  Robots usually establish contacts at rigid surfaces with near-zero relative
velocities. Otherwise, impact-induced energy propagates in the robot's linkage
and may cause irreversible damage to the hardware. Moreover, abrupt changes in
task-space contact velocity and peak impact forces also result in abrupt
changes in robot joint velocities and torques; which can compromise
controllers' stability, especially for those based on smooth models. In
reality, several tasks would require establishing contact with moderately high
velocity. We propose to enhance task-space multi-objective controllers
formulated as a quadratic program to be resilient to frictional impacts in
three dimensions. We devise new constraints and reformulate the usual ones to
be robust to the abrupt joint state changes mentioned earlier. The impact event
becomes a controlled process once the optimal control search space is aware of:
(1) the hardware-affordable impact bounds and (2) analytically-computed
feasible set (polyhedra) that constrain post-impact critical states. Prior to
and nearby the targeted contact spot, we assume, at each control cycle, that
the impact will occur at the next iteration. This somewhat one-step preview
makes our controller robust to impact time and location. To assess our
approach, we experimented its resilience to moderate impacts with the Panda
manipulator and achieved swift grabbing tasks with the HRP-4 humanoid robot.
