Orienting in mid-air through configuration changes to achieve a rolling landing for reducing impact after a fall

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. I. INTRODUCTION When falling, an ordinary house cat has the remarkable ability to twist its body in mid-air to land on its feet. This behavior is made more extraordinary by the fact that the cat is able to do this without any initial angular velocity and using no external forces to orient itself. Despite the consid- erable advances in robotics, this feat of agility is beyond the capability of current hardware platforms. However, as articulated robots advance and become more dynamic, it will be necessary to have at least a modest ability to properly survive the impact of a fall. Here we present an algorithm that leverages nonholonomic trajectory planning inspired by the falling cat to orient an articulated robot by configuration changes to achieve a final pose that rolls and reduces the impact during landing. We define a pose as the combination of configuration (joint state) and orientation (attitude of the root body with respect to the inertial frame). Beyond orienting we also address the impact of landing, because, as the saying goes, "It's not the fall that kills you. It's the sudden stop at the end." The key word is sudden in this aphorism. The damage incurred by an impact with the ground is largely due to the magnitude of the impulse required to change the momentum of the falling body. Therefore, we suggest two strategies to reduce the detrimental effects of "the sudden stop at the end." First, perform a rolling action to reduce the change in momentum caused by the impact. Second, lengthen the duration of the impulse by acting like a damped spring-mass system, which decreases the magnitude of the impulse force at peak. To achieve these two goals on an articulated robot, we propose algorithms that compute the optimal impact pose and a set of joint stiffnesses to reduce the change in momentum and peak contact force during landing. In this work we provide a theoretical framework for find- ing an impact pose and joint stiffness that reduce the impact impulse, as well as the sequence of configurations to orient an articulated robot to the impact pose during falling. The theoretical framework is general and should be applicable to any system that can be modeled as a connected tree of rigid bodies. Next, we present an application of this framework to a planar three-link robot with implementation details. Finally, we present simulation and experimental results to show the feasibility of our control algorithm.