This paper presents the design of a four degree-of-freedom (DoF) spatial tail and demonstrates the dynamic stabilization of a bipedal robotic platform through a hardware-in-loop simulation. The proposed tail design features three active revolute joints with an active prismatic joint, the latter of which provides a variable moment of inertia. Real-time experimental results validate the derived mathematical model when compared to simulated reactive moment results, both obtained while executing a pre-determined trajectory. A 4-DoF tail prototype was constructed and the tail dynamics, in terms of reactive force and moments, were validated using a 6-axis load cell. The paper also presents a case study where a zero moment point (ZMP) placement-based trajectory planner, along with a model-based controller, was developed in order for the tail to stabilize a simulated unstable biped robot. The case study also demonstrates the capability of the motion planner and controller in reducing the system's kinetic energy during periods of instability by maintaining ZMP within the support polygon of the host biped robot. Both experimental and simulation results show an improvement in the tail-generated reactive moments for robot stabilization through the inclusion of prismatic motion while executing complex trajectories.
Keywords: ZMP; dynamic stabilization; robotic tail; variable inertia.