Discrete Configuration Space Research Articles

Workspace decomposition based path planning for fruit-picking robot in complex greenhouse environment

The working environment of fruit-picking robots is very complicated. Generally, there are a large number of obstacles such as branches, immature crops, etc. Besides, the agricultural scene is not as static. For sampling-based methods such as Probabilistic RoadMap (PRM) and Rapidly-exploring Random Trees (RRT), they suffer from inferior path quality in obstacle condensed environments. This paper proposes a local search path planning method in the feasible region of fruit-picking robots based on discrete workspace guidance and configuration space exploration correction. It is used to plan the motion of fruit-picking robots for avoiding obstacles and grasping in dynamic and complex agricultural environments. First, the workspace is discretized, which makes the location information of obstacles computable. Then, a connected region path is found to guide the robot to search in the local configuration space. This greatly improves the continuity of the generated paths in the configuration space. The local search is further used to correct the weights of discrete regions of the workspace to find better connected paths with higher planning speed. The experimental results show that the quality of paths planned by proposed method is generally better than that of RRT and RRT-CONNECT, and the planning speed is faster than that of Task-Space RRT (TSRRT). Proposed algorithm enables real-world picking at 10.5 piece/s and a recovery rate of 80.0 %. This method significantly improves the path quality in dynamic and complex agricultural scenarios.

Geometry‐based flipper motion planning for articulated tracked robots traversing rough terrain in real‐time

AbstractTracked robots operating on rough terrain are often equipped with controllable flippers to help themselves overcome large obstacles or gaps. How to automate the control of these auxiliary flippers to achieve autonomous traversal remains an open question, which still necessitates inefficient manual teleoperation in practice. To tackle this problem, this article presents a geometry‐based motion planning method for an articulated tracked robot to self‐control its flippers during autonomous or semiautonomous traversal over rough terrain in urban search and rescue environments. The proposed method is developed by combining dynamic programming with a novel geometry‐based pose prediction method of high computational efficiency, which is applicable for typical challenging rescue terrains, such as stairs, Stepfields, and rails. The efficient pose prediction method allows us to make thousands of predictions about the robot poses at future locations for given flipper configurations within the onboard sensor range. On the basis of such predictions, our method evaluates the entire discretized configuration space and thereby determines the optimal flipper motion online for a smooth traversal over the terrain. The overall planning algorithm is tested with both simulated and real‐world robots and compared with a reinforcement‐learning‐based method using the RoboCup Rescue Robot League standard testing scenarios. The experimental results show that our method enables the robots to automatically control the flippers, successfully go over challenging terrains, and outperform the baseline method in passing smoothness and robustness to different terrains.

Explicit kinematic equationsfor degree-4 rigid origami vertices, Euclidean and non-Euclidean.

We derive algebraic equationsfor the folding angle relationships in completely general degree-4 rigid-foldable origami vertices, including both Euclidean (developable) and non-Euclidean cases. These equationsin turn lead to elegant equationsfor the general developable degree-4 case. We compare our equationsto previous results in the literature and provide two examples of how the equationscan be used: in analyzing a family of square twist pouches with discrete configuration spaces, and for proving that a folding table design made with hyperbolic vertices has a single folding mode.

Multi-Objective Optimal Path Planning for Autonomous Robots with Moving Obstacles Avoidance in Dynamic Environments

Path planning is vital for robust autonomous robot navigation. Driving in dynamic environments is particularly difficult. The majority of the work is based on the premise that a robot possesses a comprehensive and precise representation of its surroundings prior to its starting. The problem of partially knowing and dynamic environments has received little attention. This circumstance occurs when an exploratory robot or a robot without a floor plan or terrain map must move to its destination. Existing approaches for dynamic-path-planning design a preliminary path based-on known knowledge of the environment, then adjust locally by replanning the total path as obstacles are discovered by the robot's sensors, thereby sacrificing either optimality or computational efficacy. This paper presents a novel algorithm. A Near-Optimal Multi-Objective Path Planner (NO-MOPP), capable of planning time-efficient, near-optimal, and drivable paths in partially known and dynamic environments. It is an expansion of our earlier research contributions called "A Multi-Objective Hybrid Collision-free Optimal Path Finder (MOHC-OPF) for Autonomous Robots in known static environments" and "A Multi-Objective Hybrid Collision-free Near-Optimal Path Planner (MOHC-NODPP) for Autonomous Robots in Dynamic environments". In the environment, a mix of static and moving dynamic obstacles are present, both of which are expressed by a hybrid, discrete configuration space in an occupancy-grid map. The proposed approach is executed at two distinct levels. Using our earlier method, A Multi-Objective Collision-free Optimal Path Finder (MOHC-OPF), the initial optimal path is found in environment that includes only known stationery obstacles at the Global-path-planning level. On the second level, known as Local Re-planning, this optimal path is continuously refined by online re-planning to account for the movement of obstacles in the environment. The proposed method, A Near-Optimal Multi-Objective Path Planner (NO-MOPP), is used to keep the robot's sub-paths optimum while also avoiding dynamic obstacles. This is done while still obeying the robot's non-holonomic restrictions. The proposed technique is tested in simulation using a collection of standard maps. The simulation findings demonstrate the proposed method's ability to avoid static as well as dynamic obstacles, as well as its capacity to find a near-optimal-path to a goal location in environments that are constantly changing without collision. The optimal-path is determined by taking into account several performance measures, including path length, collision-free path, execution time, and smooth paths. 90% of studies utilizing the proposed method demonstrate that it is more effective than other methods for determining the shortest length and time-efficient smooth drivable paths. The proposed technique reduced average 15% path length and execution time compared to the existing methods.

Universal Reconfiguration of Facet-Connected Modular Robots by Pivots: The O(1) Musketeers

We present the first universal reconfiguration algorithm for transforming a modular robot between any two facet-connected square-grid configurations using pivot moves. More precisely, we show that five extra “helper” modules (“musketeers”) suffice to reconfigure the remaining n modules between any two given configurations. Our algorithm uses $$O(n^2)$$ pivot moves, which is worst-case optimal. Previous reconfiguration algorithms either require less restrictive “sliding” moves, do not preserve facet-connectivity, or for the setting we consider, could only handle a small subset of configurations defined by a local forbidden pattern. Configurations with the forbidden pattern do have disconnected reconfiguration graphs (discrete configuration spaces), and indeed we show that they can have an exponential number of connected components. But forbidding the local pattern throughout the configuration is far from necessary, as we show that just a constant number of added modules (placed to be freely reconfigurable) suffice for universal reconfigurability. We also classify three different models of natural pivot moves that preserve facet-connectivity, and show separations between these models.

Two-Stage Optimized Trajectory Planning for ASVs Under Polygonal Obstacle Constraints: Theory and Experiments

We propose a method for energy-optimized trajectory planning for autonomous surface vehicles (ASVs), which can handle arbitrary polygonal maps as obstacle constraints. The method comprises two stages: The first is a hybrid A* search that finds a dynamically feasible trajectory in a polygonal map on a discretized configuration space using optimal motion primitives. The second stage uses the resulting hybrid A* trajectory as an initial guess to an optimal control problem (OCP) solver. In addition to providing the OCP with a warm start, we use the initial guess to create convex regions encoded as halfspace descriptions, which converts the inherent nonconvex obstacle constraints into a convex and smooth representation. The OCP uses this representation in order to optimize the initial guess within a collision-free corridor. The OCP solves the trajectory planning problem in continuous state space. Our approach solves two challenges related to optimization-based trajectory planning: The need for a dynamically feasible initial guess that can guide the solver away from undesirable local optima and the ability to represent arbitrary obstacle shapes as smooth constraints. The method can take into account external disturbances such as wind or ocean currents. We compare our method to two similar trajectory planning methods in simulation and have found significant computation time improvements. Additionally, we have validated the method in full-scale experiments in the Trondheim harbor area.

Discrete configuration spaces of squares and hexagons

A fixed fraction of a large box is occupied by tiny spheres; how difficult is it for those spheres to move around in the space available in the box, and how does that difficulty depend on the chosen density? We consider a discrete version of this problem, a generalization of the familiar fifteen-piece sliding puzzle on the 4 by 4 square grid. On larger grids with more pieces and more holes, asymptotically how fast can we move the puzzle into the solved state? We consider these questions for both sliding squares and sliding hexagons, to model very densely packed disks.

Remarks on homotopy equivalence of configuration spaces of a polyhedron

We show that the configuration space F_n(M) of n particles in a compact connected PL manifold M with nonempty boundary partial M is homotopy equivalent to the configuration space F_n({mathrm{Int}}, M) where . Actually we prove some generalization of this result for polyhedra. Similar results recently have been obtained independently for topological manifolds by Zapata (Collision-free motion planning on manifolds with boundary, 2017. arXiv:1710.00293), using different techniques. We also address the question of whether a compact PL manifold M can be approximated up to homotopy type by discrete configuration spaces defined combinatorially via a simplicial subdivision of M.

Advances in milestoning. II. Calculating time-correlation functions from milestoning using stochastic path integrals.

In the milestoning framework, and more generally in related transition interface sampling schemes, one significantly enhances the calculation of relaxation rates for complex equilibrium kinetics from molecular dynamics simulations between the milestones or interfaces. The goal of the present paper is to advance milestoning applications into the realm of non-equilibrium statistical mechanics, in particular, to calculate entire time correlation functions. In order to accomplish this, we introduce a novel methodology for obtaining the flux through a given milestone configuration as a function of both time and initial configuration and build upon it with a novel formalism describing autocorrelation for Langevin motion in a discrete configuration space. The method is then applied to three different test systems: a harmonic oscillator, which we solve analytically, a two-well potential, which is solved numerically, and an atomistic molecular dynamics simulation of alanine dipeptide.

Discretized configurations and partial partitions

We show that the discretized configuration space of $k$ points in the $n$-simplex is homotopy equivalent to a wedge of spheres of dimension $n-k+1$. This space is homeomorphic to the order complex of the poset of ordered partial partitions of $\{1,...,n+1\}$ with exactly $k$ parts. We compute the exponential generating function for the Euler characteristic of this space in two different ways, thereby obtaining a topological proof of a combinatorial recurrence satisfied by the Stirling numbers of the second kind.

A Generalized Free Energy Perturbation Theory Accounting for End States with Differing Configuration Space Volume

We present a generalized free energy perturbation theory that is inspired by Monte Carlo techniques and based on a microstate description of a transformation between two states of a physical system. It is shown that the present free energy perturbation theory stated by the Zwanzig equation follows as a special case of our theory. Our method uses a stochastic mapping of the end states that associates a given microstate from one ensemble with a microstate from the adjacent ensemble according to a probability distribution. In contrast, previous free energy perturbation methods use a static, deterministic mapping that associates fixed pairs of microstates from the two ensembles. The advantages of our approach are that end states of differing configuration space volume can be treated easily also in the case of discrete configuration spaces and that the method does not require the potentially cumbersome search for an optimal deterministic mapping. The application of our theory is illustrated by some example problems. We discuss practical applications for which our findings could be relevant and point out perspectives for further development of the free energy perturbation theory.

On the construction of discretized configuration space of manipulators

In this research, we study the construction of configuration space (C-space) of manipulators. The proposed approach is based upon precomputing the global topology of a robot's free space, and consists of an offline phase and an online phase. In the offline phase, a C-space obstacle database (COD) for a given robot is developed in which the C-space obstacle (C-obstacle) maps are stored and indexed by the cells of the workspace; in the online phase when the same robot is operated in a real environment, those maps whose indices match the real obstacle cells are identified and then extracted from the COD. The superposition of these maps forms forbidden region in operation. This proposed approach is a generic one and can be applied to manipulators with arbitrary kinematic structures and geometries. The construction of the COD, which is generally the most time-consuming step, is implemented in the offline phase, and the online computing only involves the identification of the components matching the COD indices. Therefore, this proposed approach for C-space construction can be realized in a real-time online fashion and is especially suitable for robot manipulation under dynamic operations. We carry out analyses on several types of manipulators to verify and demonstrate the feasibility and efficiency of the proposed approach.

Real-time Monte-Carlo simulations for dissipative tight-binding systems and time local master equations

The numerically exact path integral Monte-Carlo approach for the real-time evolution of dissipative quantum systems (PIMC), particularly suited for systems with discrete configuration space (tight-binding systems), is extended to treat spatially continuous and correlated many-body systems. This way, one has to consider generalized tight-binding lattices with either non-equidistant spacing or in higher dimensions, which in turn allows to analyze to what extent Markovian master equations can be applied beyond the usually studied spin-boson type of models.

Superselection from canonical constraints

The evolution of both quantum and classical ensembles may be described via the probability density P on configuration space, its canonical conjugate S, and an_ensemble_ Hamiltonian H[P,S]. For quantum ensembles this evolution is, of course, equivalent to the Schroedinger equation for the wavefunction, which is linear. However, quite simple constraints on the canonical fields P and S correspond to_nonlinear_ constraints on the wavefunction. Such constraints act to prevent certain superpositions of wavefunctions from being realised, leading to superselection-type rules. Examples leading to superselection for energy, spin-direction and `classicality' are given. The canonical formulation of the equations of motion, in terms of a probability density and its conjugate, provides a universal language for describing classical and quantum ensembles on both continuous and discrete configuration spaces, and is briefly reviewed in an appendix.

Path planning for a quadruped robot: an artificial field approach

In this paper, we consider the problem of planning a feasible path for a quadruped walking robot in an environment of obstacles. In conventional path-planning problems, the main focus is merely collision avoidance with obstacles since a wheeled robot is involved. However, in the case of a legged robot, both collision avoidance and crossing over obstacles must be taken into account in the process of path planning. Furthermore, the constraints of the gait should be considered to guarantee the feasibility of a planned path. To resolve this complicated problem in a systematic way, a new concept of an artificial thermal field is proposed. Specifically, with the assumption that a robot walks with a periodic crab gait, a robot and obstacles in a three-dimensional (3D) space are projected on a 2D plane. Next, the 2D obstacles are transformed into the configuration space of a quadruped robot. A feasible path is finally sought in an artificial thermal field which is constructed numerically on the discretized configuration space. To verify the efficacy of the proposed approach, three notable simulation results are provided.

Algorithms for rough terrain trajectory planning

This paper deals with motion planning on rough terrain for mobile robots. The aim is to develop efficient algorithms, suitable for various types of robots. On rough terrain, the planned trajectory must verify several validity constraints : stability of the robot, mechanical limits and collision avoidance with the ground. Our approach relies on a static and kinematic model of the robot. Efficient geometric algorithms have been developed, taking advantage of each vehicle's specificities. Motion planning relies on an incremental search in the discretized configuration space and uses efficient heuristics based on terrain characteristic to limit the size of the search space. Simulation results present trajectories planned in a few seconds. The second part takes into account uncertainties to improve trajectory robustness: uncertainties on the terrain model and the position of the robot. The adaptation of the previous algorithms allows us to find robust trajectories, without any excessive time increase.

A new solution for path planning in partially known or unknown environment for nonholonomic mobile robots

This paper presents the theoretical analysis of different methods, which can be used in online path generation for mobile robots with nonholonomic constraints in a partially known workspace. Then the new method is introduced which works very fast and gives the optimal path in a complex environment. The algorithm of the presented method is based on A∗ graph searching with the nodes placed in the discretized configuration space. This paper is focused on the analysis of different heuristic cost functions and introduces a new statement of this function. The presented method is equipped with the procedures of fast path replanning — very useful in partially known workspaces. The series of simulation tests and experimental results of online control for car-like robot are also discussed.

Self-organization and mismatch tolerance in protein folding: General theory and an application

The folding of a protein is a process both expeditious and robust. The analysis of this process presented here uses a coarse, discretized representation of the evolving form of the backbone chain, based on its torsional states. This coarse description consists of discretizing the torsional coordinates modulo the Ramachandran basins in the local softmode dynamics. Whenever the representation exhibits “contact patterns” that correspond to topological compatibilities with particular structural forms, secondary and then tertiary, the elements constituting the pattern are effectively entrained by a reduction of their rates of exploration of their discretized configuration space. The properties “expeditious and robust” imply that the folding protein must have some tolerance to both torsional “frustrated” and side-chain contact mismatches which may occur during the folding process. The energy-entropy consequences of the staircase or funnel topography of the potential surface should allow the folding protein to correct these mismatches, eventually. This tolerance lends itself to an iterative pattern-recognition-and-feedback description of the folding process that reflects mismatched local torsional states and hydrophobic/polar contacts. The predictive potential of our algorithm is tested by application to the folding of bovine pancreatic trypsin inhibitor (BPTI), a protein whose ability to form its active structure is contingent upon its frustration tolerance.

Computational Complexity for Continuous Time Dynamics

Dissipative flows model a large variety of physical systems. In this Letter the evolution of such systems is interpreted as a process of computation; the attractor of the dynamics represents the output. A framework for an algorithmic analysis of dissipative flows is presented, enabling the comparison of the performance of discrete and continuous time analog computation models. A simple algorithm for finding the maximum of n numbers is analyzed, and shown to be highly efficient. The notion of tractable (polynomial) computation in the Turing model is conjectured to correspond to computation with tractable (analytically solvable) dynamical systems having polynomial complexity. The computation of a digital computer, and its mathematical abstraction, the Turing machine is described by a map on a discrete configuration space. In recent years scientists have developed new approaches to computation, some of them based on continuous time analog systems. The most promising are neuromorphic systems [1], models of human memory [2], and experimentally realizable quantum computers [3]. Although continuous time systems are widespread in experimental realizations, no theory exists for their algorithmic analysis. The standard theory of computation and computational complexity [4] deals with computation in discrete time and in a discrete configuration space, and is inadequate for the description of such systems. This Letter describes an attempt to fill this gap. Our model of a computer is based on dissipa

On quasi-number algebras

Generalizations of complex numbers suggested by Weierstrass, Bruwier, Mikusiński et al. are investigated in detail. These generalizations are intrinsincly related to hyperbolic and elliptic mappings via polar representation of “quasi-numbers” proposed by Fleury et al. Relevance of these quasi-number systems to Potts-like models, fractals and Weyl's finite quantum mechanics with discrete configuration space is indicated. The note is based on [0].