  Numerical optimization has become a popular approach to plan smooth motion
trajectories for robots. However, when sharing space with humans, balancing
properly safety, comfort and efficiency still remains challenging. This is
notably the case because humans adapt their behavior to that of the robot,
raising the need for intricate planning and prediction. In this paper, we
propose a novel optimization-based motion planning algorithm, which generates
robot motions, while simultaneously maximizing the human trajectory likelihood
under a data-driven predictive model. Considering planning and prediction
together allows us to formulate objective and constraint functions in the joint
human-robot state space. Key to the approach are added latent space modifiers
to a differentiable human predictive model based on a dedicated recurrent
neural network. These modifiers allow to change the human prediction within
motion optimization. We empirically evaluate our method using the publicly
available MoGaze dataset. Our results indicate that the proposed framework
outperforms current baselines for planning handover trajectories and avoiding
collisions between a robot and a human. Our experiments demonstrate
collaborative motion trajectories, where both, the human prediction and the
robot plan, adapt to each other.
