Modeling and Validation of Soft Robotic Snake Locomotion
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Modeling and Validation of Soft Robotic Snake Locomotion Dimuthu D. Arachchige1, Yue Chen2, and Isuru S. Godage1 Abstract— Snakes are a remarkable evolutionary success story. Many snake-inspired robots have been proposed over the years. Soft robotic snakes (SRS) with their continuous and smooth bending capability better mimic their biological counterparts’ unique characteristics. Prior SRSs are limited to planar operation with a limited number of planar gaits. We propose a novel SRS with spatial bending and investigate snake locomotion gaits beyond the capabilities of the state-of-the-art systems. We derive a complete floating-base kinematic model of the robot and use the model to derive jointspace trajectories Fig. 1: (A) The proposed Soft robotic snake (SRS) prototype, for serpentine and inward/outward rolling locomotion gaits. (B) Replicating rolling locomotion, and (C) Replicating serpentine The locomotion gaits for the proposed SRS are experimentally locomotion. validated under varying frequency and amplitude of gait cycles. The results qualitatively and quantitatively validate the SRS ability to leverage spatial bending to achieve locomotion gaits not possible with current SRS. locomotion. RRS, with few rigid links, limits the robot from achieving the smooth bending observed in snakes and, I. INTRODUCTION therefore, can affect locomotion. On the other hand, soft Snakes are highly capable animals with a wide range robotic snakes (SRS), constructed mainly from fluidic muscle of habitats, including hostile deserts, dense tropical forests, actuator-powered bodies, can better leverage smooth bending and uninhabitable marshes. One key feature that makes to imitate snake body movements. However, the latest SRS snakes unique in their ability to navigate in different terrains prototypes are limited to planar bending deformation, limit- using various locomotion gaits is supported by their long, ing the number of gaits they can demonstrate. In addition, high degrees of freedom (DoF) slender bodies. The body’s snakes use differential friction property of their skin to continuous and smooth bending structure enables snakes generate locomotion in planar gaits such as serpentine gait. to overcome numerous environmental challenges such as Noting the absence of such quality in current SRS, it is climbing, swimming despite having no sophisticated ap- extremely challenging to propel robots solely via planar pendages such as limbs. Their high DoF body can generate locomotion gaits. Consequently, SRSs rely on wheels to a range of locomotion gaits such as lateral undulation, circumvent uniform friction and generate locomotion [10], rectilinear movement, sidewinding, concertina movement. [11]. Thus, we posit that it is essential to exploit the out-of- Snake-like robots can harness this traversability in different plane deformation (spatial bending) to replicate locomotion and challenging terrains in applications such as inspection gaits such as rolling and sidewinding. The SRS reported tasks, reconnaissance, search, and rescue operations. Their in [9], [12] generates serpentine locomotion but utilizes small cross-section to length ratio allows them to gain wheeled bases to generate friction anisotropy necessary for access through tight spaces, little narrow openings (i.e., movement. The ‘WPI SRS’ [13] reported 10-fold locomotion sewage lines), and perform assigned operations. Robotics speed increase than the previous version [8]. The SRS arXiv:2010.11476v1 [cs.RO] 22 Oct 2020 have developed various snake robot prototypes [1]–[10] to presented in [14] and [15] is self-contained with integrated meet the aforementioned application challenges. sensing and feedback control. It improves the accuracy of dynamic undulatory locomotion. We propose a novel SRS A. Prior Work with spatial bending capabilities to address these limitations. Prior work on snake robots mainly evolved with modular B. Contribution rigid robots [1], [2], [5]–[7]. Rigid robotic snakes (RRS) use The main contributions of this work are (a) propose jointed rigid links to achieve bending motion and generate a novel SRS with spatial bending capability, (b) derive 1Dimuthu D. Arachchige and Isuru S. Godage are with School of Comput- complete floating base kinematic model, (c) derive jointspace ing, DePaul University, Chicago, IL, 60604. [email protected] trajectories of serpentine, inward rolling, and outward rolling 2Yue Chen is with the Department of Mechanical Engineering, University snake locomotion gaits, (d) experimentally validate the said of Arkansas Fayetteville, AR, 72701. locomotion gaits for a range of pressure-frequency combina- This work supported in part by the National Science Foundation grants IIS- tions on the propose SRS, (e) demonstrate the need for spatial 1718755 and and IIS-2008797 and UARK Chancellor’s Fund for Innovation and Collaboration. bending to overcome the limitations of friction anisotropy This paper has been submitted to IEEE International Conference on Robotics present in practical SRS. The experimental results show that and Automation 2021. SRS can successfully track the spatial shape trajectories for Fig. 3: Trajectory sampling at different time instances within a gait cycle for (a) serpentine gait and (b) outward rolling gait. B. Kinematic Model Consider the schematic of any ith module (i 2 f1;2;3g) of Fig. 2: A schematic of the SRS and a schematic of a single section. the SRS, as shown in Fig. 2-a. It depicts three mechanically identical variable length actuators (PMAs) with an unac- tuated length Li0 2 R and length change li j (t) 2 R, where all the gaits. This is the first SRS to utilize spatial bending j 2 f1;2;3g is the actuator index, and t is the time. Hence, capability and demonstrate meaningful locomotion (using the length of an actuator at any time is Li j = Li0 +li j(t). The inward/outward rolling gait) without wheels and utilizing the kinematic model of the proposed SRS can be formulated friction forces generated by skin-ground interactions. by extending the modal kinematics proposed by Godage et al. in [17]. Let the joint space vector of any ith soft robot T module be qi = [li1 (t); li2; li3 (t)] . Utilizing the results from II. SYSTEM MODEL [17], we can derive the homogeneous transformation matrix (HTM) at any point along the neutral axis of the ith soft A. Prototype Description 3 module, Ti 2 SE , as Fig. 1 shows the prototype of the proposed SRS. It is R (q ;x ) p (q ;x ) R (s ) p (d ) T (q ;x ) = i i i i i i z i x i (1) made of three serially attached soft bending modules (or i i i 0 1 0 1 sections). They are powered by McKibben type extending 3 3 mode pneumatic muscle actuators (PMA). These actuators where Ri 2 SO is the rotational matrix, pi 2 R is the proportionally extend the body to supplied pneumatic pres- position vector xi 2 [0;1] is a scalar to define points along sure up to 4 bars. In a single soft module, 3 PMAs are the soft module with 0, and 1 denotes the base and the p tip, and I3 is the rank 3 identity matrix. In addition to the assembled at 3 separation from each other to ensure sym- metric spatial bending and facilitate room to route pneumatic previous results in [17], note that we introduce two HTMs 3 supply lines within the module for a streamlined physical with Rz 2 SO is the rotation matrix about the +Z axis, and 3 0 profile required for a slender snake-like body. Each PMA px 2 R is the position offset along the +Z of Oi where has an unactuated length, Li0=0.15 m, and can extend by si 2 [0;2p]. 3 0.065 m at 4 bar pressure. Rigid 3D printed mounting frames Utilizing (1) with a floating coordinate system, Tb 2 SE , (made of ABS thermoplastic) are used to mount PMAs the complete kinematic model along the body of the snake at ri=0.0125 m from the centerline of soft modules (Fig. robot (Fig. 2-b) is given by 3 1). Similarly, laser-cut plastic constrainer plates of ri and 0.0025 m thickness are used along the soft modules’ length T(qb;q;x) = Tb (qb)∏Ti (qi;xi) i=1 to maintain PMAs parallel to soft modules’ central axis with R(q ;q;x) p(q ;q;x) a r clearance from the central axis. The constrainer plates = b b (2) i 0 1 also provide structural strength for this long and slender SRS to maintain its structural integrity during locomotion where qb = [xb;yb;zb;a;b;g] are the parameters of the float- and generate reaction forces required for locomotion. All ing coordinate system with [xb;yb;zb] denote the translation actuators are bundled within the soft module as a single and [a;b;g] denote the XYZ Euler angle offset of the base of unit, similar to the continuum sections reported in [16]. The module 1, i.e., the origin of the robot coordinate frame, with 9 pressure differential among PMAs of a soft module causes respect to fOg. The composite vector q = [q1;q2;;q3] 2 R the module to bend in any direction or extend axially. Thus and x = [0;3] 2 R. we can control the bends synchronously in order to generate various types of robot locomotion gaits. Soft modules are III. TRAJECTORY GENERATION p then connected via the mounting frames at a 3 offset to each In this work, we consider serpentine, inward rolling, other to create the SRS (Fig. 1). Finally, the SRS is wrapped and outward rolling locomotion gaits, which are cyclic in with rubber skin, and without the pneumatic supply lines, it nature. We can mathematically model these gaits associated weighs close to 0.3 kg. with different locomotion gaits to generate the taskspace point along the curve. We then derive a local coordinate frame with respect to the inertial frame at those points.