non-gaited motion by solving an overall optimization problem. Our algorithm takes as input the contact stances, the model of the robot and its environment, and generates the joints trajectories that achieve multi-contact motion under explicit constraints such as joint position, velocity and torque limits, equilibrium and eventually other task objectives. We improve our previous work in order to consider floatting contacts for which some components of the contact position and/or orientation are not specified. We also discuss how, in practice, we bridge theoretical computations based on a rigid model of the robot to actual experiments by considering additional constraints during the optimization process.