  This paper presents a study on the use of the Talos humanoid robot for
performing assistive sit-to-stand or stand-to-sit tasks. In such tasks, the
human exerts a large amount of force (100--200 N) within a very short time
(2--8 s), posing significant challenges in terms of human unpredictability and
robot stability control. To address these challenges, we propose an approach
for finding a spatial reference for the robot, which allows the robot to move
according to the force exerted by the human and control its stability during
the task. Specifically, we focus on the problem of finding a 1D manifold for
the robot, while assuming a simple controller to guide its movement on this
manifold. To achieve this, we use a functional representation to parameterize
the manifold and solve an optimization problem that takes into account the
robot's stability and the unpredictability of human behavior. We demonstrate
the effectiveness of our approach through simulations and experiments with the
Talos robot, showing robustness and adaptability.
