We hypothesize that online movement videos have untapped potential for teaching physical skills, and we developed a platform that automatically generates practice plans from raw TikTok dance videos. The practice plans teach one segment at a time using fading guidance and part-learning principles and are presented using a web-based interface featuring concurrent visual aids. Two user studies (n=54, n=38) were conducted. The first showed significant improvements in learning outcomes compared to standard tutorials, underscoring the importance of well-structured practice plans and offering nuanced insights into the design and effectiveness of visual aids. The second study found that segmentation and emoji-based dual-coding only benefit learning when integrated into a well-designed lesson structure. We provide a set of practical recommendations for enhancing online movement learning, focusing on the need for substantive part-learning activities and careful use of visual aids to prevent cognitive overload.

Traditional swarm robots rely on specific communication and planning strategies to coordinate particular tasks. Human swarms exhibit distinctive characteristics due to their capacity for language-based communication and active reasoning. This paper presents an exploratory approach to robotic swarm intelligence that leverages Large Language Models (LLMs) to emulate human-like active problem-solving behaviors. We introduce a decentralized multi-robot system where each robot initially only has its local information and does not know of the existence of the other robots. The robots utilize LLMs for reasoning and natural language for inter-robot communication, enabling them to discover peers, share information, and coordinate actions dynamically. In a series of experiments in zero-shot settings, we observed human-like social behaviors, including mutual discovery, identification, information exchange, collaboration, negotiation, and error correction. While the technical approach is straightforward, the main contribution lies in exploring the interactive societies that LLM-driven robots form – a form of robot social dynamics (or robotic social behavior analysis), examining how human-like communication protocols and collaborative structures emerge among robots through language-based interaction. In this context, we use the term "robot social dynamics" to describe the interaction patterns that arise within robot collectives, inspired by, but distinct from traditional human anthropology.

We present a scalable combined localization infrastructure deployment and task planning algorithm for underwater assembly. Infrastructure is autonomously modified to suit the needs of manipulation tasks based on an uncertainty model on the infrastructure’s positional accuracy. Our uncertainty model can be combined with the noise characteristics from multiple sensors. For the task planning problem, we propose a layer-based clustering approach that completes the manipulation tasks one cluster at a time. We employ movable visual fiducial markers as infrastructure and an autonomous underwater vehicle (AUV) for manipulation tasks. The proposed task planning algorithm is computationally simple, and we implement it on AUV without any offline computation requirements. Combined hardware experiments and simulations over large datasets show that the proposed technique is scalable to large areas.

We present a new class of curved block-based line structures whose component chains are flexible when separated, and provably rigid when assembled together into an interlocking double chain. The joints are inspired by traditional zippers, where a binding fabric or mesh connects individual teeth. Unlike traditional zippers, the joint design produces a rigid interlock with programmable curvature. This allows fairly strong curved structures to be built out of easily stored flexible chains. In this paper, we introduce a pipeline for generating these curved structures using a novel block design template based on revolute joints. Mesh embedded in these structures maintains block spacing and assembly order. We evaluate the rigidity of the curved structures through mechanical performance testing and demonstrate several applications.

We present the first free-floating autonomous underwater construction system capable of using active bal-lasting to transport cement building blocks efficiently. It is the first free-floating autonomous construction robot to use a paired set of resources: compressed air for buoyancy and a battery for thrusters. In construction trials, our system built structures of up to 12 components and weighing up to 100 Kg (75 Kg in water). Our system achieves this performance by combining a novel one-degree-of-freedom manipulator, a novel two-component cement block construction system that corrects errors in placement, and a simple active ballasting system combined with compliant placement and grasp behaviors. The passive error correcting components of the system minimize the required complexity in sensing and control. We also explore the problem of buoyancy allocation for building structures at scale by defining a convex program which allocates buoyancy to minimize the predicted energy cost for transporting blocks.

A skid-steer rover's power consumption is highly dependent on the turning radius of its path. For example, a point turn consumes a lot of power compared to a straight-line motion. Thus, in path planning for this kind of rover, turning radius is a factor that should be considered explicitly. There is a lack of any analytical approach in literature for finding energy-optimal paths for skid-steer rovers. The key contribution of this work is an energy-time equivalency theorem, for skid-steer rovers on obstacle-free hard ground. The theorem converts the energy-optimal problem into an equivalent time-optimal problem. This non-intuitive result stems from the fact that with this model of the system the total energy is fully parameterized by the geometry of the path alone. Hence, instead of directly solving the energy-optimal path planning problem, which is highly nonlinear, the equivalent time-optimal problem can be solved. Furthermore, experimental results are provided to experimentally prove the equivalency theorem while using Husky UGV skid-steer rover.

This article presents a design for interlocking blocks and an algorithm that allows these blocks to be assembled into desired shapes. During and after assembly, the structure is kinematically interlocked if a small number of blocks are immobilized relative to other blocks. There are two types of blocks: cubes and double-height posts, each with a particular set of male and female joints. Layouts for shapes involving thousands of blocks have been planned automatically, and shapes with several hundred blocks have been built by hand. This article also describes a method for assembling structures from blocks in parallel. As a proof of concept, a dual-robot system was used to assemble 48 blocks, forming an interlocking cube-like structure.Note to Practitioners—This article was inspired by existing work on interlocking joinery structures, modular robots, and construction robots. We present designs for two interlocking blocks that can be assembled into larger rigid structures. Blocks of this type are a promising future construction material. Only translation is needed to assemble the blocks, simplifying robotic assembly, and the mortarless construction allows for later disassembly and reuse of the blocks. We propose an algorithm that lays out blocks into desired shapes in series and developed a dual-robot system to assemble 48 blocks automatically. Our physical experiments show that joint manufacturing precision is critical to the ease of construction and the rigidity of the finished structure. We also present a layout algorithm that enables parallel assembly, allowing multiple robots to work on the same structure.

This paper presents a method of computing free motions of a planar assembly of rigid bodies connected by loose joints. Joints are modeled using local distance constraints, which are then linearized with respect to configuration space velocities, yielding a linear programming formulation that allows analysis of systems with thousands of rigid bodies. Potential applications include analysis of collections of modular robots, structural stability perturbation analysis, tolerance analysis for mechanical systems, and formation control of mobile robots.

Discrete graphs are commonly used to approximately represent configuration spaces used in robot motion planning. This paper explores a representation in which the costs of crossing local regions of the configuration space are represented using piecewise linear regression (PLR). We explore a few simple motion planning problems, and show that for these problems, the memory required to store the representation compares favorably to that required for standard discrete vertex-and-edge models, while preserving the quality of paths returned from searches.

This paper investigates the connection between the kinematics of robots arms and the shortest paths for mobile robots. Lagrange multipliers are used to show that the shortest paths are equivalent to arms in configurations that balance an external force, while applying equal torques and forces at each joint. Analysis of the arm Jacobian yields a further geometric interpretations of optimal paths, constraining the locations of rotation centers and the directions of translations that may occur along optimal paths.

This paper considers an assembly problem. Let there be two interlocking parts, only one of which may be cut into pieces. How many pieces should we cut the divisible part into to separate the parts using a sequence of rigid-body motions? In this initial exploration, we primarily consider 2-D polygonal parts. This paper presents an algorithm that computes a lower bound on the number of pieces that the divisible part must be cut into. This paper also presents a complete algorithm that constructs a set of cuts and a motion plan for disassembly, yielding an upper bound on the required number of pieces. Applications of the future extension of this paper to 3-D may include robot self-assembly, interlocking 3-D model design, search-and-rescue, packaging, and robotic surgery.

This paper presents a simple prototype of a lightweight sensing and tactile communication system that allows bidirectional communication between two humans, or between a human and a computer. This system tracks the user's actions with simple sensors, and uses tiny vibration motors as feedback devices. Vibration motors provide feedback that is both intuitive and minimally intrusive. The design is simple, flexible, and extensible to large-scale, full-body motion tasks.

This paper explores a problem of reconfiguration of a large set of agents using global control signals: right, left, up and down. A field of obstacles guides the reconfiguration by limiting motion in the various directions. This paper extends work by Becker et al. ([4], [5] and [7]), and shows there exists a workspace a constant factor larger than the number of agents that enables complete rearrangement for a rectangle of agents.

Simply pulling on the ends of string is sufficient to tighten simple knots such as the overhand knot, but many knots used for decoration or binding need to be tightened at particular locations along the string. For example, a shoelace knot should have equally-sized bows, as should a decorative cloverleaf knot. Knots tied in sounding lines (historically used to measure depth in the ocean) must be placed at precise distances apart. Precise control of tying also allows tangling to be avoided in complex knots. This paper explores an approach to tying knots precisely, so that friction locks occur at specified locations along the string. First, the knot is laid out on a fixture using an arm and a specialized gripper; then, the fixture contracts as string is pulled to tighten the knot. This is the first work we know of in robotic manipulation focused on precise knot tightening (rather than loose arrangement), and presents tying of a fairly complex decorative knot, the Ruyi knot, as a proof of concept. The fixtures are each specific to particular knots, but are designed automatically using the algorithm presented.

String stretched tightly along a sequence of fixed grasp points takes the shape of a polygonal arc. In this work, we investigate how many points are necessary and sufficient to grasp and tie arbitrary knots while maintaining tension, so that the string remains polygonal. This approach allows reasoning that is entirely geometric, which does not rely on potentially inaccurate dynamic models of the string or detailed knowledge of physical characteristics of the string. Algorithms are proposed to determine the contact locations, and generate the motions needed to tie arbitrary knots. This work shows that a number of grasp points that is linear in the number of crossings in a knot diagram is sufficient to immobilize string in a polygonal shape with the topology of an arbitrary knot, or to fold or unfold the knot from a straight configuration.

This paper explores the problem of building a structure of a desired shape, using re-usable interlocking blocks. Blocks are cubes; we make use of nine different types of cubes, each with different arrangements of male and female connectors on the six sides of the cube. The desired shape is specified by a set of voxels. We propose an algorithm that lays out cubes in a particular pattern to give the desired shape and gives a fairly simple assembly order.

This paper presents a fast tight-tolerance threading technique for string and rope. Instead of relying on simulations of these deformable objects to plan a path or compute control actions, we control the movement of the string with a virtual magnetic vector field emanating from the narrow openings we wish to thread through. We compute an approximate Jacobian to move the tip of the string through the vector field and propose a method to promote alignment of the head of the string to the opening. We also propose a method for re-grasping the string based on the relationship between the string's configuration, the orientation of the opening, and direction of gravity. This re-grasping method in conjunction with our controller can be used to thread the string through a sequence of openings. We evaluated our method in simulation (with simulated sensor noise) and on the Da Vinci surgical robot. Our results suggest that our method is quite robust to errors in sensing, and is capable of real-world threading tasks with the da Vinci robot, where the diameter of the string (3.5mm) and opening (4.9mm) differ by only 1.4 mm.

This paper presents a definition of convexity useful for describing local optimality in configuration spaces, proves that finding convex regions is relatively easy, and presents an algorithm for approximating the free configuration space using a set of such convex regions. The paper examines simple but interesting systems: serial planar arms with revolute joints, and a Reeds-Shepp car. The paper experimentally explores an approach for finding good (although not necessarily optimal) trajectories using the derived data structure.

This paper presents a controlled tying approach for knots using fixtures and simple pulling motions applied to the ends of string. Each fixture is specific to a particular knot; the paper gives a design process that allows a suitable fixture to be designed for an input knot. Knot tying is separated into two phases. In the first phase, a fixture is used to loosely arrange the string around a set of rods, with the required topology of the given knot. In the second phase, the string is pulled taut around the tightening fixtures. Two tightening fixture designs are presented. The first design is a fixture with no moving parts; tilted rods whose cross-sections get closer near the tips, guiding string in a controlled fashion as string slides up the rods during tightening. The second design is a collection of straight rods that can move passively along predefined paths during tightening. Successful tying is shown for three interesting cases: a “cloverleaf knot” design, a “double coin” knot design, and the top of a shoelace knot.

Analytical results describing the optimal trajectories for general classes of robot systems have proven elusive, in part because the optimal trajectories for a complex system may not exist, or may be computed only numerically from differential equations. This paper studies a simpler optimization problem: finding an optimal sequence and optimal durations of motion primitives (simple preprogrammed actions) to reach a goal. By adding a fixed cost for each switch between primitives, we ensure that optimal trajectories exist and are well-behaved. To demonstrate this approach, we prove some general results that geometrically characterize time-optimal trajectories for rigid bodies in the plane with costly switches (allowing comparison with previous analysis of optimal motion using Pontryagin's Maximum Principle), and also present a complete analytical solution for a problem of moving a heavy park bench by rotating the bench around each end point in sequence.

This paper presents an algorithm for folding a serial revolute chain into a rigid structure of essentially any desired planar shape. The algorithm is fast (linear in the number of links), and the constructed folding plan only requires an actuation method that sequentially folds triangles as the pattern is laid out, maintaining incremental rigidity of the structure during folding.

Sampling-based probabilistic roadmap algorithms such as PRM and PRM* have been shown to be effective at solving certain motion planning problems, but the large graphs generated to express the connectivity and a metric on the configuration space may require much storage space and be expensive to search. Recent work by Marble and Bekris [14], [19] applied spanner algorithms to PRM* these algorithms prune some edges in a dense graph, while guaranteeably maintaining an approximation to the metric. In this paper, we apply (and improve) a state-of-the-art streaming spanner algorithm to prune PRM* roadmaps. The algorithm we present has the main advantage of computational speed; when applied to PRM*, the processing time per vertex is independent of the number of sampled vertices, n, as compared to O(nlog2nloglogn) in [19]. In practice, the algorithm we present prunes a graph with about 20 million edges in less than 20 seconds on a modern desktop computer; compared to the time required for generating such a roadmap, this additional processing time is essentially trivial. In fact, because the combination of this algorithm with PRM* avoids the need for many collision detections, the combination runs several times faster than PRM*alone.

We present the first analytical solution method for finding a time-optimal trajectory between any given pair of configurations for a three-wheeled omni-directional vehicle in an obstacle-free plane. The mathematical model of the vehicle bounds the velocities of the wheels independently. The timeoptimal trajectories can be divided into two categories: singular and generic. An analytical solution method has previously been presented for singular trajectories; this paper completes the work and presents the solution for generic trajectories. The speed and precision of the algorithm allow dense sampling of the configuration space, to determine how the time and structure of time-optimal trajectories change across configurations. Simulation results show that time-optimal trajectories tend to be ten to twenty percent faster than a simple but practical driving strategy: turn until the fastest translation direction faces the goal, drive to the goal, and turn to the current angle.

This paper presents first attempts at a method for searching for time-optimal trajectories for a general model of mobile robots that includes Dubins and Reeds-Shepp cars, differential-drive robots, and omnidirectional robots as special cases. The paper takes as a starting point recent results by the authors that describe necessary conditions on the trajectories, based on Pontryagin's Maximum Principle. These necessary conditions reduce the problem of finding an optimal trajectory between start and goal to a few one-dimensional search problems. This search is not formally guaranteed to find a near-optimal trajectory if the sampling of the search space is not fine enough, but comparison to existing analytical results for specific systems, and a complete numerical search over trajectories with only a few control switches, demonstrates effectiveness of the method.

Knot tying poses a challenge to robotic and human manipulation due to the need to regrasp a flexible string. Without sensing, it becomes nearly impossible to guess where the string is. However, by using a fixture, the string can be continually grasped during the entire tying process. We have developed fixtures for a simple overhand knot and a square knot, and have started developing a fixture for the two half hitches knot. We can tie knots in different types of wire and fishing line using these fixtures. In addition, we used a Cobra i600 SCARA arm to autonomously tie multiple overhand knots in sequence without sensing, using solder as the string-like material.

What is the shortest or fastest path a mobile robot can follow between two configurations in the unobstructed plane? The answer to this fundamental question is only known analytically for a few planar mobile robots: the Dubins and Reeds-Shepp steered cars, the differential drive, and a particular omnidirectional robot. This paper explores the optimal trajectories for a general parameterized model of a mobile robot that includes each previously-studied vehicle as a special case. The model also allows characterization of the optimal trajectories for several other mobile robot designs for which the optimal trajectories have not been previously explored. The paper applies Pontryagin's Maximum Principle to the generalized robot to find necessary conditions that optimal trajectories must satisfy, and gives geometric interpretations of the conditions. We also present an algorithm that generates and classifies all optimal trajectories for a given design.

Characterizing optimal paths for mobile robots is an interesting, important, and challenging endeavor. Not only they are interesting with respect to the optimized criteria, but also they offer a family of motion primitives that can be used for motion planning in the presence of obstacles. This paper presents characterization of shortest paths for differential-drive mobile robots, with the goal of classifying solutions in the spirit of Dubins curves and Reeds-Shepp curves for car-like robots. To obtain a well-defined notion of shortest., the total amount of wheel rotation is optimized. Using Pontryagin maximum principle and other tools, we establish the existence of optimal trajectories, and derive the set of optimal paths. Some Reeds-Shepp curves appear in the set of optimal paths, whereas there are optimal paths which are different from Reeds-Shepp curves. To the best of our knowledge, this is the first progress on the problem

The accelerations of and forces among contacting rigid bodies may be computed by formulating the dynamics equations and contact constraints as a complementarity problem (P. Lotstedt, 1981). Dantzig's algorithm, when applicable, will find a solution to the linear complementarity problem corresponding to an assembly with n contacts in O(n) major cycles. Can the dynamics of an assembly be computed more quickly if the dynamics of a subassembly are already known? This paper shows that Dantzig's algorithm will find a solution in O(n - k) major cycles if the algorithm is initialized with a solution to the dynamics problem for a subassembly with k internal contacts. We apply this observation to two robotics problems: dynamic simulation and assembly sequence planning. In dynamic simulation, the positions of several bodies might remain fixed during a sequence of frames. We compute the dynamics of this motionless subset (which might not be motionless when considered in isolation), and use the result to initialize the computation for the entire assembly. In assembly planning, non-disjoint sets of objects are typically considered sequentially by the planner. If the configuration of only one body is varied, the dynamics of successive assemblies can be computed in a constant number of major cycles

Origami, the human art of paper sculpture, is a fresh challenge for the field of robotic manipulation, and provides a concrete example for many difficult and general manipulation problems. This paper presents some initial results, including the world's first origami-folding robot, definition of a simple class of origami for which we have designed a complete automatic planner, an analysis of the kinematics of more complicated folds, and some new theorems about foldability.

The companion paper (see ibid. "Computing wrench cones for planar contact tasks", p869 (2002)) derives an algorithm that determines the external wrenches consistent with constraints on the contact interactions between two rigid planar bodies. In this paper, we show how this algorithm may be used to create sensorless plans which guarantee that a workpiece is correctly inserted into a fixture. Our method explicitly removes all wrenches consistent with undesirable contact modes, and therefore avoids the frictional indeterminacy problem.

Previous work has presented the time optimal trajectories for three classes of nonholonomic mobile robots: steered cars that can only go forwards, steered cars that go forwards or backwards, and differential drives. Each of the vehicles is modelled as a rigid body in the plane with velocity and angular velocity controls. The systems are differentiated only by the bounds on the controls, but the optimal trajectories are qualitatively different for each system. We explore this difference by considering the effect that control bounds have on the extremal trajectories of bounded velocity vehicles, where the extremal trajectories are defined to be the set of trajectories that satisfy Pontryagin's maximum principle, a necessary condition for optimality.

The successful execution of any contact task fundamentally requires the application of wrenches (forces and moments) consistent with the task. We develop an algorithm for computing the entire set of wrenches consistent with achieving a given augmented contact mode (e.g., sliding at contact 1, rolling at contact 2, and approaching potential contact 3) for one fixed and one moving part in the plane.

This paper applies Pontryagin's maximum principle to the time optimal control of differential drive mobile robots with velocity bounds. The maximum principle gives necessary conditions for time optimality. Extremal trajectories are those which satisfy these conditions, and are thus a superset of the time optimal trajectories. This paper derives a compact geometrical structure for extremal trajectories and shows that extremal trajectories are always composed of rotations about the robot center and straight line motions. Further necessary conditions are obtained.

A differential drive robot is perhaps the simplest type of mobile robot, and the bounded velocity model is perhaps the simplest useful model of the admissible controls. This paper develops the bounded velocity model for differential drive mobile robots, and derives the time-optimal trajectories.