  A key challenge to ensuring the rapid transition of robotic systems from the
industrial sector to more ubiquitous applications is the development of
algorithms that can guarantee safe operation while in close proximity to
humans. Motion planning and control methods, for instance, must be able to
certify safety while operating in real-time in arbitrary environments and in
the presence of model uncertainty. This paper proposes Wrench Analysis for
Inertial Transport using Reachability (WAITR), a certifiably safe motion
planning and control framework for serial link manipulators that manipulate
unsecured objects in arbitrary environments. WAITR uses reachability analysis
to construct over-approximations of the contact wrench applied to unsecured
objects, which captures uncertainty in the manipulator dynamics, the object
dynamics, and contact parameters such as the coefficient of friction. An
optimization problem formulation is presented that can be solved in real-time
to generate provably-safe motions for manipulating the unsecured objects. This
paper illustrates that WAITR outperforms state of the art methods in a variety
of simulation experiments and demonstrates its performance in the real-world.
