Magnetic modular millibots, capable of deterministic self-assembly and reconfiguration under wireless magnetic fields, offer a promising route toward mesoscale manipulation in structured and confined environments. This work presents a modular chain millibot composed of cubic units with free-to-spin internal magnets that align under external fields. While individual cubes cannot propel independently, their assembly into chains enables controlled locomotion through sliding and tumbling modes. We first demonstrate open-loop operation in confined workspaces, including chain formation, navigation, controlled disassembly, and wall climbing, supported by a dynamic model and parametric analysis that identify the actuation and geometric conditions required for successful climbing. Building on this foundation, we introduce a closed-loop control framework that integrates vision-based feedback. As the millibot’s movement speed increases with chain length, the order of assembly strongly affects task completion time; we therefore formulate the sequence-planning problem as a harmonic traveling salesman problem (HTSP) and solve it to compute deterministic cube-collection sequences that minimize the effective travel cost. The controller applies sliding and tumbling dynamics to realize obstacle-aware navigation and reliable self-assembly. Experiments validate autonomous assembly of four cubes with a two-cube chain into a six-cube chain in free space and collection of three cubes with wall climbing in a confined workspace, both with 100% success. The measured mean unit travel times were 0.67 s/mm in free space and 0.89 s/mm in confined environments. Collectively, these results establish a robust automation framework for reversible mesoscale self-assembly, programmable navigation, and lab-on-chip applications.

Alginate hydrogels are widely researched in phar-maceutical applications for their abilities to encapsulate and dis-perse therapeutics in response to stimuli. While effective, their utility can be greatly improved once converted into artificial cell soft-microrobots, allowing them to actively navigate through complex in vivo environments and facilitate targeted drug deliv-ery. In this study, artificial cells were fabricated by crosslinking alginate with magnetic nanoparticles and then deployed within mucus solutions to characterize their propulsion capabilities. The goal of this study was to understand how variations in simplified gastrointestinal fluid, artificial cell properties, and magnetic field characteristics could affect surface locomotion. A comparison between automatic feedback control and manual “open-loop” operation was also quantitatively explored. Under feedback control, individual artificial cells were navigated with automatically generated waypoints and a PID controller. Simu-lations were used to verify controller performance and accuracy. User operation was carried out using an Xbox controller, where the joystick could directly change navigation direction. We conclude in this study that the surface navigation of artificial cells is highly predictable within mucus concentrations and that both feedback and open-loop control are equally successful in navigation.

Reconfigurable modular robots, which can actively assemble and disassemble on command, offer the possibility of mesoscale (milliscale and microscale) manufacturing with robustness and controllability. In this study, we present a design of a scalable modular subunit with embedded permanent magnets in a 3-D printed cubic body. The subunit can be wirelessly controlled by an external uniform magnetic field. We also present controlled assembly–disassembly techniques for these subunits. Our modular robotic platform is highly reconfigurable and can create programmable, predetermined patterns based on open-loop control. The 2-D motion planner computes all reachable polyomino shapes from an arbitrary initial configuration and provides the shortest movement sequences to form each shape. Experimental results match computational modeling, demonstrating robust and reproducible behavior of the modular robotic platform that is promising for mesoscale manufacturing applications. Two cube sizes were tested: 10-mm edge lengths and 2.8-mm edge lengths.

This paper presents an adaptive backstepping controller for the reference tracking of an alginate artificial cell. An adaptive controller was implemented to precisely manipulate a magnetic artificial cell actuated by rotating magnetic fields. The rolling motion of a small-scale robot in a fluidic environment is challenging, especially when the fluid imparts an unknown response at low Reynolds number. In order to compensate for this uncertainty, an unknown tuning parameter encapsulating these effects was added to the governing equations of motion. A controller with an update law was then designed to estimate the unknown parameter and force the artificial cell to produce the desired response. The stability of the proposed controller was established by a candidate Lyapunov function. Real-time experiments were conducted to demonstrate the effectiveness of the designed controller at guiding an artificial cell to an arbitrary target position. Alginate cells were guided through a maze using the controller and was later combined with wall constraints to allow multiple alginate cells to reach the same target location. This controller can be applied to both surface motion and swimming-based small-scale robots in future applications for micro-assembly and targeted drug delivery.

This paper examines a family of designs for magnetic cubes and counts how many configurations are possible for each design as a function of the number of modules. Magnetic modular cubes are cubes with magnets arranged on their faces. The magnets are positioned so that each face has either magnetic south or north pole outward. Moreover, we require that the net magnetic moment of the cube passes through the center of opposing faces. These magnetic arrangements enable coupling when cube faces with opposite polarity are brought in close proximity and enable moving the cubes by controlling the orientation of a global magnetic field. This paper investigates the 2D and 3D shapes that can be constructed by magnetic modular cubes, and describes all possible magnet arrangements that obey these rules. We select ten magnetic arrangements and assign a "color" to each of them for ease of visualization and reference. We provide a method to enumerate the number of unique polyominoes and polycubes that can be constructed from a given set of colored cubes. We use this method to enumerate all arrangements for up to 20 modules in 2D and 16 modules in 3D. We provide a motion planner for 2D assembly and through simulations compare which arrangements require fewer movements to generate and which arrangements are more common. Hardware demonstrations explore the self-assembly and disassembly of these modules in 2D and 3D.

This paper presents scalable designs and fabrication, actuation, and manipulation techniques for soft millirobots under uniform magnetic field control. The millirobots were fabricated through an economic and robust moulding technique using polydimethylsiloxane (PDMS), acrylonitrile butadiene styrene (ABS) filaments, and 3D printed polylactic acid (PLA) rings. The soft millirobots were simple hollow rod-like structures with different configurations of embedded permanent magnets inside of their soft-body or at their ends. The soft-robots were actuated using six different motion modes including: pivot walking, rolling, tumbling, side-tapping, wiggling, and wavy-motion under an external uniform magnetic field control system. The velocities of the millirobots under different motion modes were analyzed under varying magnetic flux densities (B). Moreover, deformation of the soft-robotic body in response to the magnetic field strength was measured and a deflection curve showing bending angle (φ) was produced. Soft millirobots were navigated through a maze using a combination of the available motion modes. Different arrangements of the embedded permanent magnets enabled individual soft millirobots to respond heterogeneously under the same magnetic field inputs towards performing assembly and disassembly operation as modular subunits. Overall, this soft millirobot platform shows enormous potential for minimally invasive in vivo applications.

The modular assembly and actuation of 3D printed milliscale cuboid robots using a globally applied magnetic field is presented. Cuboids are composed of a rectangular resin shell embedded with two spherical permanent magnets that can independently align with any applied magnetic field. Placing cuboids within short distances of each other allows for modular assembly and disassembly by changing magnetic field direction. Assembled cuboids are demonstrated to stably self-propel under sequential field inputs allowing for both rolling and pivot walking motion modes. Swarms of cuboids could be actuated within the working space and exhibit near identical behavior. Specialized `trap robots' were developed to capture objects, transport them within the working space, and subsequently release the payload in a new location. Cuboids with male and female connectors were developed to exhibit the selective mating between cuboids. The results show that cuboids are a diverse and adaptable platform that has the potential to be scaled down to the sub-millimeter regime for use in medical or small-scale assembly applications.

This paper presents 2D feedback control and open loop 3D trajectories of heterogeneous chemically catalyzing Janus particles. Self-actuated particles have enormous implications for both in vivo and in vitro environments, which make them a diverse resource for a variety of medical and assembly applications. Janus particles, consisting of cobalt and platinum hemispheres, can self-propel in hydrogen peroxide solutions due to platinum's catalyzation properties. These particles are directionally controlled using static magnetic fields produced from a triaxial approximate Helmholtz coil system. Since the magnetization direction of Janus particles is often heterogeneous, and thereby not consistent with the propulsion direction, this creates a unique opportunity to explore the motion effects of these particles under 2D feedback control and open loop 3D control. Using a modified closed loop controller, Janus particles with magnetization both closely aligned and greatly misaligned to the propulsion vectors, were instructed to perform complex trajectories. These trajectories were then compared between trials to measure both consistency and accuracy. The effects of increasing offset between the magnetization and propulsion vectors were also analyzed. The effects this heterogeneity had on 3D motion is also briefly discussed. It is our hope going forward to develop a 3D closed loop control system that can retroactively account for variations in the magnetization vector.

This article discusses the design, modeling, and application of a powerful hexapole magnetic tweezer system for closed-loop 3D swarm control applications. The system consists of six sharp tapered magnetic poles that are integrated with six electromagnetic coils and mounted on two yokes composed of 3D printed magnetic material. Magnetic field gradients are generated at the sharp tips of the magnetic poles when current is applied through the attached electromagnetic coils. Different combinations of current input can interact with magnetized microparticles to create three-dimensional motion. A closed-loop control algorithm based on image processing and hardware integration through MATLAB was developed to automatically operate external power supplies connected to the magnetic tweezer system. Coordinate system transformation is utilized to transform the tilted actuation coordinates, by virtue of the system hardware configuration, to the measurement coordinates used during experiments and analysis. This magnetic tweezer system has the advantage of a larger working space and higher magnetic field strengths when compared to several other similar designs. The magnetic tweezer system allows for more diverse applications within the microscale, such as microparticle swarm control, cell penetration, and cell therapy. Experimental analysis performed in this article demonstrates the closed-loop navigation of a microparticle swarm moving freely in both 2D and 3D environments. Results show highly consistent trajectories within the swarm with only a few fluctuations due to microflows. This system will keep being updated and optimized to investigate the performance of microparticles in in vivo environments.

This paper presents the design, development and implementation of a novel, high power hexapole magnetic tweezer system for 3D micromanipulations. Six tapering-tipped magnetic poles are deployed in a tilted Cartesian coordinate system, with an electromagnetic coil on each for actuation, connected by two 3D printed magnetic yokes to form a double layer structure. The power source is integrated to the magnetic tweezer system through a control algorithm on the software level; image processing was used for experiment analysis. Because of the high magnetic field that the magnetic coils can generate, the working space in the system is relatively larger than other similar designs, which provides better performance on microscale robotic swimmer manipulations. Simulations and experiments performed in this paper demonstrate the agile and powerful manipulation of microswimmers with desired control input to follow complex trajectories, avoid obstacles and move against micro-flow in the samples. We prove that the developed hexapole magnetic tweezer has enough power and controllability to guide microswimmers in Newtonian and Non-Newtonian fluid environments. The system will be optimized continuously and implemented into cell penetration experiments. Finally, the application will be deployed into in vivo based environments.

Microrobots have great potential for microassembly and non-invasive surgery applications. Motivated by studies proposing MRI-guided drug delivery to tumor cells using magnetic micro carriers, this paper studies two major challenges of this problem: (i) microrobot swarm trajectory generation, and (ii) swarm aggregation using a global input. We propose an augmented RRT for trajectory generation to reduce environment interference, and a divide-and-conquer algorithm for swarm aggregation to improve performance. Simulations demonstrate the utility of these approaches in comparison to alternate heuristics. Our trajectory generation and aggregation strategies are implemented on a swarm of ferromagnetic microparticles in oil using a 6-coil electromagnetic system with image feedback.

A bacteria-powered microrobot (BPM) is a hybrid robotic system consisting of an SU-8 microstructure with active surfaces or bacterial carpets, in which massive arrays of biomolecular flagellar motors work cooperatively. This paper suggests an obstacle-avoidance method based on a BPM's response to electric fields. The negatively charged bacteria enable the BPM to follow electric fields. In our previous demonstration of the single BPM controllability, we observed a vast change in the control dynamics when obstructions distorted the applied electric field and affected BPM steering and control. In this paper, we demonstrate an obstacle avoidance method that takes the electric field distortion into account to navigate a BPM through multiple static obstacles in real time. We used an artificial potential field and configuration space in our algorithm to generate an objective function for the electric field distortion and collision around/with obstacles, respectively. In addition, finite-element modeling through COMSOL Multiphysics engineering software was used to simulate charged-particle trajectories in a distorted electric field. Finally, we describe the feasibility of our proposed obstacle avoidance approach through experiments and compared these data with simulation results.

This paper investigates the use of single control signal (magnetic field direction) and PSO-MPC algorithm to control multiple magnetized Tetrahymena pyriformis (T. pyriformis) cells to move from their initial positions to their target positions simultaneously while avoiding the obstacle. The magnetized T. pyriformis cells are generated by adding iron-oxide spherical particles into the cells. We control the cells' moving direction by changing the magnetic field direction. Based on Model Predictive Control (MPC) algorithm, we define a cost function which is composed of the target cost function and the obstacle potential function. The target cost function is to measure the sum of differences between cells' predicted positions and their target positions. The obstacle potential function is used to measure the repulsive force of the obstacle. The input variables of the cost function are the sequence of control signals. We use Particle Swarm Optimization (PSO) method to find a cost value which is close to the global minimum of the cost function. In the experimental result section, we show the control of three m3pi robots to move from their initial positions to their target positions with avoiding the obstacle. Since the similar control strategy has successfully controlled one T. pyriformis cell in our previous work, we believe our PSO-MPC algorithm is applicable on the multiple T. pyriformis cells' control task.

As microscale robots are becoming increasingly popular due to their potential for medical and industrial applications, various designs of microscale robotic system have been developed. However, there has not been much work on autonomous control algorithms for microscale robots in microfluidic environments. In this paper, we introduce an autonomous navigation algorithm for the bacteria-powered microrobots (BPMs) in a workspace with moving obstacles. A BPM consists of a rigid inorganic body with bacteria attached on the surface. The attached bacteria provide propulsive force and are controllable using electric fields, which had been demonstrated in previous work. We take the controllability of BPMs and the unpredictable motion of dynamic obstacles into account to develop a dynamic obstacle avoidance approach. Moreover, we use finite element simulation to observe an electric field around a moving obstacle to model the field's deformation. Demonstration of dynamic obstacle avoidance approach through simulation results and experimental data are presented in the paper.

Biological robots can be produced in large numbers, but are often controlled by uniform inputs. This makes position control of multiple robots inherently challenging. This paper uses magnetically-steered ciliate eukaryon {Tetrahymena pyriformis) as a case study. These cells swim at a constant speed, and can be turned by changing the orientation of an external magnetic field. We show that it is possible to steer multiple T. pyriformis to independent goals if their turning - modeled as a first-order system - has unique time constants. We provide system identification tools to parameterize multiple cells in parallel. We construct feedback control-Lyapunov methods that exploit differing phase-lags under a rotating magnetic field to steer multiple cells to independent target positions. We prove that these techniques scale to any number of cells with unique first-order responses to the global magnetic field. We provide simulations steering hundreds of cells and validate our procedure in hardware experiments with multiple cells.

We demonstrate three-dimensional control with the eukaryotic cell Tetrahymena pyriformis (T. pyriformis) using two sets of Helmholtz coils for xy-plane motion and a single electromagnet for vertical motion. T. pyriformis is modified to have artificial magnetotaxis with internalized magnetite. Since the magnetic fields exerted by electromagnets are relatively uniform in the working space, the magnetite exerts only torque, without translational force, which enabled us to guide the cell's swimming direction while the swimming force is exerted only by the cell's motile organelles. A stronger magnetic force was necessary to steer cells to the z-axis, and, as a result, a single electromagnet placed just below our sample area is utilized for vertical motion. To track the cell's positions in the z-axis, intensity profiles of non-motile cells at varying distances from the focal plane are used. During vertical motion along the z-axis, the intensity difference from the background decreases while the cell size increases. Since the cell is pear-shaped, the eccentricity is high during planar motion, but lowers during vertical motion due to the change in orientation. The three-dimensional control of the live organism T. pyriformis as a cellular robot shows great potential to be utilized for practical applications in microscale tasks, such as target transport and cell therapy.

The use of live microbial cells as microscale robots is an attractive premise, primarily because they are easy to produce and to fuel. In this paper, we study the motion control of magnetotactic Tetrahymena pyriformis cells. Magnetotactic T. pyriformis is produced by introducing artificial magnetic dipole into the cells. Subsequently, they can be steered by using an external magnetic field. We observe that the external magnetic field can only be used to affect the swimming direction of the cells, while the swimming velocity depends largely on the cells' own propulsion. Feedback information for control is obtained from a computer vision system that tracks the cell. The contribution of this paper is twofold. First, we construct a discrete-time model for the cell dynamics that is based on first principle. Subsequently, we identify the model parameters using the Least Squares approach. Second, we formulate a model predictive approach for feedback control of magnetotactic T. pyriformis. Both the model fitness and the performance of the feedback controller are verified using experimental data.

In this paper, we present a control strategy using real-time feedback combined with feasible path planning to manipulate a type of microorganism, Tetrahymena pyriformis (T. pyriformis), as a micro-bio-robot using artificial magnetotaxis. Artificially magnetotactic T. pyriformis cells were created by the internalization of iron oxide nano particles. Following the magnetization of the internalized particles, the cells become controllable using an external time-varying magnetic field. The behavior of artificially magnetotactic T. pyriformis under a magnetic field has been investigated in a manual control experiment. A feasible path planner called rapidly-exploring random tree (RRT) and a feedback control scheme are implemented to guide the cell to a desired position and orientation. Since the motion of T. pyriformis is nonlinear like that of a car, combining the RRT and feedback control allows the cell to be controlled in 3-dimensional (x, y, ¸) space. In the results, real-time feedback control of T. pyriformis in 3-dimensional space demonstrated the potential of utilizing T. pyriformis as a micro-bio-robot for microscale tasks.

In this paper, we describe how signaling networks and actuation in bacterial cells and biomolecular networks of bacteria can be used to develop an integrated micro-bio-robotic system. SU8 microstructures blotted with swarmer cells of Serratia Marcescens in a monolayer are propelled by the bacteria in the absence of any environmental stimulus. We call such microstructures with bacteria Micro Bio Robots (MBRs) and the uncontrolled motion in the absence of stimuli self actuation. Our paper has two primary contributions. First, we demonstrate the control of MBRs using self-actuation, DC electric fields and ultra-violet radiation, and develop experimentally validated mathematical model for the MBRs. This model allows us to use self-actuation and electrokinetic actuation to steer the MBR to any position and orientation in a planar micro channel. Second, we describe the development of biosensors for the MBRs. This is done by attaching genetically engineered Escherichia coli cells that are capable of sensing nonmetabolizable lactose analog methyl-β-D-thiogalactoside (TMG). We describe the fabrication process for MBRs and show experimental results demonstrating sensing, actuation and control.

This paper presents a systematic analysis of the motion of microscale structures actuated by flagellated bacteria. We perform the study both experimentally and theoretically. We use a blotting procedure to attach flagellated bacteria to a buoyancy-neutral plate called a microbarge. The motion of the plate depends on the distribution of the cells on the plate and the stimuli from the environment. We construct a stochastic mathematical model for the system, based on the assumption that the behavior of each bacterium is random and independent of that of its neighbors. The main finding of the paper is that the motion of the barge plus bacteria system is a function of a very small set of parameters. This reduced-dimensional model can be easily estimated using experimental data. We show that the simulation results obtained from the model show an excellent match with the experimentally-observed motion of the barge.

In order to characterize the random walk of E. coli, biologists have studied several parameters, such as the motility speed, run duration, and random motility coefficient. Previously, biologists indicated that the probability distributions of these parameters may vary depending on the presence or absence of a chemical gradient in the environment. For instance, in a gradient, the cell of E. coli exhibits a biased-random walk. Although it is suggested that the parameter distributions change from unbiased to biased conditions, there are contradicting reports of the actual distributions since they are usually derived from observations of cell movement. In this paper, we consider the problem conversely. We try hypotheses for the parameter distributions respectively for the unbiased and biased cases to simulate random walks. Then we can validate our chemotaxis model through the simulated random motility coefficient, under unbiased and biased environments.