Pid Sliding Mode Control of Prolate Flexible Pneumatic Actuators

The inherent compliance, high power-density, and musclelike properties of soft actuators are especially attractive and useful in many applications, including robotics. In comparison to classical/modern control approaches, model-based control techniques, e.g., sliding mode control (SMC), applied to flexible fluidic actuators (FFAs) offer significant performance advantages and are considered to be state-of-the-art. Improvements in position tracking are possible using nonlinear control approaches that offer enhanced performance for common applications such as tracking of sinusoidal trajectories at high frequencies. This paper introduces a SMC approach that increases the tracking capabilities of prolate flexible pneumatic actuators (PFPAs). A model-based proportional, integral, derivative sliding mode control (PIDSMC) approach designed for position control of PFPAs is proposed. SMC and PIDSMC systems are implemented on low-cost open-source controls hardware and tested for tracking sinusoidal trajectories at frequencies of 0.5 Hz and 1.0 Hz with an amplitude of 8.255 mm and an offset of 12.7 mm. The PIDSMC approach reduced the maximum tracking error by 20.0%, mean error by 18.6%, and root-mean-square error by 10.5% for a 1 Hz sinusoidal trajectory and by 8.7%, 14.7%, and 3.8%, respectively, for a 0.5 Hz sinusoidal trajectory. These reductions in tracking errors demonstrate performance advantages of the PIDSMC over conventional sliding mode position controllers. INTRODUCTION A prolate flexible pneumatic actuator (PFPA) is a tube of hyperelastic material within a sleeve of braided polymer. When pressurized with compressed air, the composite tube inflates circumferentially and contracts longitudinally resulting in a force and displacement that is analogous to muscle [1]. These types of actuators are sometimes called pneumatic artificial muscles (or McKibben actuators), where a flexible fluidic actuator (FFA) describes the actuation type and prolate identifies the geometric aspect ratio of the device [2]. This paper presents the motivation and background to inspire a new class of controlled actuators for robotics and many other applications. PFPAs offer unrivaled power density, with values reported from 5 10 kW/kg [1], [3]. Moreover, they can achieve high forces at relatively low pressures that are typically available in labs, schools, and hospitals. PFPAs are controllable nonlinear springs, i.e., their output force is both pressure and position dependent. This property makes them ideal for biologically-inspired applications, mobile robots, and human assistive devices (prosthetics and orthotics) [4]. This paper sets the stage for improvements in motion control for these applications. BACKGROUND PFPAs were modeled by describing the change in enthalpy in the control volume [5], [2]. Using this approach Henry Paynter demonstrated accurate open-loop control with experimentally determined parameters [6]. Applications of this work include vehicle suspensions and engine mount vibration dampening [7]. Caldwell illustrated that closed-loop control could be achieved using discrete linear feedback control theory [8]. Model-based nonlinear control techniques have proven to be practical and superior in many cases to linear 1 Copyright c © 2016 by ASME control theory for pneumatic and highly nonlinear motion control applications. Sliding mode control (SMC) has been a topic of substantial research, especially in applied fluid power applications such as the motion control of FFAs. SMC approaches have seen many successes due to their ability to mathematically converge the error dynamics to zero over a given trajectory and implement high speed digital switching that enables powerful and robust tracking behavior [9]. For example, Comber et al. successfully applied a sliding mode position controller on a pneumatic five degree-of-freedom (DOF) magnetic resonance imaging (MRI) compatible steerable needle robot that exhibited needle tip errors of 0.78 mm or less, smaller than the voxel size of most MRI machines [10]. De Volder et al. illustrated positioning accuracy of +30 μm using a PI sliding mode controller [11]. Additionally, SMC systems have been implemented on hydraulic manipulators and chemically powered pneumatic FFAs [12], [13]. Some literature points out the limited performance using linear control theory for FFAs. Surdilovic et al. used linear control theory for motion control of flexible pneumatic actuators reporting a low position accuracy of 10 mm [14]. Linear control theory applied to the motion control of FFAs exhibited significant overshoot (12%) and was sensitive to noise, changes in supply pressure, temperature, and pipe length [8]. Undesirable steady-state errors were achieved using PI position control in antagonistic pairs of PFPAs, while also suggesting implementing nonlinear control methods [15]. In contrast, SMC approaches show substantial tracking improvements when compared to classical PID controllers for PFPAs [16]. Model-based control of soft actuators such as FFAs is of high interest in current research and was identified as one of the top scientific needs to realize human-robot interaction by 2015 Multi-Annual Roadmap for Robotics in Europe [17]. Lilly et al. developed and simulated a sliding mode angular position controller for an antagonistic pair of PFPAs and reported an approximate maximum tracking error of 1.15 deg with a 20 kg payload [18]. Comber et al. reported a maximum steady-state error of 0.015 mm using sliding mode position control of an oblate flexible pneumatic needle driver [19]. Nakamura et al. used modelbased force and position control of PFPAs reinforced with glass fibers [20]. Applications in multi-DOF systems further show the capabilities of model-based control techniques for prolate and oblate FFAs. A haptic device made using a delta robot driven by PFPAs implemented position and stiffness control with a PI computed torque and stiffness control method, resulting in an average maximum position error of 1.17 mm [21]. Sardellitti reported sliding mode torque and stiffness control for antagonistically actuated contractile flexible pneumatic pairs that experimentally confirmed excellent tracking, i.e., maximum error of 0.12 N-m and 0.06 N-m/rad for torque and stiffness tracking, respectively [22]. Ugurlu et al. described a novel torque and force control using feedback linearization to be implemented in future exoskeleton systems [23]. Driver and Shen tested a SMC system on a hybrid sleeve flexible pneumatic actuator that exhibited approximately a maximum of 3 deg tracking error when following a sinusoid wave at 1 Hz and an angular amplitude of 20 deg [24]. A maximum of 0.41 deg tracking error resulted when using a sliding mode position controller on an oblate rotary flexible pneumatic actuator [25]. Ivlev reported that along with the precise control of oblate rotary flexible pneumatic actuators in [25], the inherent compliance would be suitable for safe human-robot interaction, e.g., exoskeletons [26]. This paper is motivated by significant errors presented in the tracking of sinusoidal trajectories about their inflection points, especially at higher frequencies (1 Hz or greater) as illustrated by experimental results in [18], [24], and [16]. This paper presents a similar modeling approach taken by Comber et al. and Driver et al. and uses experimental methods to accurately model the highly nonlinear behavior of PFPAs [19], [24]. Furthermore, a sliding mode position controller is derived from the actuator and pressure dynamics while introducing proportional, integral, and derivative gain action to the SMC as done with the PI SMC in [11] and alternatively to the Fuzzy SMC presented in [27] to eliminate the errors about inflection points in sinusoidal tracking problems. MODELING Actuator Dynamics A diagram of the PFPA system being modeled and controlled is illustrated in Figure 1. The model of the system is shown in Figure 2 The length L of the PFPA is defined by