Equilibrium Postural Control of a Spatial Underactuated Robot Based on Angular Momentum

The spatial underactuated robot, which consists of two links moving in 3D space, serves as a simplified model for human postural control. The robot is supported at a single point, with 2 degrees of freedom (DoF) underactuated at the ankle joint and 2-DoF actuated at the hip joint. This letter proposes an angular momentum-based feedback controller for the robot. The controller can locally stabilize the robot to a given equilibrium point and enable transitions between different equilibrium points. Firstly, this letter extends the angular momentum model from planar to 3D space, revealing that the robot's balance behavior is determined by eight key parameters closely related to the choice of state variables. This letter analyzes the impact of these parameters on the controllability of the angular momentum model. Secondly, this letter provides analytical expressions for the control gain parameters using the pole placement method. Finally, this letter identifies the equilibrium points where the controller may encounter singularities and demonstrates through simulations that the controller can effectively stabilize the robot to a given equilibrium point and enable transitions between different equilibrium points while maintaining balance.