Model-Based Sliding Mode Control for a Robot With SMA Actuators

ABSTRACT This paper presents a model-based sliding mode control law for a planar three-degree-of-freedom robot arm actuated by two rotary Shape Memory Alloy (SMA) actuat ors and a servomotor. The SMA actuators use a combination of SMA wires and pulleys to produce rotational motion. A model of the robot is developed which combines robot equations of motion with the SMA wire heat convection, constitutive law, and phase transformation equations. Two second-order sliding surfaces are defined leading to derivation of asymptotically stable co ntrol laws within the actuation region of the SMA wires. Outside the actuation region, constant inputs are used based on the one-way nature of the SMA actuators. The control law is shown to be effective in several simulations for both set point and trajectory tracking of the robot. Introduction Shape Memory Alloy (SMA) actuators have certain advantages that makes them suitable for robotics applications [1-2] including high power to mass ratio, lack of frictional parts, silence, and simplicity of their mechanisms. However, precise motion control, speed, and efficiency of these actuators have remained problematic. Control difficulties generally arise from large uncertainties in the macro-model of the actuator and delays in response due to dependency of the actuation on heating and cooling of the material. Considerable research for modeling the microscopic and macroscopic behavior of shape memory alloys has been performed in past forty yea rs. Since the mechanical behavior of shape memory alloys is closely related to microscopic phase transformation (between Martensite and Austenite phases), constitutive relatio n are ot merely stress-strain based andmustinclude phase transformation and heat transfer characteristics [3-5]. Mre recently researchers have developed Preisach model ing met h ods ad accunte fr bt maj r and mnohysteresis loops to overcome precision control difficulties associated with SMA actuators [6]. In the controls area, researchers have explored linear controllers as well as Pulse Wid th Modulatio n, optimal co rol, fuzzy logic, and variable structu re and sl id ng mode control a poaches [7-15]. Amothese sl id g mode cont ro lhas sh w p omi sng resu because of significant parameter uncertainties in SMA models. In this work, we derive present an asymptotically stable sliding mode control law for an in-house three-link planar robot arm actuated by a combination of two bias type SMA actuators and a servomotor. The control law is based on a model of the robot that includes coupled robot equations of motion and SMA constitutive law, heat convection, and phase transformation. Two second-order sliding mode surfaces are defined leading to derivation of a control law which guarantees asymptotic stability when the SMA actuators are within the actuation region defined based on the alloy’s stress and temperature. Simulations are performed to show that the control law is able to accurately position the robot in both set point and trajectory tracking cases.