A Finite-Time State-Dependent Differential Riccati Equation Control Design for Closed-Loop SMA-Actuated Hip Joint

This paper presents the modeling and closed loop control of the shape-memory-alloy (SMA)-actuated hip joint of a flapping-wing flying robot (FWFR). Despite the lightweight legs/claw mechanism, a strong force of grasping is needed. The SMAs show high force delivery; however, it is difficult to control (position and temperature) the actuation due to the necessity of high currents for warming up, and time for cooling down process. This paper presents a state-dependent differential Riccati equation (SDDRE) controller taking into account the SMA dynamic and the actuator limits to control the leg/claw system. The use of nonlinear optimal control, specifically, the SDDRE, has been reported for the first time for bio-inspired leg/claw control of FWFR. The dynamics of the SMA actuators and on-off switching of the MOSFETs to provide current for the system demands switching in the design of the controller as a constraint for inputs which was considered in the design. Simulation and experimental results and analysis of different phases of heating of SMAs were discussed and resulted in satisfactory control performance.