Stabilization of underactuated planar acrobot based on motion-state constraints

• We present a control strategy based on motion-state constraints for a planar acrobot.
• The control strategy stabilizes the planar acrobot at a target position.
• An algorithm for solving an optimal target problem is proposed that incorporates the motion characteristics.
• The control strategy is easy to apply to underactuated multilink planar manipulators with a passive first joint.

An underactuated planar acrobot (UPA) is a two-link manipulator with a passive first joint. The control objective for a UPA in a horizontal plane is to move it from an initial position and stabilize it at a target position. Since a UPA is not small-time locally controllable, motion control is a big challenge. This paper presents a new control strategy based on constraints on the motion state. First, constraints on the angles and angular velocities of the two links are devised by integrating the dynamic equation of the UPA. Next, the state constraints are analyzed to discover the motion characteristics. Then, the optimal target position is obtained by solving a motion optimization problem that incorporates those characteristics. Finally, a control strategy based on the Lyapunov function method is devised to achieve the control objective. A numerical example demonstrates the validity of the control strategy.