  In recent years, impressive results have been achieved in robotic
manipulation. While many efforts focus on generating collision-free reference
signals, few allow safe contact between the robot bodies and the environment.
However, in human's daily manipulation, contact between arms and obstacles is
prevalent and even necessary. This paper investigates the benefit of allowing
safe contact during robotic manipulation and advocates generating and tracking
compliance reference signals in both operational and null spaces. In addition,
to optimize the collision-allowed trajectories, we present a hybrid solver that
integrates sampling- and gradient-based approaches. We evaluate the proposed
method on a goal-reaching task in five simulated and real-world environments
with different collisional conditions. We show that allowing safe contact
improves goal-reaching efficiency and provides feasible solutions in highly
collisional scenarios where collision-free constraints cannot be enforced.
Moreover, we demonstrate that planning in null space, in addition to
operational space, improves trajectory safety.
