Daniel I. Goldman

Juntao He, Baxi Chong, Zhaochen Xu et al.

Navigating rugged landscapes poses significant challenges for legged locomotion. Multi-legged robots (those with 6 and greater) offer a promising solution for such terrains, largely due to their inherent high static stability, resulting from a low center of mass and wide base of support. Such systems require minimal effort to maintain balance. Recent studies have shown that a linear controller, which modulates the vertical body undulation of a multi-legged robot in response to shifts in terrain roughness, can ensure reliable mobility on challenging terrains. However, the potential of a learning-based control framework that adjusts multiple parameters to address terrain heterogeneity remains underexplored. We posit that the development of an experimentally validated physics-based simulator for this robot can rapidly advance capabilities by allowing wide parameter space exploration. Here we develop a MuJoCo-based simulator tailored to this robotic platform and use the simulation to develop a reinforcement learning-based control framework that dynamically adjusts horizontal and vertical body undulation, and limb stepping in real-time. Our approach improves robot performance in simulation, laboratory experiments, and outdoor tests. Notably, our real-world experiments reveal that the learning-based controller achieves a 30\% to 50\% increase in speed compared to a linear controller, which only modulates vertical body waves. We hypothesize that the superior performance of the learning-based controller arises from its ability to adjust multiple parameters simultaneously, including limb stepping, horizontal body wave, and vertical body wave.

Kehinde O. Aina, Ram Avinery, Hui-Shun Kuan et al.

Social organisms which construct nests consisting of tunnels and chambers necessarily navigate confined and crowded conditions. Unlike low-density collectives like bird flocks and insect swarms, in which hydrodynamic and statistical phenomena dominate, the physics of glasses and supercooled fluids is important to understand clogging behaviors in high-density collectives. Our previous work revealed that fire ants flowing in confined tunnels utilize diverse behaviors like unequal workload distributions, spontaneous direction reversals, and limited interaction times to mitigate clogging and jamming and thus maintain functional flow; implementation of similar rules in a small robophysical swarm led to high performance through spontaneous dissolution of clogs and clusters. However, how the insects learn such behaviors, and how we can develop "task capable" active matter in such regimes, remains a challenge in part because interaction dynamics are dominated by local, time-consuming collisions and no single agent can guide the entire collective. Here, we hypothesized that effective flow and clog mitigation could emerge purely through local learning. We tasked small groups of robots with pellet excavation in a narrow tunnel, allowing them to modify reversal probabilities over time. Initially, robots had equal probabilities and clogs were common. Reversals improved flow. When reversal probabilities adapted via collisions and noisy tunnel length estimates, workload inequality and performance improved. Our robophysical study of an excavating swarm shows that, despite the seeming complexity and difficulty of the task, simple learning rules can mitigate or leverage unavoidable features in task-capable dense active matter, leading to hypotheses for dense biological and robotic swarms.

Kehinde O. Aina, Hosain Bagheri, Daniel I. Goldman

As robots are increasingly deployed to collaborate on tasks within shared workspaces and resources, the failure of an individual robot can critically affect the group's performance. This issue is particularly challenging when robots lack global information or direct communication, relying instead on social interaction for coordination and to complete their tasks. In this study, we propose a novel fault-tolerance technique leveraging physical contact interactions in multi-robot systems, specifically under conditions of limited sensing and spatial confinement. We introduce the "Active Contact Response" (ACR) method, where each robot modulates its behavior based on the likelihood of encountering an inoperative (faulty) robot. Active robots are capable of collectively repositioning stationary and faulty peers to reduce obstructions and maintain optimal group functionality. We implement our algorithm in a team of autonomous robots, equipped with contact-sensing and collision-tolerance capabilities, tasked with collectively excavating cohesive model pellets. Experimental results indicate that the ACR method significantly improves the system's recovery time from robot failures, enabling continued collective excavation with minimal performance degradation. Thus, this work demonstrates the potential of leveraging local, social, and physical interactions to enhance fault tolerance and coordination in multi-robot systems operating in constrained and extreme environments.

Zhaochen J. Xu, Juntao He, Delfin Aydan et al.

Multi-legged elongate robots hold promise for maneuvering through complex environments. Prior work has demonstrated that reliable locomotion can be achieved using open-loop body undulation and foot placement on rugose terrain. However, robust navigation through confined spaces remains challenging when body-environment contact is extensive and terrain rheology varies rapidly. To address this challenge, we develop a pair of tactile antennae for multi-legged robots that enable real-time sensing of surrounding geometry, modeling the morphology and function of biological centipede antennae. Each antenna features gradient compliance, with a stiff base and soft tip, allowing repeated deformation and elastic recovery. Robophysical experiments reveal a relationship between continuous antenna curvature and contact force, leading to a simplified mapping from antenna deformation to inferred discrete collision states. We incorporate this mapping into a controller that selects among a set of locomotor maneuvers based on the inferred collision state. Experiments in obstacle-rich and confined environments demonstrate that tactile feedback enables reliable steering and allows the robot to recover from near-stuck conditions without requiring global environmental information or real-time vision. These results highlight how mechanically tuned tactile appendages can simplify sensing and enhance autonomy in elongate multi-legged robots operating in constrained spaces.

Shengkai Li, Hussain N. Gynai, Steven Tarr et al.

Systems consisting of spheres rolling on elastic membranes have been used to introduce a core conceptual idea of General Relativity (GR): how curvature guides the movement of matter. However, such schemes cannot accurately represent relativistic dynamics in the laboratory because of the dominance of dissipation and external gravitational fields. Here we demonstrate that an ``active" object (a wheeled robot), which moves in a straight line on level ground and can alter its speed depending on the curvature of the deformable terrain it moves on, can exactly capture dynamics in curved relativistic spacetimes. Via the systematic study of the robot's dynamics in the radial and orbital directions, we develop a mapping of the emergent trajectories of a wheeled vehicle on a spandex membrane to the motion in a curved spacetime. Our mapping demonstrates how the driven robot's dynamics mix space and time in a metric, and shows how active particles do not necessarily follow geodesics in the real space but instead follow geodesics in a fiducial spacetime. The mapping further reveals how parameters such as the membrane elasticity and instantaneous speed allow the programming of a desired spacetime, such as the Schwarzschild metric near a non-rotating blackhole. Our mapping and framework facilitate creation of a robophysical analog to a general relativistic system in the laboratory at low cost that can provide insights into active matter in deformable environments and robot exploration in complex landscapes.

Tianyu Wang, Baxi Chong, Yuelin Deng et al.

Reorientation (turning in plane) plays a critical role for all robots in any field application, especially those that in confined spaces. While important, reorientation remains a relatively unstudied problem for robots, including limbless mechanisms, often called snake robots. Instead of looking at snakes, we take inspiration from observations of the turning behavior of tiny nematode worms C. elegans. Our previous work presented an in-place and in-plane turning gait for limbless robots, called an omega turn, and prescribed it using a novel two-wave template. In this work, we advance omega turn-inspired controllers in three aspects: 1) we use geometric methods to vary joint angle amplitudes and forward wave spatial frequency in our turning equation to establish a wide and precise amplitude modulation and frequency modulation on omega turn; 2) we use this new relationship to enable robots with fewer internal degrees of freedom (i.e., fewer joints in the body) to achieve desirable performance, and 3) we apply compliant control methods to this relationship to handle unmodelled effects in the environment. We experimentally validate our approach on a limbless robot that the omega turn can produce effective and robust turning motion in various types of environments, such as granular media and rock pile.

Baxi Chong, Yasemin O. Aydin, Jennifer M. Rieser et al.

Serially connected robots are promising candidates for performing tasks in confined spaces such as search-and-rescue in large-scale disasters. Such robots are typically limbless, and we hypothesize that the addition of limbs could improve mobility. However, a challenge in designing and controlling such devices lies in the coordination of high-dimensional redundant modules in a way that improves mobility. Here we develop a general framework to control serially connected multi-legged robots. Specifically, we combine two approaches to build a general shape control scheme which can provide baseline patterns of self-deformation ("gaits") for effective locomotion in diverse robot morphologies. First, we take inspiration from a dimensionality reduction and a biological gait classification scheme to generate cyclic patterns of body deformation and foot lifting/lowering, which facilitate generation of arbitrary substrate contact patterns. Second, we use geometric mechanics methods to facilitates identification of optimal phasing of these undulations to maximize speed and/or stability. Our scheme allows the development of effective gaits in multi-legged robots locomoting on flat frictional terrain with diverse number of limbs (4, 6, 16, and even 0 limbs) and body actuation capabilities (including sidewinding gaits on limbless devices). By properly coordinating the body undulation and the leg placement, our framework combines the advantages of both limbless robots (modularity) and legged robots (mobility). We expect that our framework can provide general control schemes for the rapid deployment of general multi-legged robots, paving the ways toward machines that can traverse complex environments under real-life conditions.

Pavel Chvykov, Thomas A. Berrueta, Akash Vardhan et al.

Self-organization is frequently observed in active collectives, from ant rafts to molecular motor assemblies. General principles describing self-organization away from equilibrium have been challenging to identify. We offer a unifying framework that models the behavior of complex systems as largely random, while capturing their configuration-dependent response to external forcing. This allows derivation of a Boltzmann-like principle for understanding and manipulating driven self-organization. We validate our predictions experimentally in shape-changing robotic active matter, and outline a methodology for controlling collective behavior. Our findings highlight how emergent order depends sensitively on the matching between external patterns of forcing and internal dynamical response properties, pointing towards future approaches for design and control of active particle mixtures and metamaterials.

Tianyu Wang, Bo Lin, Baxi Chong et al.

Snake robots composed of alternating single-axis pitch and yaw joints have many internal degrees of freedom, which make them capable of versatile three-dimensional locomotion. In motion planning process, snake robot motions are often designed kinematically by a chronological sequence of continuous backbone curves that capture desired macroscopic shapes of the robot. However, as the geometric arrangement of single-axis rotary joints creates constraints on the rotations in the robot, it is challenging for the robot to reconstruct an arbitrary 3D curve. When the robot configuration does not accurately achieve the desired shapes defined by these backbone curves, the robot can have unexpected contacts with the environment, such that the robot does not achieve the desired motion. In this work, we propose a method for snake robots to reconstruct desired backbone curves by posing an optimization problem that exploits the robot's geometric structure. We verified that our method enables fast and accurate curve-configuration conversions through its applications to commonly used 3D gaits. We also demonstrated via robot experiments that 1) our method results in smooth locomotion on the robot; 2) our method allows the robot to approach the numerically predicted locomotive performance of a sequence of continuous backbone curve.

Shengkai Li, Bahnisikha Dutta, Sarah Cannon et al.

Active matter physics and swarm robotics have provided powerful tools for the study and control of ensembles driven by internal sources. At the macroscale, controlling swarms typically utilizes significant memory, processing power, and coordination unavailable at the microscale, e.g., for colloidal robots, which could be useful for fighting disease, fabricating intelligent textiles, and designing nanocomputers. To develop principles that that can leverage physics of interactions and thus can be utilized across scales, we take a two-pronged approach: a theoretical abstraction of self-organizing particle systems and an experimental robot system of active cohesive granular matter that intentionally lacks digital electronic computation and communication, using minimal (or no) sensing and control, to test theoretical predictions. We consider the problems of aggregation, dispersion, and collective transport. As predicted by the theory, as a parameter representing interparticle attraction increases, the robots transition from a dispersed phase to an aggregated one, forming a dense, compact collective. When aggregated, the collective can transport non-robot "impurities" in their environment, thus performing an emergent task driven by the physics underlying the transition. These results point to a fruitful interplay between algorithm design and active matter robophysics that can result in new nonequilibrium physics and principles for programming collectives without the need for complex algorithms or capabilities.

Shengkai Li, Yasemin Ozkan Aydin, Charles Xiao et al.

In many systems motion occurs on deformed and deformable surfaces, setting up the possibility for dynamical interactions solely mediated by the coupling of the entities with their environment. Here we study the "two-body" dynamics of robot locomotion on a highly deformable spandex membrane in two scenarios: one in which a robot orbits a large central depression and the other where the two robots affect each other's motion solely through mutual environmental deformations. Inspired by the resemblance of the orbits of the single robot with those of general relativistic orbits around black holes, we recast the vehicle plus membrane dynamics in physical space into the geodesic motion of a "test particle" in a fiducial curved space-time and demonstrate how this framework facilitates understanding the observed dynamics. The two-robot problem also exhibits a resemblance with Einstein's general relativistic view of gravity, which in the words of Wheeler: "spacetime tells matter how to move; matter tells spacetime how to curve." We generalize this case the mapping to include a reciprocal coupling that translates into robotic curvature-based control schemes which modify interaction (promoting avoidance or aggregation) without long-range sensing. Our work provides a starting point for developing a mechanical analog gravity system as well as develops a framework that can provide insights into active matter in deformable environments and robot exploration in complex landscapes.

Ross Warkentin, William Savoie, Daniel I. Goldman

Robotic materials are multi-robot systems formulated to leverage the low-order computation and actuation of the constituents to manipulate the high-order behavior of the entire material. We study the behaviors of ensembles composed of smart active particles, smarticles. Smarticles are small, low cost robots equipped with basic actuation and sensing abilities that are individually incapable of rotating or displacing. We demonstrate that a "supersmarticle", composed of many smarticles constrained within a bounding membrane, can harness the internal collisions of the robotic material among the constituents and the membrane to achieve diffusive locomotion. The emergent diffusion can be directed by modulating the robotic material properties in response to a light source, analogous to biological phototaxis. The light source introduces asymmetries within the robotic material, resulting in modified populations of interaction modes and dynamics which ultimately result in supersmarticle biased locomotion. We present experimental methods and results for the robotic material which moves with a directed displacement in response to a light source.

Jennifer M. Rieser, Perrin E. Schiebel, Arman Pazouki et al.

Natural and artificial self-propelled systems must manage environmental interactions during movement. Such interactions, which we refer to as active collisions, are fundamentally different from momentum-conserving interactions studied in classical physics, largely because the internal driving of the locomotor can lead to persistent contact with heterogeneities. Here, we experimentally and numerically study the effects of active collisions on a laterally-undulating sensory-deprived robophysical model, whose dynamics are applicable to self-propelled systems across length scales and environments. The robot moves via spatial undulation of body segments, with a nearly-linear center-of-geometry trajectory. Interactions with a single rigid post scatter the robot, and these deflections are proportional to the head-post contact duration. The distribution of scattering angles is smooth and strongly-peaked directly behind the post. Interactions with a single row of evenly-spaced posts (with inter-post spacing $d$) produce distributions reminiscent of far-field diffraction patterns: as $d$ decreases, distinct secondary peaks emerge as large deflections become more likely. Surprisingly, we find that the presence of multiple posts does not change the nature of individual collisions; instead, multi-modal scattering patterns arise from multiple posts altering the likelihood of individual collisions to occur. As $d$ decreases, collisions near the leading edges of the posts become more probable, and we find that these interactions are associated with larger deflections. Our results, which highlight the surprising dynamics that can occur during active collisions of self-propelled systems, can inform control principles for locomotors in complex terrain and facilitate design of task-capable active matter.

Sarah Cannon, Joshua J. Daymude, William Savoie et al.

Smarticles, or smart active particles, are small robots equipped with only basic movement and sensing abilities that are incapable of rotating or displacing individually. We study the ensemble behavior of smarticles, i.e., the behavior a collective of these very simple computational elements can achieve, and how such behavior can be implemented using minimal programming. We show that an ensemble of smarticles constrained to remain close to one another (which we call a supersmarticle), achieves directed locomotion toward or away from a light source, a phenomenon known as phototaxing. We present experimental and theoretical models of phototactic supersmarticles that collectively move with a directed displacement in response to light. The motion of the supersmarticle is approximately Brownian, and is a result of chaotic interactions among smarticles. The system can be directed by introducing asymmetries among the individual smarticle's behavior, in our case by varying activity levels in response to light, resulting in supersmarticle biased motion.

Jeffrey Aguilar, Tingnan Zhang, Feifei Qian et al.

In this review we argue for the creation of a physics of moving systems -- a locomotion "robophysics" -- which we define as the pursuit of the discovery of principles of self generated motion. Robophysics can provide an important intellectual complement to the discipline of robotics, largely the domain of researchers from engineering and computer science. The essential idea is that we must complement study of complex robots in complex situations with systematic study of simplified robophysical devices in controlled laboratory settings and simplified theoretical models. We must thus use the methods of physics to examine successful and failed locomotion in simplified (abstracted) devices using parameter space exploration, systematic control, and techniques from dynamical systems. Using examples from our and other's research, we will discuss how such robophysical studies have begun to aid engineers in the creation of devices that begin to achieve life-like locomotor abilities on and within complex environments, have inspired interesting physics questions in low dimensional dynamical systems, geometric mechanics and soft matter physics, and have been useful to develop models for biological locomotion in complex terrain. The rapidly decreasing cost of constructing sophisticated robot models with easy access to significant computational power bodes well for scientists and engineers to engage in a discipline which can readily integrate experiment, theory and computation.

Jeffrey Aguilar, Alex Lesov, Kurt Wiesenfeld et al.

We study vertical jumping in a simple robot comprising an actuated mass-spring arrangement. The actuator frequency and phase are systematically varied to find optimal performance. Optimal jumps occur above and below (but not at) the robot's resonant frequency $f_0$. Two distinct jumping modes emerge: a simple jump which is optimal above $f_0$ is achievable with a squat maneuver, and a peculiar stutter jump which is optimal below $f_0$ is generated with a counter-movement. A simple dynamical model reveals how optimal lift-off results from non-resonant transient dynamics.