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Today’s robots are expected to fulfill different requirements originated from executing complex tasks in uncertain environments, often in collaboration with humans. To deal with this type of multi-objective control problem, hierarchical least-square optimization techniques are often employed, defining multiple tasks as objective functions, listed in hierarchical manner. The solution to the Inverse Kinematics problem requires to plan and constantly update the Cartesian trajectories. However, we propose an extension to the classical Hierarchical Quadratic Programming formulation, that allows to optimally generate these trajectories at control level. This is achieved by augmenting the optimization variable, to include the Cartesian reference and allow for the formulation of an adaptive compliance controller, which retains an impedancelike behaviour under external disturbances, while switching to an admittance-like behavior when collaborating with a human. The effectiveness of this approach is tested using a 7-DoF Franka Emika Panda manipulator in three different collaborative scenarios.
Tassi et al. (Sun,) studied this question.