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.
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