  Physical reasoning is a core aspect of intelligence in animals and humans. A
central question is what model should be used as a basis for reasoning.
Existing work considered models ranging from intuitive physics and physical
simulators to contact dynamics models used in robotic manipulation and
locomotion. In this work we propose descriptions of physics which directly
allow us to leverage optimization methods for physical reasoning and sequential
manipulation planning. The proposed multi-physics formulation enables the
solver to mix various levels of abstraction and simplifications for different
objects and phases of the solution. As an essential ingredient, we propose a
specific parameterization of wrench exchange between object surfaces in a path
optimization framework, introducing the point-of-attack as decision variable.
We demonstrate the approach on various robot manipulation planning problems,
such as grasping a stick in order to push or lift another object to a target,
shifting and grasping a book from a shelve, and throwing an object to bounce
towards a target.
