High-dimensional Winding-Augmented Motion Planning with 2D topological task projections and persistent homology

This paper presents a novel adaptive approach to fast sampling-based motion planning by learning models of collision and collision-free regions in configuration spaces in an online manner. The proposed approach incrementally learns Gaussian Mixture Models (GMMs) for collision detection in high dimensional configuration spaces. In practical applications for robotic manipulation, the representation of collision and collision-free regions in configuration space can change due to relative motion between the robot base and workspace. We show how to rapidly adapt to such changes by using inverse kinematics to transform the parameters of the Gaussian mixture model to new configurations. The transformed model is initially used as a prior and then continually updated and refined as the RRT planning algorithm proceeds in real-time. This approach is extremely computationally efficient, and our proposed method is compared with traditional sampling-based planning methods on a number of experimental robot arm planning scenarios.

A topological theory initiated recently by the author uses methods of algebraic topology to estimate numerically the character of instabilities arising in motion planning algorithms. The present paper studies random motion planning algorithms and reveals how the topology of the robot's configuration space influences their structure. We prove that the topological complexity of motion planning TC(X) coincides with the minimal n such that there exists an n-valued random motion planning algorithm for the system; here $X$ denotes the configuration space. We study in detail the problem of collision free motion of several objects on a graph G. We describe an explicit motion planning algorithm for this problem. We prove that if G is a tree and if the number of objects is large enough, then the topological complexity of this motion planning problem equals 2m(G)+1 where m(G) is the number of the essential vertices of G. It turns out (in contrast with the results on the collision free control of many objects in space obtained earlier jointly with S. Yuzvinsky) that the topological complexity is independent of the number of particles.

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.

This work presents an efficient framework to generate a motion plan of a robot with high degrees of freedom (e.g., a humanoid robot). High-dimensionality of the robot configuration space often leads to difficulties in utilizing the widely-used motion planning algorithms, since the volume of the decision space increases exponentially with the number of dimensions. To handle complications arising from the large decision space, and to solve a corresponding motion planning problem efficiently, two key concepts are adopted in this work: First, the Gaussian process latent variable model (GP-LVM) is utilized for low-dimensional representation of the original configuration space. Second, an approximate inference algorithm is used, exploiting through the duality between control and estimation, to explore the decision space and to compute a high-quality motion trajectory of the robot. Utilizing the GP-LVM and the duality between control and estimation, we construct a fully probabilistic generative model with which a high-dimensional motion planning problem is transformed into a tractable inference problem. Finally, we compute the motion trajectory via an approximate inference algorithm based on a variant of the particle filter. The resulting motions can be viewed in the supplemental video. ( https://youtu.be/kngEaOR4Esc )

Bin picking using vision based sensors requires accurate estimation of location and pose of the object for positioning the end effector of the robotic arm. The computational burden and complexity depends upon the parametric model adopted for the task. Learning based techniques to implement the scheme using low dimensional manifolds offer computationally more efficient alternatives. In this paper we have employed Locally Linear Embedding (LLE) and Deep Learning (with auto encoders) for manifold learning in the visual domain as well as for the parameters of robotic manipulator for visual servoing. Images of clusters of cylindrical pellets were used as the training data set in the visual domain. Corresponding parameters of the six degrees of freedom robot for picking designated cylindrical pellet formed the training dataset in the robotic configuration space. The correspondence between the weight coefficients of LLE manifold in the visual domain and robotic domain is established through regression. Autoencoders in conjunction with feed forward neural networks were used for learning of correspondence between the high dimensional visual space and low dimensional configuration space. We have compared the results of the two implementations for the same dataset and found that manifold learning using auto encoders resulted in better performance. The eye-in-hand configuration used with KUKA KR5 robotic arm and Basler camera offers a potentially effective and efficient solution to the bin picking problem through learning based visual servoing.

The light collection and concentration subsystem (LCCS) of any concentrating solar thermal (CST) system is composed of the surfaces that collect and concentrate the sunlight and of the input surfaces of the receivers, or receivers’ envelopes, where the light is concentrated. For all commercial CST technologies the LCCS is, together with the power block, the subsystem that has more influence in the overall performance and cost. Thus, its optimization is critical to increase the cost-competitiveness of these systems. This optimization requires, in many cases, the optimization of the position, geometry and size of a very large number of solar collecting and concentrating surfaces as well as the optimization of the shape and size of the input surfaces of the receivers where the sunlight is concentrated. Because a full optimization requires the exploration of a configuration space with a very large number of dimensions, the traditional approach consist in making many initial assumptions to drastically reduce the number of dimensions of the configuration space to a handful, so that the optimization can be carried out using conventional high-end workstations in a matter of hours. However, to achieve relevant breakthroughs and to substantially increase the cost-competitiveness of CST systems a bolder approach is needed, where sophisticated design and analysis tools, engineered from the start to be used in High Performance Computers (HPC), will be combined with sophisticated optimization strategies targeted to explore and find optimal solutions in very high dimensional configuration spaces. This paper presents the first of a series of such design and analysis tools. The tool, call Flux Tracer, partitions the three-dimensional space in which the LCC subsystem under analysis is immersed into volumetric pixels (voxels) and computes the radiant energy flux that traverses each voxel as a function of time. It integrates the energy density in every voxel overtime, providing detailed information regarding how the radiant energy flows in space in a given LCC subsystem and in a given period of time. This information is the cornerstone of the highly sophisticated computational LCC subsystem optimization framework The Cyprus Institute (CYI) is developing, in collaboration with the Australian National University (ANU), targeted to be used in HPC’s.

In order to characterize molecular structures we introduce configurational fingerprint vectors which are counterparts of quantities used experimentally to identify structures. The Euclidean distance between the configurational fingerprint vectors satisfies the properties of a metric and can therefore safely be used to measure dissimilarities between configurations in the high dimensional configuration space. In particular we show that these metrics are a perfect and computationally cheap replacement for the root-mean-square distance (RMSD) when one has to decide whether two noise contaminated configurations are identical or not. We introduce a Monte Carlo approach to obtain the global minimum of the RMSD between configurations, which is obtained from a global minimization over all translations, rotations, and permutations of atomic indices.

The reduction of the kinematics and/or dynamics of a high-DOF robotic manipulator to a low-dimension ldquotask spacerdquo has proven to be an invaluable tool for designing feedback controllers. When obstacles or other kinodynamic constraints complicate the feedback design process, motion planning techniques can often still find feasible paths, but these techniques are typically implemented in the high-dimensional configuration (or state) space. Here we argue that providing a Voronoi bias in the task space can dramatically improve the performance of randomized motion planners, while still avoiding non-trivial constraints in the configuration (or state) space. We demonstrate the potential of task-space search by planning collision-free trajectories for a 1500 link arm through obstacles to reach a desired end-effector position.

Motion planning for robotic manipulation of clothing is a challenging problem as clothing articles have high-dimensional configuration spaces and are computationally expensive to simulate. We present an algorithm for robotic cloth folding that, given a sequence of desired folds, outputs a motion plan consisting of a sequence of primitives for a robot to fold the cloth. Previous work on cloth folding does not take into account the constraints of the robot, and thus produces plans which are often infeasible given the kinematics of robots like the Willow Garage PR2. In this paper we introduce a class of motion primitives that start and end in a subset of the cloth’s state space. To find a sequence of primitives that achieves all required folds, the algorithm takes advantage of the partial ordering inherent in folding, and produces a time-optimal motion plan (given the set of primitives) for the robot if one exists. We describe experiments with a general purpose mobile robotic platform, the PR2, folding articles that require dragging and base motion in addition to folding. Our experiments show that (1) many articles of clothing conform well enough to the assumptions made in our model and (2) this approach allows our robot to perform a wide variety of folds on articles of various sizes and shapes.

Informative path planning is an important and challenging problem in robotics that remains to be solved in a manner that allows for wide-spread implementation and real-world practical adoption. Among various reasons for this, one is the lack of approaches that allow for informative path planning in high-dimensional spaces and non-trivial sensor constraints. In this work we present a sampling-based approach that allows us to tackle the challenges of large and high-dimensional search spaces. This is done by performing informed sampling in the high-dimensional continuous space and incorporating potential information gain along edges in the reward estimation. This method rapidly generates a global path that maximizes information gain for the given path budget constraints. We discuss the details of our implementation for an example use case of searching for multiple objects of interest in a large search space using a fixed-wing UAV with a forward-facing camera. We compare our approach to a sampling-based planner baseline and demonstrate how our contributions allow our approach to consistently out-perform the baseline by 18.0%. With this we thus present a practical and generalizable informative path planning framework that can be used for very large environments, limited budgets, and high dimensional search spaces, such as robots with motion constraints or high-dimensional configuration spaces. [Code] <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sup> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sup> Codebase: https://github.com/castacks/tigris [Video] <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sup> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sup> Video: https://youtu.be/bMw5nUGL5GQ

One difficulty of task-oriented grasp planning is task modeling. In this paper, a manipulation task was modeled by building a non-parametric statistical distribution model from disturbance data captured during demonstrations. This paper proposes a task-oriented grasp quality criterion based on distribution of task disturbance and uses the criterion to search for a grasp that covers the most significant part of the disturbance distribution. To reduce the computational complexity of the search in a high-dimensional robotic hand configuration space, as well as to avoid a correspondence problem, the candidate grasps are computed from a reduced configuration space that is confined by a set of given thumb placements and thumb directions. The proposed approach has been validated with a Barrett hand and a Shadow hand on several objects in simulation. The resulting grasps in the evaluation generated by our approach increase the coverage of frequently-occurring disturbance rather than the coverage of a large area with a scattered distribution.

Traditional motion planning can be computationally burdensome for practical robots, due to extensive collision checking and considerable iterative propagation of cost values. We present a novel neural network architecture which can directly generate the cost-to-go (c2g) function for a given configuration space and a goal configuration. The output of the network is a continuous function whose gradient in configuration space can be directly used to generate trajectories in motion planning without the need for protracted iterations or extensive collision checking. This higher order function (i.e. a function generating another function) representation lies at the core of our motion planning architecture, c2g-HOF, which can take a workspace as input, and generate the cost-to-go function over the configuration space map (C-map). Simulation results for 2D and 3D environments show that c2g-HOF can be orders of magnitude faster at execution time than methods which explore the configuration space during execution. We also present an implementation of c2g-HOF which generates trajectories for robot manipulators directly from an overhead image of the workspace.

When robots perform manipulation tasks, they need to determine their own movement, as well as how to grasp and release an object. Reasoning about the motion of the robot and the object simultaneously leads to a multi-modal planning problem in a high-dimensional configuration space. In this paper we propose an asymptotically optimal manipulation planner. Our approach extends optimal sampling-based roadmap planners to efficiently explore the configuration space of the robot and the object. We prove probabilistic completeness and global, asymptotic optimality. Extensive simulations of a typical pick-and-place scenario show that our approach significantly outperforms a (nonoptimal) state-of-the-art approach. We implemented our planner on a real manipulator and were able to compute high quality solutions in less than a second.

Reducing the energy to carry out computational tasks is key to almost any computing application. We focus in this paper on iterative applications that have explicit computational deadlines per iteration. Our objective is to meet the computational deadlines while minimizing energy. We leverage the vast configuration space offered by heterogeneous multicore platforms which typically expose three dimensions for energy saving configurability: Voltage/frequency levels, thread count and core type (e.g. ARM big/LITTLE). We note that when choosing the most energy-efficient configuration that meets the computational deadline, an iteration will typically finish before the deadline and execution-time slack will build up across iterations. Our proposed slack management policy - SaC (Slack as a Currency) - proactively explores the configuration space to select configurations that can save substantial amounts of energy. To avoid the overheads of an exhaustive search of the configuration space, our proposal also comprises a low-overhead, on-line method by which one can assess each point in the configuration space by linearly interpolating between the endpoints in each configuration-space dimension. Overall, we show that our proposed slack management policy and linear-interpolation configuration assessment method can yield 62% energy savings on top of race-to-idle without missing any deadlines.

Visual feedback can play a crucial role in a dynamic robotic task such as the interception of a moving target. To utilize the feedback effectively, there is a need to develop robot motion planning techniques that also take into account properties of the sensed data. We propose a motion planning framework that achieves this with the help of a space called the perceptual control manifold (PCM) defined on the product of the robot configuration space and an image-based feature space. We show how the task of intercepting a moving target can be mopped to the PCM. This leads to the generation of motion plans that satisfy various constraints and optimality criteria derived from the robot kinematics, the control system, and the sensing mechanism.