Collision-free Configurations Research Articles

A barrier method for contact avoiding particles in Stokes flow

Rigid particles in a Stokesian fluid experience an increasingly strong lubrication resistance as particle gaps narrow. Numerically, resolving these lubrication forces comes at an intractably large cost, even for moderate system sizes. Hence, it can typically not be guaranteed that artificial particle collisions and overlaps do not occur in a dynamic simulation, independently of the choice of method to solve the Stokes equations. In this work, the potentially large set of non-overlap constraints, in terms of the Euclidean distance between boundary points on disjoint particles, are efficiently represented via a barrier energy. We solve for the minimum magnitudes of repelling contact forces and torques between any particle pair in contact to correct for overlaps by enforcing a zero barrier energy at the next time level, given a contact-free configuration at a previous instance in time. Robustness for the method is illustrated using a multiblob method to solve the mobility problem in Stokes flow, applied to suspensions of spheres, rods and boomerang shaped particles. Collision free configurations are obtained at all instances in time, and considerably larger time-steps can be taken than without the technique. The effect of the contact forces on the collective order of a set of rods in a background flow that naturally promote particle interactions is also illustrated.

Certified polyhedral decompositions of collision-free configuration space

Understanding the geometry of collision-free configuration space (C-free) in the presence of Cartesian-space obstacles is an essential ingredient for collision-free motion planning. While it is possible to check for collisions at a point using standard algorithms, to date no practical method exists for computing C-free regions with rigorous certificates due to the complexity of mapping Cartesian-space obstacles through the kinematics. In this work, we present the first to our knowledge rigorous method for approximately decomposing a rational parametrization of C-free into certified polyhedral regions. Our method, called C-Iris (C-space Iterative Regional Inflation by Semidefinite programming), generates large, convex polytopes in a rational parameterization of the configuration space which are rigorously certified to be collision-free. Such regions have been shown to be useful for both optimization-based and randomized motion planning. Based on convex optimization, our method works in arbitrary dimensions, only makes assumptions about the convexity of the obstacles in the 3D Cartesian space, and is fast enough to scale to realistic problems in manipulation. We demonstrate our algorithm’s ability to fill a non-trivial amount of collision-free C-space in several 2-DOF examples where the C-space can be visualized, as well as the scalability of our algorithm on a 7-DOF KUKA iiwa, a 6-DOF UR3e, and 12-DOF bimanual manipulators. An implementation of our algorithm is open-sourced in Drake . We furthermore provide examples of our algorithm in interactive Python notebooks .

A Hierarchical Motion Planning Method for Mobile Manipulator.

This paper focuses on motion planning for mobile manipulators, which includes planning for both the mobile base and the manipulator. A hierarchical motion planner is proposed that allows the manipulator to change its configuration autonomously in real time as needed. The planner has two levels: global planning for the mobile base in two dimensions and local planning for both the mobile base and the manipulator in three dimensions. The planner first generates a path for the mobile base using an optimized A* algorithm. As the mobile base moves along the path with the manipulator configuration unchanged, potential collisions between the manipulator and the environment are checked using the environment data obtained from the on-board sensors. If the current manipulator configuration is in a potential collision, a new manipulator configuration is searched. A sampling-based heuristic algorithm is used to effectively find a collision-free configuration for the manipulator. The experimental results in simulation environments proved that our heuristic sampling-based algorithm outperforms the conservative random sampling-based method in terms of computation time, percentage of successful attempts, and the quality of the generated configuration. Compared with traditional methods, our motion planning method could deal with 3D obstacles, avoid large memory requirements, and does not require a long time to generate a global plan.

A snake-inspired path planning algorithm based on reinforcement learning and self-motion for hyper-redundant manipulators

Redundant manipulators are flexible enough to adapt to complex environments, but their controller is also required to be specific for their extra degrees of freedom. Inspired by the morphology of snakes, we propose a path planning algorithm named Swinging Search and Crawling Control, which allows the snake-like redundant manipulators to explore in complex pipeline environments without collision. The proposed algorithm consists of the Swinging Search and the Crawling Control. In Swinging Search, a collision-free manipulator configuration that of the end-effector in the target point is found by applying reinforcement learning to self-motion, instead of designing joint motion. The self-motion narrows the search space to the null space, and the reinforcement learning makes the algorithm use the information of the environment, instead of blindly searching. Then in Crawling Control, the manipulator is controlled to crawl to the target point like a snake along the collision-free configuration. It only needs to search for a collision-free configuration for the manipulator, instead of searching collision-free configurations throughout the process of path planning. Simulation experiments show that the algorithm can complete path planning tasks of hyper-redundant manipulators in complex environments. The 16 degrees of freedom and 24 degrees of freedom manipulators can achieve 83.3% and 96.7% success rates in the pipe, respectively. In the concentric pipe, the 24 degrees of freedom manipulator has a success rate of 96.1%.

Division-merge based inverse kinematics for multi-DOFs humanoid robots in unstructured environments

A Two-step Division-Merge (TDM) based inverse kinematics (IK) mechanism is proposed for robots with multiple degrees of freedom (multi-DOFs) in unstructured environments. For any robot with n-DOFs (n>6), a division point is selected first to divide it into a lower part subsystem from its base to the division point, together with an upper part one from the point to its end-effector. Once a collision-free configuration is found for the upper part subsystem to match with the target, the lower part subsystem is then planned to merge with the upper part subsystem at the division point. Specifically, the division point is selected such that the lower part subsystem has 6-DOFs, while the upper part subsystem has (n-6)-DOFs. Furthermore, a Reverse & Random Rotation (RRR) algorithm is also proposed to solve the IK of the upper part subsystem in unstructured environments, while the IK of the lower part subsystem is solved analytically. The proposed TDM based mechanism is verified via experiments using a lab-customized humanoid apple harvesting robot with 11- and 13-DOFs, respectively. Under the various scenarios with different target and obstacle configurations, errors in position coordinates and orientation angles between the target pose and those of the end-effector obtained with forward kinematics (FK) are calculated. Results show that the errors in position and orientation are less than 0.005 mm and 0.007°, respectively, and the average computational time is less than 2 s for the IK solution of the entire robot. Such results indicate that the proposed mechanism is reliable and capable of reducing the complexity of IK for multi-DOFs humanoid robots. With the proposed algorithm, the apple harvesting success rate of a lab-customized 11-DOFs robot reaches 89.2%, which can be further increased up to 93.3% with error compensation, while the average time starting from the robot action to the end-effector reaching the target pose of the apple is around 12.3 s.

Optimal Trajectory Generation for Intelligent Vehicles in Complex Traffic Based on Iteration Convex Optimization

Intelligent vehicles face considerable challenges in the complex traffic environment since they need to deal with various constraints and elements. This dissertation puts forward a novel trajectory planning framework for intelligent vehicles to generate safe and optimal driving trajectories. First, we design a spatiotemporal occupancy framework to deal with all kinds of elements in the complex driving environment based on the Frenét frame. This framework unifies various constraints on the road in the three-dimensional spatiotemporal representation and clearly describes the collision-free configuration space. Then we use the convex approximation method to construct a time-varying convex feasible region based on the above accurate temporal and spatial description. We formulate the trajectory planning problem as a standard quadratic programming formulation with collision-free and dynamics constraints. Finally, we apply the iterative convex optimization algorithm to solve the quadratic programming problem in the time-varying convex feasible region. Moreover, we design several typical experimental scenarios and have verified that the proposed method has good effectiveness and real-time.

Morse Theory for S-balanced Configurations in the Newtonian n-body Problem

For the Newtonian (gravitational) n-body problem in the Euclidean d-dimensional space, the simplest possible solutions are provided by those rigid motions (homographic solutions) in which each body moves along a Keplerian orbit and the configuration of the n-body is a (constant up to rotations and scalings) central configuration. For dle 3, the only possible homographic motions are those given by central configurations. For d ge 4 instead, new possibilities arise due to the higher complexity of the orthogonal group mathrm {O}(d), as observed by Albouy and Chenciner (Invent Math 131(1):151–184, 1998). For instance, in mathbb {R}^4 it is possible to rotate in two mutually orthogonal planes with different angular velocities. This produces a new balance between gravitational forces and centrifugal forces providing new periodic and quasi-periodic motions. So, for dge 4 there is a wider class of S-balanced configurations (containing the central ones) providing simple solutions of the n-body problem, which can be characterized as well through critical point theory. In this paper, we first provide a lower bound on the number of balanced (non-central) configurations in mathbb {R}^d, for arbitrary dge 4, and establish a version of the 45^circ -theorem for balanced configurations, thus answering some of the questions raised in Moeckel (Central configurations, 2014). Also, a careful study of the asymptotics of the coefficients of the Poincaré polynomial of the collision free configuration sphere will enable us to derive some rather unexpected qualitative consequences on the count of S-balanced configurations. In the last part of the paper, we focus on the case d=4 and provide a lower bound on the number of periodic and quasi-periodic motions of the gravitational n-body problem which improves a previous celebrated result of McCord (Ergodic Theory Dyn Syst 16:1059–1070, 1996).

Implicit untangling

We propose a robust method for untangling an arbitrary number of cloth layers, possibly exhibiting deep interpenetrations, to a collision-free state, ready for animation. Our method relies on an intermediate, implicit representation to solve the problem: the user selects a few garments stored in a library together with their implicit approximations, and places them over a mannequin while specifying the desired order between layers. The intersecting implicit surfaces are then combined using a new family of N-ary composition operators, specially designed for untangling layers. Garment meshes are finally projected to the deformed implicit surfaces in linear time, while best preserving triangles and avoiding loss of details. Each of the untangling operators computes the target surface for a given garment in a single step, while accounting for the order between cloth layers and their individual thicknesses. As a group, they guarantee an intersection-free output configuration. Moreover, a weight can be associated with each layer to tune their relative influence during untangling, such as leather being less deformed than cloth. Results for each layer then reflect the combined effect of the other layers, enabling us to output a plausible configuration in contact regions. As our results show, our method can be used to generate plausible, new static shapes of garments when underwear has been added, as well as collision-free configurations enabling a user to safely launch animations of arbitrarily complex layered clothing.

An efficient motion generation method for redundant humanoid robot arms based on motion continuity

ABSTRACTThis paper proposes a novel method of motion generation for redundant humanoid robot arms, which can efficiently generate continuous collision-free arm motion for the preplanned hand trajectory. The proposed method generates the whole arm motion first and then computes the actuators’ motion, which is different from IK (inverse kinematics)-based motion generation methods. Based on the geometric constraints of the preplanned trajectory and the geometric structure of humanoid robot arms, the wrist trajectory and elbow trajectory can be got first without solving inverse kinematics and forward kinematics. Meanwhile, the constraints restrict all feasible arm configurations to an elbow-circle and reduce the arm configuration space to a two-dimension space. By combining the configuration space and collision distribution of arm motion, collision-free arm configurations can be identified and be used to generate collision-free arm motion, which can avoid unnecessary forward and inverse kinematics. The experiments show that the proposed method can generate continuous and collision-free arm motion for preplanned hand trajectories.

Probabilistic Roadmaps with Higher Expressive Power

Sampling-based motion planning had an enormous impact on robot motion planning because of its efficiency and scalability. Many sampling-based motion planners construct a probabilistic roadmap (PRM) that captures the connectivity of the robot's free configuration space. A valid node of a PRM contains a collision-free robot configuration (also known as a sample) and a valid edge of a PRM connects two valid nodes with a collision-free path. Nodes connected by an edge are usually also required to satisfy additional requirements based on the distance between them. PRM planners use PRMs. Increasing the expressive power will allow PRMs to be used for a wider set of motion planning problems. In this paper we report on increasing the expressive power of PRMs by including the following five features in PRMs-nodes with multiple samples that need not be organized as a graph, temporal intervals of validity of nodes and edges, nodes with samples of multiple robots, special edges for the state transitions performed by humans sharing a workspace with robots, and conditional validity of samples and edges. We report on motion planning problems solvable using these new features.

Optimized joint motion planning for redundant industrial robots

Abstract The paper presents a model and solution method for optimized robot joint motion planning of redundant industrial robots that execute a set of tasks in a complex work environment, in face of various technological and geometric constraints. The approach aims at directly exploiting redundancy to optimize a given performance measure, e.g., cycle time. Alternative configurations along the path are captured in a graph model, whereas bi-directional transition between task and configuration spaces facilitates generating relevant, collision-free configurations only. Re-parametrization of the trajectory warrants compliance with the robot's kinematic constraints. Successful application of the method is demonstrated in remote laser welding.

Topological trajectory classification with filtrations of simplicial complexes and persistent homology

In this work, we present a sampling-based approach to trajectory classification which enables automated high-level reasoning about topological classes of trajectories. Our approach is applicable to general configuration spaces and relies only on the availability of collision free samples. Unlike previous sampling-based approaches in robotics which use graphs to capture information about the path-connectedness of a configuration space, we construct a multiscale approximation of neighborhoods of the collision free configurations based on filtrations of simplicial complexes. Our approach thereby extracts additional homological information which is essential for a topological trajectory classification. We propose a multiscale classification algorithm for trajectories in configuration spaces of arbitrary dimension and for sets of trajectories starting and ending in two fixed points. Using a cone construction, we then generalize this approach to classify sets of trajectories even when trajectory start and end points are allowed to vary in path-connected subsets. We furthermore show how an augmented filtration of simplicial complexes based on an arbitrary function on the configuration space, such as a costmap, can be defined to incorporate additional constraints. We present an evaluation of our approach in 2-, 3-, 4- and 6-dimensional configuration spaces in simulation and in real-world experiments using a Baxter robot and motion capture data.

Precise gouging-free tool orientations for 5-axis CNC machining

We present a precise approach to the generation of optimized collision-free and gouging-free tool paths for 5-axis CNC machining of freeform NURBS surfaces using flat-end and rounded-end (bull nose) tools having cylindrical shank. To achieve high approximation quality, we employ analysis of hyper-osculating circles (HOCs) (Wang et al., 1993a,b), that have third order contact with the target surface, and lead to a locally collision-free configuration between the tool and the target surface. At locations where an HOC is not possible, we aim at a double tangential contact among the tool and the target surface, and use it as a bridge between the feasible HOC tool paths. We formulate all such possible two-contact configurations as systems of algebraic constraints and solve them. For all feasible HOCs and two-contact configurations, we perform a global optimization to find the tool path that maximizes the approximation quality of the machining, while being gouge-free and possibly satisfying constraints on the tool tilt and the tool acceleration. We demonstrate the effectiveness of our approach via several experimental results.

Probabilistic Roadmaps Based Motion Planning of a 4 Degree of Freedom Robot

In this paper, we used a probabilistic roadmaps(PRM) method to plan a motion path for a 4 degrees of freedom(DOF) robot in static workspace. This methods includes two phases: a learning phase and a query phase. In learning phase, a roadmap is constructed and stored as a graph , in which stores all of the random collision-free configurations in free configuration space denoted by and keeps all of the edges corresponding to feasible paths between these configurations. In query phase, the algorithm tries to connect any given initial and goal configuration to the nodes in the graph. And then the Dijkstra's algorithm searches for a shortest path to concatenate these two nodes. The experiment result demonstrates that this method applying to this 4 degrees of freedom robot works well.

Simultaneous Grasp and Motion Planning: Humanoid Robot ARMAR-III

In this work, we present an integrated approach for planning collision-free grasping motions. Therefore, rapidly exploring random tree (RRT)-based algorithms are used to build a tree of reachable and collision-free configurations. During tree generation, both grasp hypotheses and approach movements toward them are computed. The quality of reachable grasping poses is evaluated using grasp wrench space (GWS) analysis. We present an extension to a dual-arm planner that generates bimanual grasps together with collision-free dual-arm grasping motions. The algorithms are evaluated with different setups in simulation and on the humanoid robot ARMAR-III (Figure 1).

PolyDepth

We present a real-time algorithm that finds the Penetration Depth (PD) between general polygonal models based on iterative and local optimization techniques. Given an in-collision configuration of an object in configuration space, we find an initial collision-free configuration using several methods such as centroid difference, maximally clear configuration, motion coherence, random configuration, and sampling-based search. We project this configuration on to a local contact space using a variant of continuous collision detection algorithm and construct a linear convex cone around the projected configuration. We then formulate a new projection of the in-collision configuration onto the convex cone as a Linear Complementarity Problem (LCP), which we solve using a type of Gauss-Seidel iterative algorithm. We repeat this procedure until a locally optimal PD is obtained. Our algorithm can process complicated models consisting of tens of thousands triangles at interactive rates.

Trajectory Generation of Robot Manipulators Using an Artificial Potential Function and Genetic Algorithms

This work presents the problem of trajectory generation based on the use of artificial potential fields associated to articulated robotic manipulators, in order to find a trajectory so that a manipulator reaches a goal from an initial position without colliding with obstacles within its workspace. The search of a continuous sequence of collision-free configurations between an initial configuration and the final position implies the exploration of a non-linear solution space which can be described and solved with an optimization approach. It does not take into account the use of complex mathematics in an analytical or numerical solution of the inverse kinematics, where are shown manifolds solutions as a result of the angular displacements of each joint of the robot. The genetic algorithm used as strategy, reduces the complexity of the problem, because the geometric connection equations are obtained systematically. In addition, the artificial potential field simulates the attraction and repulsion forces between the goal and the obstacles, where the goal is identified as the global minimum and the obstacles as restricted points. Altogether the potential field and the genetic algorithm generate trajectories for the robot among the obstacles through the design of an appropriate fitness function that effectively drives the manipulator to the desired while avoiding collide with the obstacles.

An efficient trajectory planning approach for autonomous robots in complex bridge environments

This paper presents an efficient trajectory planning approach for a 6DOF robotic manipulator conducting grit-blasting in complex bridge structural environments. The proposed approach extends upon robotic grit-blasting planning and incorporates joint movement minimisation in addition to path length minimisation. A genetic algorithm is implemented to optimise initial path plans based on a heuristic pattern for the coverage of surface areas to be blasted. A customised gradient based method is applied for the generation of collision-free joint configurations for grit-blasting based on the identified path plan. A grit-blasting coverage model is developed for discrete non-planar 3D coverage determination to verify the performance of the plan. Extensive simulation and experimental results are also presented in this paper.

Hough transform for distance computation and collision avoidance

A new technique for collision detection based on the application of the Hough transform is presented in this paper. As a consequence of applying this technique, a method for computing the minimum translational distance (MTD) between two spherically extended polytopes is introduced. This distance algorithm is based on the Gilbert-Johnson-Keerthi (GJK) algorithm. Parameters returned by the MTD algorithm hold collision-free configurations that avoid a predicted collision.

On Delaying Collision Checking in PRM Planning: Application to Multi-Robot Coordination

This paper describes the foundations and algorithms of a new probabilistic roadmap (PRM) planner that is: single-query—instead of pre-computing a roadmap covering the entire free space, it uses the two input query configurations to explore as little space as possible; bi-directional—it explores the robot's free space by building a roadmap made of two trees rooted at the query configurations; and lazy in checking collisions—it delays collision tests along the edges of the roadmap until they are absolutely needed. Several observations motivated this strategy: (1) PRM planners spend a large fraction of their time testing connections for collision; (2) most connections in a roadmap are not on the final path; (3) the collision test for a connection is most expensive when there is no collision; and (4) any short connection between two collision-free configurations has high prior probability of being collision-free. The strengths of single-query and bi-directional sampling techniques and those of delayed collision checking reinforce each other. Experimental results show that this combination reduces planning time by a large factor, making it possible to efficiently handle difficult planning problems, such as problems involving multiple robots in geometrically complex environments. This paper specifically describes the application of the planner to multi-robot planning and compares results obtained when the planner uses a centralized planning approach (PRM planning is then performed in the joint configuration space of the robots) and when it uses a decoupled approach (the PRM planner is invoked several times, first to compute a path of each robot independent of the others, and then to coordinate those paths). On a simulated six-robot welding station combining 36 degrees of freedom, centralized planning has proven to be a much more effective approach than decoupled planning.