Mechatronics 46 (2017) 154–167 Contents lists available at ScienceDirect Mechatronics journal homepage: www.elsevier.com/locate/mechatronics An iteratively optimized resolution to hyper redundancy for dissimilarly doped compliant IPMC actuators  Ritwik Chattaraj a,∗ , Siladitya Khan b , Aritra Dasgupta c , Gautam Gare d , Debabrata Chatterjee e , Subhasis Bhaumik a a School of Mechatronics and Robotics, Indian Institute of Engineering Science and Technology, Shibpur 711103 Howrah, India b Department of Applied Electronics and Instrumentation Engineering, RCC Institute of Information Technology, Kolkata 700015, India c Department of Electronics and Communication Engineering, National Institute of Technology, Durgapur 713209, India d Department of Electronics and Communication Engineering, BMS College of Engineering, Bangalore 560019, India e Chemistry & Biomimetics Group, CSIR-CMERI-Durgapur, Burdwan 713209, India a r t i c l e i n f o Article history: Received 6 January 2017 Revised 22 June 2017 Accepted 3 August 2017 Keywords: Ionic polymer metal composite Hyper-redundancy Cyclic coordinate descent Ionic dopants a b s t r a c t Soft-robotics is gradually emerging as one of the promising fields of research and innovation. Owing to the blend of material-chemistry and conventional mechanics, complex motions have been successfully generated by flexible polymeric composites that act upon external activation stimuli. However, lack of ro- bust deterministic models which can command reliable actuator performance, hinder their widespread deployments in diverse paradigms. The present article seeks to address the argument by modelling Ionic Polymer Metal Composites (IPMC) as multi-segmented chains of connected rigid bodies. A Cyclic- Coordinate-Descent (CCD) based Inverse Kinematic solver is employed to resolve the redundancy, by min- imizing an objective function in joint space at gradual iterative steps. The algorithm is validated for its ability to model dissimilarly doped polymeric curvatures bearing distinct spatial postures. The 2-D shape estimation problem is addressed to generate patterns akin to original IPMCs for deployment on potential applications that anticipate a foresight of actuator geometry. © 2017 Elsevier Ltd. All rights reserved. 1. Introduction Robotic designs have often sought inspiration from nature, to build mechanisms targeted at bridging the gap between machines and humans. The emergence of ‘Soft Robotics’ has ensured arti- ficially designed systems to demonstrate agility, compliance and adaptability to perform various operational manoeuvres. Electro- active Polymer Actuators (EAP) like Ionic Polymer Metal Compos- ites (IPMC) possesses a deformable structure, one apt to emulate the elastic rheology of natural body articulations. Their close affin- ity to organic poly-electrolytes like fibrous proteins and collagens have earned them the epithet of ‘Artificial Muscles’. The IPMC strip is constituted by a thin ion-exchange membrane composed primarily of polymers like Nafion/Flemion, impregnated with micro-filmic depositions of a noble metal (Pt, Ag). A volt- age gradient across the metal-polymer substrate induces a steady movement of hydrated cations and water molecules, that are re-  This paper was recommended for publication by Associate Editor Garrett M. Clayton. ∗ Corresponding author. E-mail address: ritwik.chattaraj@gmail.com (R. Chattaraj). sponsible for deflection of the actuator from its neutral state [1–2]. The ionic groups present within the polymer backbone form hy- drophilic clusters, which are regions of accumulation of polar sol- vents and mobile cations. The non-polar fragments of the polymer lying in the vicinity of their polar counterparts enable ion and sol- vent transport that is necessary for generating desired actuations [3]. Fig. 1 illustrates the bi-directional actuated state of an IPMC along with its operational ion-exchange mechanism under the in- fluence of a low activation potential. Application of a gradient of electric potential across the metallic plates is seen to gener- ate a movement of solvated mobile cations towards the negatively charged electrodes. The cationic drift generates a simultaneous swelling and shrinkage phenomenon at the opposite end, yielding a substantial deflection of the actuator tri-layer. The IPMCs have been exploited for diverse applications on ac- count of their light weight, marked miniaturizations and ability to generate large deviations upon meagre actuation [4–5]. However lack of simplistic modelling methodologies, order complexities and model uncertainties hinder their use as a reliable actuator. The growing emergence of IPMC applications have raised de- mands for an accurate as well as practicable model which is po- http://dx.doi.org/10.1016/j.mechatronics.2017.08.004 0957-4158/© 2017 Elsevier Ltd. All rights reserved.