With no initial angular momentum an ordinary house cat is capable of flipping over onto its feet in mid-air and landing safely after a fall. As the field of robotics advances and robots become more dynamic, control algorithms for landing safely from a long, intended fall will become more necessary. Here we present an algorithm that leverages nonholonomic trajectory planning inspired by the falling cat to orient an articulated robot through configuration changes to achieve a pose that reduces the impact at landing. The calculated impact pose results in minimal loss of energy through rolling, while maximizing the rolling time. In addition to orienting and rolling, our controller guides the system to behave like a damped spring- mass system to reduce the magnitude of contact forces. Our framework is general and is applicable to systems that can be modeled as a connected tree of rigid bodies. We illustrate the feasibility of the algorithm through simulation and physical experiments with a planar three-link robot.