This work presents a new path classification criterion to distinguish paths geometrically and topologically from the workspace, which is divided through cell decomposition, generating a medial-axis-like skeleton structure. We use this information as well as the topology of the robot to bound and classify different paths in the configuration space. We show that the path class found by the proposed method is equivalent to and finer than the path class defined by the homotopy of paths. The proposed path classes are easy to compute, compare, and can be used for various planning purposes. The classification builds heavily upon the topology of the robot and the geometry of the workspace, leading to an alternative fiber-bundle-based description of the configuration space. We introduce a planning framework to overcome obstacles and narrow passages using the proposed path classification method and the resulting path classes.

We present a novel method for extracting geometric and topological features from a robot’s configuration space. To accomplish this, we define a discrete Morse function on the Vietoris-Rips simplicial complex to identify critical points on the surface of obstacles present. These critical points serve as waypoints for determining feasible bounds near an identified obstacle. This work builds on previous work that provides a method to approximate the number of samples required to generate pathways. Our results achieve near-optimal paths with a low computation time and reduced path distance in this work. We conduct experiments in different environments and with various robots, including the Kuka YouBot and PR2 robots in simulation, and demonstrate the performance gains compared to state-of-the-art methods.

This work presents the analysis of the properties of the shortest path control synthesis for the rigid body system. The systems we focus on in this work have only kinematic constraints. However, even for seemingly simple systems and constraints, the shortest paths for generic rigid body systems were only found recently, especially for 3D systems. Based on the Pontraygon's Maximum Principle (MPM) and Lagrange equations, we present the necessary conditions for optimal switches, which form the control synthesis boundaries. We formally show that the shortest path for nearby configurations will have similar adjoint functions and parameters, i.e., Lagrange multipliers. We further show that the gradients of the necessary condition equation can be used to verify whether a configuration is inside a control synthesis region or on the boundary. We present a procedure to find the shortest kinematic paths and control synthesis, using the gradients of the control constraints. Given the shortest path and the corresponding control sequences, the optimal control sequence for nearby configurations can be derived if and only if they belong to the same control synthesis region. The proposed procedure can work for both 2D and 3D rigid body systems. We use a 2D Dubins vehicle system to verify the correctness of the proposed approach. More verifications and experiments will be presented in the extensions of this work.

In this work, we present a workspace-based planning framework, which though using redundant workspace key-points to represent robot states, can take advantage of the interpretable geometric information to derive good quality collision-free paths for even complex robots. Using workspace geometries, we first find collision-free piece-wise linear paths for each key point so that at the endpoints of each segment, the distance constraints are satisfied among the key points. Using these piece-wise linear paths as initial conditions, we can perform optimization steps to quickly find paths that satisfy various constraints and piece together all segments to obtain a valid path. We show that these adjusted paths are unlikely to create a collision, and the proposed approach is fast and can produce good quality results.

We study a pursuit-evasion problem which can be viewed as an extension of the keep-away game. In the game, pursuer(s) will attempt to intersect or catch the evader, while the evader can visit a fixed set of locations, which we denote as the anchors. These anchors may or may not be stationary. When the velocity of the pursuers is limited and considered low compared to the evaders, we are interested in whether a winning strategy exists for the pursuers or the evaders, or the game will draw. When the anchors are stationary, we show an algorithm that can help answer the above question. The primary motivation for this study is to explore the boundaries between kinematic and dynamic constraints. In particular, whether the solution of the kinematic problem can be used to speed up the search for the problems with dynamic constraints and how to discretize the problem to utilize such relations best. In this work, we show that a geometric branch-and-bound type of approach can be used to solve the stationary anchor problem, and the approach and the solution can be extended to solve the dynamic problem where the pursuers have dynamic constraints, including velocity and acceleration bounds.

Dynamic tensegrity robots are inspired by tensegrity structures in architecture; arrangements of rigid rods and flexible elements allow the robots to deform. This work proposes the use of multiple, modular, tensegrity robots that can move and compliantly connect to assemble larger, compliant, lightweight, strong structures, and scaffolding. The focus is on proof-of-concept designs for the modular robots themselves and their docking mechanisms, which can allow the easy deployment of structures in unstructured environments. These mechanisms include (electro)magnets to allow each individual robot to connect and disconnect on cue. An exciting direction is the design of specific module and structure designs to fit the mission at hand. For example, this work highlights how the considered three bar structures could stack to form a column or deform on one side to create an arch. A critical component of future work will involve the development of algorithms for automatic design and layout of modules in structures.

In this work, we analyze and present an algorithm to find shortest-paths for generic rigid bodies. We derived the necessary conditions for optimality using Lagrange multipliers, and compared it to the conditions derived from Pontraygin’s Maximum Principle. We derived the equations of the necessary conditions using geometric Jacobian, drawing inspiration from the similarity between the rigid-body systems and the arm-like systems. In the previous work [30], the analysis focused on finding shortest-paths to reach goals in positions only. This work extends the analysis to find the shortest-path to reach a goal with complete configuration in 3D. We show that the algorithm is resolution complete even when the orientations are included. To overcome the complexity of 3D orientations, we describe the system using three points in the robot frame, and show that this parameter system is redundant but can derive the same necessary conditions as those derived using the minimum parameters (configuration). We used a 3D Dubins system to demonstrate the correctness of the analysis and the algorithm.

This paper presents a first low-cost autonomous robotic system for underwater assembly of mortarless structures. The long-term goal is to enable the construction of large-scale underwater structures, such as retaining walls and artificial reefs. The approach follows the principle of co-design; the 2-DOF manipulator and blocks are designed to complement the localization and control strategies. The blocks and gripper are designed with a connector geometry that removes error during pickup of blocks and drop assembly. This error correction feature allows a simplification of localization and control, which are based on fiducial markers on custom platforms. We developed the proposed system on a low-cost heavily modified BlueROV2 autonomous vehicle - which we call Droplet - with a two-degree of freedom hand that can open and close a gripper and rotate over the yaw. We performed extensive experiments in the pool to evaluate each component and the system as a whole. Results showed a 100 % success rate in dropping blocks in the presence of some localization and control errors as well as the assembly of several different 3D structures composed of up to eight blocks.

为了查找高压洗涤器换热管出现微裂纹并发生泄漏的原因,分析了高压洗涤器换热管检修数据、高压调温水运行数据和换热管失效部位,通过计算机辅助模拟换热管失效过程,发现:奥氏体不锈钢换热管泄漏是由氯离子应力腐蚀造成的.提出了运行建议措施:对壳程介质成分要精确控制,控制氯离子质量浓度小于5 mg/L,在高压调温水入口处增加防冲挡板.

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.

Tensegrity-based robots can achieve locomotion through shape deformation and compliance. They are highly adaptable to their surroundings, have light weight, low cost and high endurance. Their high dimensionality and highly dynamic nature, however, complicate motion planning. So far, only rudimentary quasi-static solutions have been achieved, which do not utilize tensegrity dynamics. This work explores a spectrum of planning methods that increasingly allow dynamic motion for such platforms. Symmetries are first identified for a prototypical spherical tensegrity robot, which reduce the number of needed gaits. Then, a numerical process is proposed for generating quasi-static gaits that move forward the system’s center of mass in different directions. These gaits are combined with a search method to achieve a quasi-static solution. In complex environments, however, this approach is not able to fully explore the space and utilize dynamics. This motivates the application of sampling-based, kinodynamic planners. This paper proposes such a method for tensegrity locomotion that is informed and has anytime properties. The proposed solution allows the generation of dynamic motion and provides good quality solutions. Evaluation using a physics-based model for the prototypical robot highlight the benefits of the proposed scheme and the limits of quasi-static solutions.

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 presents a data structure that summarizes distances between configurations across a robot configuration space, using a binary space partition whose cells contain parameters used for a locally linear approximation of the distance function. Querying the data structure is extremely fast, particularly when compared to the graph search required for querying Probabilistic Roadmaps, and memory requirements are promising. The paper explores the use of the data structure constructed for a single robot to provide a heuristic for challenging multi-robot motion planning problems. Potential applications also include the use of remote computation to analyze the space of robot motions, which then might be transmitted on-demand to robots with fewer computational resources.

This paper presents a data structure that summarizes distances between configurations across a robot configuration space, using a binary space partition whose cells contain parameters used for a locally linear approximation of the distance function. Querying the data structure is extremely fast, particularly when compared to graph search required for querying Probabilistic Roadmaps, and memory requirements are promising. The paper explores the use of the data structure constructed for a single robot to provide a heuristic for challenging multi-robot motion planning problems. Potential applications also include the use of remote computation to analyze the space of robot motions, which then might be transmitted on-demand to robots with fewer computational resources.

We present a new way of constructing sparse roadmaps using point clouds that approximates and measures the underlying topology of the C free space. The main advantage of the constructed roadmap is its homotopy equivalence to the η-offset of the C free space. Though only used to plan paths as a regular roadmap in this work, because the roadmap preserves the topology of the underlying sampled space, the information can be used to plan paths beyond the simple connection of graph vertices. To construct the roadmap, we first sample the configuration space so that the resulting graph is a n-skeleton graph that constructs a Vietoris-Rips (VR) complex. Then, we perform a series of topological collapses to remove vertices from the graph while still preserving its topological properties. The resulting roadmaps are used to plan paths for different robots and the experimental results show that the proposed topological approach is faster and more feasible in complex high-dimensional spaces.

Tensegrity-based robots can achieve locomotion through shape deformation and compliance. They are highly adaptable to their surroundings, and are lightweight, low cost, and physically robust. Their high dimensionality and strongly dynamic nature, however, can complicate motion planning. Efforts to date have primarily considered quasi-static reconfiguration and short-term dynamic motion of tensegrity robots, which do not fully exploit the underlying system dynamics in the long term. Longer-horizon planning has previously required costly search over the full space of valid control inputs. This work synthesizes new and existing approaches to produce dynamic long-term motion while balancing the computational demand. A numerical process based upon quasi-static assumptions is first applied to deform the system into an unstable configuration, causing forward motion. The dynamical characteristics of the result are then altered via a few simple parameters to produce a small but diverse set of useful behaviors. The proposed approach takes advantage of identified symmetries on the prototypical spherical tensegrity robot, which reduce the number of needed gaits but allow motion along different directions. These gaits are first combined with a standard search method to achieve long-term planning in environments where the developed gaits are effective. For more complex environments, the various motion primitives are paired with the fall-back option of random valid actions and are used by an informed sampling-based kinodynamic motion planner with anytime properties. Evaluations using a physics-based model for the prototypical robot demonstrate that modest but efficiently applied search effort can unlock the utility of dynamic tensegrity motion to produce high-quality solutions.

The distributed nature of policy violations in spectrum sharing necessitate the use of mobile autonomous agents (e.g., UAVs, self-driving cars, and crowdsourcing) to implement cost-effective enforcement systems. We define this problem as multiagent planning with cardinality (MPC), where cardinality represents multiple, unique agents visiting each infraction location to collectively improve the accuracy of the enforcement tasks. Designed as a practical and deployable system, our solution leverages crowdsourced information to determine the optimum cardinality and provide a routing schedule for the agents to achieve the desired level of accuracy of detection and localization at minimum possible cost. We show that by estimating spatial orientation of the agents with single antenna, the accuracy is improved by 96% over crowdsourcing only. Using geographical maps as the basis, we solve the scheduling problem with a 3-approximation ratio in polynomial time that exhibits statistically similar performance under variety of urban locale across multiple continents. The longest path traversed by an agent on average is 1.2 km per unit diagonal length of a rectangular geographic area, even when there are twice as many infractions as agents. Deploying UAVs to the estimated region of infraction improves localization accuracy by approximate to 70% compared to ground vehicles.

This paper analyzes the physical resources necessary and sufficient to tie a knot of given structure. We present the first sufficient bound on the number of fingers required to tie a given knot; the bound is linear in the number of crossings appearing in the knot diagram for a given knot. We also present a lower bound on the required number of fingers, under a particular model of knot tying. We study how many re-grasps are sufficient to tie an arbitrary knot, and present an algorithm that can yield a small sufficient number of re-grasps to tie the given knot. Physical experiments in which different knots are tied and untied by robots, alone and in collaboration with a human, serve as a proof of concept to show the simplicity and correctness of the approach.

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.