  This paper proposes a new control algorithm for human-robot co-transportation
based on a robot manipulator equipped with a mobile base and a robotic arm. The
primary focus is to adapt to human uncertainties through the robot's whole-body
dynamics and pose optimization. We introduce an augmented Model Predictive
Control (MPC) formulation that explicitly models human uncertainties and
contains extra variables than regular MPC to optimize the pose of the robotic
arm. The core of our methodology involves a two-step iterative design: At each
planning horizon, we select the best pose of the robotic arm (joint angle
combination) from a candidate set, aiming to achieve the lowest estimated
control cost. This selection is based on solving an uncertainty-aware Discrete
Algebraic Ricatti Equation (DARE), which also informs the optimal control
inputs for both the mobile base and the robotic arm. To validate the
effectiveness of the proposed approach, we provide theoretical derivation for
the uncertainty-aware DARE and perform simulated and proof-of-concept hardware
experiments using a Fetch robot under varying conditions, including different
nominal trajectories and noise levels. The results reveal that our proposed
approach outperforms baseline algorithms, maintaining similar execution time
with that do not consider human uncertainty or do not perform pose
optimization.
