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Soft robots, valued for their compliance and deformable nature, have demonstrated their outstanding abilities in complex environments. However, the nonlinear dynamics make it challenging to derive efficient locomotion patterns from analytical methods. This is largely due to the high computational cost associated with simulating soft-bodied models. Conversely, rigid-body models, such as those used in Gazebo, offer computational efficiency but cannot directly represent soft robots. We address these challenges by introducing customized Gazebo plugins that enable the simulation and analysis of soft robot locomotion dynamics. These plugins are complemented by a novel JointStiffnessPlugin, integrated with ROS services, for fine-tuning effort-controlled parameters. The system identification process is followed to match the simulation dynamics with the real soft robot to minimize the sim-to-real gap. Utilizing the proposed simulation framework and Bayesian Optimization, we derived a body-induced locomotion strategy that achieves enhanced efficiency. This strategy, relying solely on periodic spine bending and robot pose for forward propulsion, demonstrably reduces energy consumption compared to conventional gaits. Experimental results confirm a 42 % energy expenditure reduction relative to four-legged crawling. 

Fruit flies or Drosophila larvae exhibit a diverse range of locomotion gaits enabled by their soft, segmented bodies and intricate muscle arrangements. Their bodies, composed of multiple segments, are synchronously activated to propel forward through a combination of muscle elongation and contraction. Soft robotic systems, inspired by such biological marvels, face significant challenges in replicating these complex behaviors due to the intricate interplay between muscle activation, soft body dynamics, and frictional forces. To address these challenges, we propose a reduced-order model that captures the essential features of larval crawling. By modeling segments as a combination of prismatic and revolute joints, we can simulate the nonlinear motion resulting from muscle activation and body deformation. Our model demonstrates the potential of this approach to accurately describe larval movement, as validated by comparisons with actual larval trajectories. This research offers valuable insights into the design and control of soft robots and provides a framework for biologists to investigate the complex mechanisms of neuromuscular coordination in larvae. 

Soft robots hold significant potential in legged locomotion due to their inherent deformability, enabling enhanced adaptability to various environmental conditions and the generation of diverse locomotion gaits. While various soft robots have been proposed for terrestrial locomotion, research on dynamically-stable locomotion, such as trotting, with actuated soft bending limbs remains limited. We introduce a pneumatically-actuated soft quadruped featuring a soft body capable of a variety of dynamically-stable trotting locomotion. We utilize soft limb kinematics and parameterize fundamental limb locomotion to obtain quadrupedal locomotion trajectories for both linear and curvilinear motions. We also employ a physics-enabled dynamic model to optimize and evaluate trotting locomotion trajectories for dynamic stability. We further validate the stable locomotion trajectories through empirical experiments conducted on a soft quadruped prototype. The results demonstrate that the quadruped trots at a peak speed of 1.24 body lengths per second when traversing flat and uneven terrains, including slopes, cluttered areas, and naturalistic irregular surfaces. Furthermore, we compare the energy efficiency between trotting and crawling locomotion. The findings reveal that trotting is significantly more energy-efficient than crawling, with an average energy saving of up to 42%.Note to Practitioners—This paper was motivated by the challenge of achieving dynamically stable and efficient locomotion in soft quadrupeds. Many soft-legged robots are typically designed for statically stable, albeit inefficient and slow, locomotion gaits such as crawling. Our research aims to address this practical challenge of improving mobility in soft-legged robots. We develop a novel soft quadruped with pneumatically-actuated soft limbs that achieves efficient trotting that is 42% more energy-efficient than crawling. This work is particularly relevant for industries requiring adaptable and efficient navigation in environments, such as search and rescue, agricultural monitoring, and exploration. The development and optimization of trotting gaits through a physics-enabled dynamic model for dynamic stability provide a foundational framework for enhancing the adaptability and operational utility of soft robots. While our findings mark a significant step forward, challenges remain in deploying these locomotion strategies on autonomous untethered robots with onboard sensor feedback. Future research will focus on these areas, aiming to improve the practical deployment and robustness of soft robotic locomotive systems. 

Soft robots, due to their flexibility, adaptability, and gentle handling over rigid robots, have shown better potential in numerous applications requiring operating in constrained spaces. Most of the soft robotic prototypes are of a linear form that can be modeled as a curve in space and are found in manipulators and limbs of locomoting robots. Planar soft robots have been proposed recently that are modeled as a surface and deform in 3D. Research on planar soft robots has been less extensive due to the challenges associated with modeling surface deformations efficiently. We present a curve-parametric approach for the deformation modeling of planar soft robot modules. Along with the Bezier patch method to approximate the surface at 30 Hz. Experimental evaluations on a prototype were developed and tested to validate that the proposed model can reasonably approximate the planar robot boundaries, and the surface derived from it. 

Soft robots, known for their compliance and deformable nature, have emerged as a transformative field, giving rise to various prototypes and locomotion capabilities. Despite continued research efforts that have shown significant promise, the quest for energy-efficient mobility in soft-limbed robots remains relatively elusive. We introduce a discrete locomotion gait called “tumbling,” designed to conserve energy and implemented in a topologically symmetric soft-limbed robot. The incorporation of tumbling enhances the overall locomotive abilities of soft-limbed robots, offering advantages such as increased agility, adaptability, and the ability to correct orientation, which are essential for navigating non-engineered environments that include natural-like irregular terrains with obstacles. The principle behind tumbling locomotion involves a deliberate shift in the robot's center of gravity in the direction of motion, guided by the kinematics of its soft limbs. To validate this locomotion strategy, we developed a robot simulation model operating within a virtual environment that incorporates physics and contact interactions. After optimizing the tumbling locomotion strategy through simulations, we conducted experimental tests on a physical robot prototype. The experiments validate the effectiveness of the proposed tumbling gait. We conducted an energy cost analysis to compare the tumbling locomotion with the previously reported crawling gait of the robot. The results of this analysis demonstrate that tumbling represents an energy-efficient mode of locomotion for soft robots, saving up to 60% and 65% energy than crawling locomotion on flat and natural-like irregular terrains, respectively. 

When threatened by dangerous or harmful stimuli, animals engage in diverse forms of rapid escape behaviors. InDrosophilalarvae, one type of escape response involves C-shaped bending and lateral rolling followed by rapid forward crawling. The sensory circuitry that promotes larval escape has been extensively characterized; however, the motor programs underlying rolling are unknown. Here, we characterize the neuromuscular basis of rolling escape behavior. We used high-speed, volumetric, Swept Confocally Aligned Planar Excitation (SCAPE) microscopy to image muscle activity during larval rolling. Unlike sequential peristaltic muscle contractions that progress from segment to segment during forward and backward crawling, muscle activity progresses circumferentially during bending and rolling escape behavior. We propose that progression of muscular contraction around the larva’s circumference results in a transient misalignment between weight and the ground support forces, which generates a torque that induces stabilizing body rotation. Therefore, successive cycles of slight misalignment followed by reactive aligning rotation lead to continuous rolling motion. Supporting our biomechanical model, we found that disrupting the activity of muscle groups undergoing circumferential contraction progression leads to rolling defects. We use EM connectome data to identify premotor to motor connectivity patterns that could drive rolling behavior and perform neural silencing approaches to demonstrate the crucial role of a group of glutamatergic premotor neurons in rolling. Our data reveal body-wide muscle activity patterns and putative premotor circuit organization for execution of the rolling escape response. 

Soft robotic snakes (SRSs) have a unique combination of continuous and compliant properties that allow them to imitate the complex movements of biological snakes. Despite the previous attempts to develop SRSs, many have been limited to planar movements or use wheels to achieve locomotion, which restricts their ability to imitate the full range of biological snake movements. We propose a new design for the SRSs that is wheelless and powered by pneumatics, relying solely on spatial bending to achieve its movements. We derive a kinematic model of the proposed SRS and utilize it to achieve two snake locomotion trajectories, namely side winding and helical rolling. These movements are experimentally evaluated under different gait parameters on our SRS prototype. The results demonstrate that the SRS can successfully mimic the proposed spatial locomotion trajectories. This is a significant improvement over the previous designs, which were either limited to planar movements or relied on wheels for locomotion. The ability of the SRS to effectively mimic the complex movements of biological snakes opens up new possibilities for its use in various applications. 

Soft robotic snakes made of compliant materials can continuously deform their bodies and, therefore, mimic the biological snakes' flexible and agile locomotion gaits better than their rigid-bodied counterparts. Without wheel support, to date, soft robotic snakes are limited to emulating planar locomotion gaits, which are derived via kinematic modeling and tested on robotic prototypes. Given that the snake locomotion results from the reaction forces due to the distributed contact between their skin and the ground, it is essential to investigate the locomotion gaits through efficient dynamic models capable of accommodating distributed contact forces. We present a complete spatial dynamic model that utilizes a floating-base kinematic model with distributed contact dynamics for a pneumatically powered soft robotic snake. We numerically evaluate the feasibility of the planar and spatial rolling gaits utilizing the proposed model and experimentally validate the corresponding locomotion gait trajectories on a soft robotic snake prototype. We qualitatively and quantitatively compare the numerical and experimental results which confirm the validity of the proposed dynamic model. 

Soft robotics holds tremendous potential for various applications, especially in unstructured environments such as search and rescue operations. However, the lack of autonomy and teleoperability, limited capabilities, absence of gait diversity and real-time control, and onboard sensors to sense the surroundings are some of the common issues with soft-limbed robots. To overcome these limitations, we propose a spatially symmetric, topologically-stable, soft-limbed tetrahedral robot that can perform multiple locomotion gaits. We introduce a kinematic model, derive locomotion trajectories for different gaits, and design a teleoperation mechanism to enable real-time human-robot collaboration. We use the kinematic model to map teleoperation inputs and ensure smooth transitions between gaits. Additionally, we leverage the passive compliance and natural stability of the robot for toppling and obstacle navigation. Through experimental tests, we demonstrate the robot's ability to tackle various locomotion challenges, adapt to different situations, and navigate obstructed environments via teleoperation.