Session Y40: Robophysics: Physics Meets Robotics II

Managing and capturing the physics of robotic systems

Algorithmic and other theoretical analyses of robotic systems often use a discretized or otherwise idealized framework, while the real world is continuous-valued and noisy. This disconnect can make theoretical work sometimes problematic to apply successfully to real-world systems. One approach to bridging the separation can be to design hardware to take advantage of simple physical effects mechanically, in order to guide elements into a desired set of discrete attracting states. As a result, the system behavior can effectively approximate a discretized formalism, so that proofs based on an idealization remain directly relevant, while control can be made simpler. It is important to note, conversely, that such an approach does not make a physical instantiation unnecessary nor a purely theoretical treatment sufficient. Experiments with hardware in practice always reveal physical effects not originally accounted for in simulation or analytic modeling, which lead to unanticipated results and require nontrivial modifications to control algorithms in order to achieve desired outcomes. I will discuss these points in the context of swarm robotic systems recently developed at the Self-Organizing Systems Research Group at Harvard.   

Robot flow, clogging and jamming in confined spaces

We hypothesized that when a collection of robots operate in confined space, maximization of individual effort could negatively affect the collective performance by impeding the mobility of the individuals. To test our hypothesis, we built and programmed groups of 1-4 autonomous robotic diggers to construct a tunnel in a model cohesive soil. The robots' mobility, defined in terms of the residence time (T) required for a robot to move one body-length within the tunnel, was compared between groups of maximally active robots (mode 1), groups with different levels of activity between individuals (mode 2), and maximally active robots with a ``giving up'' behavior (mode 3), in which the robot ceased the attempt to excavate in a crowded tunnel. In small groups of two robots, T was $\sim $3 sec and did not depend on the mode of operation. However, an increase in the number of robots caused an increase in T which depended upon mode. The residence time in groups of four robots in mode 1 ($\sim $9 sec) significantly exceeded the residence time in mode 2 and 3 ($\sim $4 sec), indicating that crowding was causing slower movement of individuals, particularly under maximum effort (mode 1). We will use our robophysical studies to discover principles of collective construction in subterranean social animals.   

Legged-locomotion on inclined granular media

Animals traverse a wide variety of complex environments, including situations in which the ground beneath them can yield (e.g. dry granular media in desert dunes). Locomotion strategies that are effective on level granular media can fail when traversing a granular slope. Taking inspiration from successful legged-locomotors in sandy, uneven settings, we explore the ability of a small (15 cm long, 100 g), six-c-shaped legged robot to run uphill in a bed of ~1-mm-diameter poppy seeds, using an alternating tripod gait. Our fully automated experiments reveal that locomotor performance can depend sensitively on both environmental parameters such as the inclination angle and volume fraction of the substrate, and robot morphology and control parameters like leg shape, step frequency, and the friction between the feet of the robot and the substrate. We assess performance by measuring the average speed of the robot, and we find that the robot tends to perform better at higher step frequency and lower inclination angles, and that average speed decreases more rapidly with increasing angle for higher step frequency.   

Robotic and mathematical modeling reveal general principles of appendage control and coordination in terrestrial locomotion

The transition from aquatic to terrestrial life presented new challenges to early walkers, necessitating robust locomotion on complex, flowable substrates (e.g. sand, mud). Locomotion on such substrates is sensitive to limb morphology and kinematics. Although early walker morphologies are known, principles of appendage control remain elusive. To reveal limb control strategies that facilitated the invasion of land, we study both robotic and mathematical models. Robot experiments show that an active tail is critical for robust locomotion on granular media, enabling locomotion even with poor foot placement and limited ability to lift the body. Using a granular resistive force theory model, we construct connection vector fields that reveal how appendage coordination and terrain inclination impact locomotor performance. This model replicates experimental results, showing that moving limbs/tail in phase is most effective (suggesting a locomotor template). Varying limb trajectories and contacts, we find gaits for which tail use can be neutral or harmful, suggesting limb-tail coordination to be a nontrivial aspect of locomotion. Our findings show that robot experiments coupled with geometric mechanics provide a general framework to reveal principles of robust terrestrial locomotion.   

Compliant Synergies in Locomotion

Biological systems appear to have natural mechanisms that allow them to readily compensate for unexpected environmental variations when compared to their mechanical (i.e., robotic) counterparts. We hypothesize that the basis for this discrepancy is almost innate: what biology appears to be born with, built-in mechanisms for coordinating their many degrees of freedom, we struggle to ``program.'' We therefore look toward biology for inspiration. In particular, we are interested in kinematic synergies, low-dimensional representations that explicitly encode the underlying structure of how systems coordinate their internal degrees of freedom to achieve high-level tasks. In this work, we derive parametric representations of kinematic synergies and present a new compliant locomotion control framework that enables the parameters to be directly controlled in response to external disturbances.~ We present results of this framework implemented on two separate platforms, a snake-like and hexapod robot.~ Our results show that, using synergies, the locomotion control of these very different systems can be reduced to simple, extremely capable, and common forms, thus offering new insights into both robotic as well as biological locomotion in complex terrains.   

Instability and maneuverability of a multi-legged robot

Our previous study showed that a centipede like multi-legged robot composed of many modules, each of which has one pair of legs, produces body undulations through a supercritical Hopf bifurcation of walking in a straight line with parallel bodies when the gait speed increases over a critical value or when the body segment joint stiffness decreases below a critical value (Aoi et al., PRE 2013, featured by Nat Phys 2013). So far, it is unclear if centipedes actively produce or resist body undulations during their locomotion and the previous study discussed the underlying mechanism responsible for the body undulations in centipede locomotion based on the robot experimental results and dynamic analysis using s simplified physical model. Furthermore, centipedes produce agile locomotion despite many legs being in contact with the ground during their locomotion, which may impede their agile motions. The present study investigated the relationship between the instability of walking in a straight line and maneuverability of the robot using a quick turn task and some evaluation criteria for maneuverability.   

Are snakes particles or waves? Scattering of a limbless locomotor through a single slit

Droplets on vertically vibrated fluid surfaces can walk and diffract through a single slit by a pilot wave hydrodynamic interaction [Couder, 2006; Bush, 2015]. Inspired by the correspondence between emergent macroscale dynamics and phenomena in quantum systems, we tested if robotic snakes, which resemble wave packets, behave emergently like particles or waves when interacting with an obstacle. In lab experiments and numerical simulations we measured how a multi-module snake-like robot swam through a single slit. We controlled the snake undulation gait as a fixed serpenoid traveling wave pattern with varying amplitude and initial phase, and we examined the snake trajectory as it swam through a slit with width $d$. Robot trajectories were straight before interaction with the slit, then exited at different scattering angle $\theta$ after the interaction due to a complex interaction of the body wave with the slit. For fixed amplitude and large $d$, the snake passed through the slit with minimal interaction and $theta$ was $\approx 0$. For sufficiently small $d$, $\theta$ was finite and bimodally distributed, depending on the initial phase. For intermediate $d$, $\theta$ was sensitive to initial phase, and the width of the distribution of $\theta$ increased with decreasing $d$.   

Multi-terrain locomotor interactions in flying snakes

Arboreal snakes of the genus \textit{Chrysopelea} are the only known snakes to glide. To execute aerial locomotion, a snake uses one of several stereotyped jumps from a tree into the air, while simultaneously flattening its body into an aerodynamically favorable shape. Large amplitude traveling waves are propagated posteriorly during the stable glide, while landing involves body wrapping, passive body compression, and energy absorption through compliance in the landing substrate to dissipate the accumulated kinetic energy from the glide. In all of these locomotor events, from interacting with cylindrical branches, falling through the air, grasping compliant tree branches and leaves, to landing on solid ground, snakes appropriate the same body morphology and perhaps the same basic neural mechanisms. Here we discuss our use of computational models and animal experiments to understand how flying snakes interact with and locomote on and through multiple media, potentially providing principles for legless locomotor designs.   

Aerodynamic control with passively pitching wings

Flapping wings may pitch passively under aerodynamic and inertial loads. Such passive pitching is observed in flapping wing insect and robot flight. The effect of passive wing pitch on the control dynamics of flapping wing flight are unexplored. Here we demonstrate in simulation and experiment the critical role wing pitching plays in yaw control of a flapping wing robot. We study yaw torque generation by a flapping wing allowed to passively rotate in the pitch axis through a rotational spring. Yaw torque is generated through alternating fast and slow upstroke and and downstroke. Yaw torque sensitively depends on both the rotational spring force law and spring stiffness, and at a critical spring stiffness a bifurcation in the yaw torque control relationship occurs. Simulation and experiment reveal the dynamics of this bifurcation and demonstrate that anomalous yaw torque from passively pitching wings is the result of aerodynamic and inertial coupling between the pitching and stroke-plane dynamics.   

Crucial advantages of tail use in the evolution of vertebrate terrestrial locomotion.

In the invasion of terrestrial environment, the first tetrapods faced the challenge of locomotion on flowable substrates (e.g. sand and mud), sometimes oriented at inclines. Although the morphology of many early tetrapods is known, robotic studies have revealed that effective locomotion on these substrates also depends strongly upon kinematics; slight differences in movements of the same appendage can lead to success or failure. Using a model organism (the mudskipper) and a robotic physical model, we demonstrate how muscular tails provided critical locomotor advantages on granular substrates that the first invaders of land likely encountered. Mudskippers use their tails for additional propulsion with increasing frequency as the slope of the granular material increases, and the decline in locomotor performance with slope is shallower when the tail is used. Experiments with a robotic model of the mudskipper showed that, while the tail did not always provide a benefit to locomotion, use of the tail made the robot's performance more robust, achieving effective locomotion on a wider range of slopes, limb postures and foot placements. These results suggest that, rather than simply being an inert appendage, the tails of early tetrapods were vital to their first forays into terrestrial habitats.   

Mutually opposing forces during locomotion can eliminate the tradeoff between maneuverability and stability

A surprising feature of animal locomotion is that organisms typically produce substantial forces in directions other than what is necessary to move the animal through its environment, such as perpendicular to, or counter to, the direction of travel. The effect of these forces has been difficult to observe because they are often mutually opposing and therefore cancel out. Using a combination of robotic physical modeling, computational modeling, and biological experiments, we discovered that these forces serve an important role: to simplify and enhance the control of locomotion. Specifically, we examined a well-suited model system, the glass knifefish Eigenmannia virescens, which produces mutually opposing forces during a hovering behavior. By systematically varying the locomotor parameters of our biomimetic robot, and measuring the resulting forces and kinematics, we demonstrated that the production and differential control of mutually opposing forces is a strategy that generates passive stabilization while simultaneously enhancing maneuverability. Mutually opposing forces during locomotion are widespread across animal taxa, and these results indicate that such forces can eliminate the tradeoff between stability and maneuverability, thereby simplifying robotic and neural control.   

A robotic platform for studying sea lion thrust production

California Sea Lions are agile swimmers and, uniquely, use their foreflippers (rather than hind flipper undulation) to generate thrust. Recently, a sea lion flipper from a deceased subject was externally scanned in high detail for fluid dynamics research. The flipper's geometry is used in this work to build an accurate scaled down flipper model (approximately 68\% of the full size span). The flipper model is placed in a water flume to obtain lift and drag force measurements. The unique trailing edge features are then examined for their effect on the measured forces by comparing to similar flipper models with a smooth trailing edge, sinusoidal trailing edge, and a saw-tooth trailing edge. Additionally, a robotic flipper is being designed and built, replicating the sea lion foreflipper anatomical structure. The robot is actuated by a set of servo motors and replicates the sea lion flipper clap motion based on previously extracted kinematics. The flipper tip speed is designed to match typical full scale Reynolds numbers for an acceleration from rest maneuver. The model is tested in the water flume as well to obtain the forces and flow structures during the thrust production phase of the flipper motion.   

Controlled locomotion of robots driven by a vibrating surface

Robots typically derive their powers of movement from onboard actuators and power sources, but other scenarios are possible where the external environment provides part or all of the necessary forcing and control. I will discuss details of a system where the “robots” are just planar solid objects and the requisite driving forces originate from frictional sliding-interactions with a periodically oscillated and nominally horizontal surface. For the robots to move, the temporal symmetry of the frictional forces must be broken, which is achieved here by modulating the normal force using vertical acceleration of the surface. Independent of the initial conditions and vibration waveform, a sliding locomotor reaches a unique velocity limit cycle at a given position. Its resulting motion can be described in terms of velocity fields which specify the robot’s cycle-averaged velocity as a function of position. Velocity fields with non-zero spatial divergence can be generated by combining translational and rotational surface motions; this allows the simultaneous and open-loop collection, dispersal, and transport of multiple robots. Fields and field sequences can simultaneously move multiple robots between arbitrary positions and, potentially, along arbitrary trajectories.   

Dynamical states in the sensorimotor loop of a rolling robot

We investigate the closed sensorimotor loop of a simple rolling robot as a dynamical system. Using the LpzRobots simulation package \footnote{R. Der $\&$ G. Martius, \textbf{The Playful Machine: Theoretical Foundation and Practical Realization of Self-Organizing Robots}, Springer Science $\&$ Business Media, Vol. 15, 2012}, we construct robots with cylindrical body, controlled by a single proprioceptual neuron with a time dependent threshold. Despite its simplicity, we obtain a rich set of rolling modes, as a result of the self-organizing processes arising through the feedback within the sensorimotor loop. These rolling modes are robust against environmental noise, since they correspond to stable limit cycle attractors. However, for certain parameters they also allow for explorative behavior via internal noise induced switching. Furthermore, we also find a region of parameters in which the motion is fully embodied, where, in engineering terms, the engine powering the motion of the robot is turned on dynamically through the feedback of its very motion \footnote{B. S\'andor, T. Jahn, L. Martin $\&$ C. Gros, \textbf{The sensorimotor loop as a dynamical system: How regular motion primitives may emerge from self-organized limit cycles}, to be published, 2015}.   

Vibration Propagation in Spider Webs

Due to their poor eyesight, spiders rely on web vibrations for situational awareness. Web-borne vibrations are used to determine the location of prey, predators, and potential mates. The influence of web geometry and composition on web vibrations is important for understanding spider’s behavior and ecology. Past studies on web vibrations have experimentally measured the frequency response of web geometries by removing threads from existing webs. The full influence of web structure and tension distribution on vibration transmission; however, has not been addressed in prior work. We have constructed physical artificial webs and computer models to better understand the effect of web structure on vibration transmission. These models provide insight into the propagation of vibrations through the webs, the frequency response of the bare web, and the influence of the spider's mass and stiffness on the vibration transmission patterns.   

Proprioceptive Actuation Design for Dynamic Legged locomotion

Designing an actuator system for highly-dynamic legged locomotion exhibited by animals has been one of the grand challenges in robotics research. Conventional actuators designed for manufacturing applications have difficulty satisfying challenging requirements for high-speed locomotion, such as the need for high torque density and the ability to manage dynamic physical interactions. It is critical to introduce a new actuator design paradigm and provide guidelines for its incorporation in future mobile robots for research and industry. To this end, we suggest a paradigm called proprioceptive actuation, which enables highly- dynamic operation in legged machines. Proprioceptive actuation uses collocated force control at the joints to effectively control contact interactions at the feet under dynamic conditions. In the realm of legged machines, this paradigm provides a unique combination of high torque density, high-bandwidth force control, and the ability to mitigate impacts through backdrivability. Results show that the proposed design provides an impact mitigation factor that is comparable to other quadruped designs with series springs to handle impact. The paradigm is shown to enable the MIT Cheetah to manage the application of contact forces during dynamic bounding, with results given down to contact times of 85ms and peak forces over 450N. As a result, the MIT Cheetah achieves high-speed 3D running up to 13mph and jumping over an 18-inch high obstacle.