Redundancy of space manipulator on free-flying vehicle and its nonholonomic path planning

The nonholonomic mechanical structure of space robots and path planning is discussed. The angular momentum conservation works as a nonholonomic constraint while the linear momentum conservation is a holonomic one. Thus, a vehicle with a 6 d.o.f. manipulator is described as a 9 variable system with 6 inputs. This implies the possibility of controlling the vehicle orientation and the joint variables of the manipulator by actuating the joint variables, but only if the trajectory is carefully planned; however, both of them cannot be controlled independently. It means that by assuming feasible-path planning, a system that consists of a vehicle and a 6 d.o.f. manipulator can be utilized as 9 d.o.f. system. Initially, the nonholonomic mechanical structure of space vehicle/manipulator system is shown. Then a path planning scheme for nonholonomic systems is proposed using Lyapunov functions

Stability of Surface Contacts for Humanoid Robots: Closed-Form Formulae of the Contact Wrench Cone for Rectangular Support Areas

Humanoid robots locomote by making and breaking contacts with their environment. A crucial problem is therefore to find precise criteria for a given contact to remain stable or to break. For rigid surface contacts, the most general criterion is the Contact Wrench Condition (CWC). To check whether a motion satisfies the CWC, existing approaches take into account a large number of individual contact forces (for instance, one at each vertex of the support polygon), which is computationally costly and prevents the use of efficient inverse-dynamics methods. Here we argue that the CWC can be explicitly computed without reference to individual contact forces, and give closed-form formulae in the case of rectangular surfaces -- which is of practical importance. It turns out that these formulae simply and naturally express three conditions: (i) Coulomb friction on the resultant force, (ii) ZMP inside the support area, and (iii) bounds on the yaw torque. Conditions (i) and (ii) are already known, but condition (iii) is, to the best of our knowledge, novel. It is also of particular interest for biped locomotion, where undesired foot yaw rotations are a known issue. We also show that our formulae yield simpler and faster computations than existing approaches for humanoid motions in single support, and demonstrate their consistency in the OpenHRP simulator.Comment: 14 pages, 4 figure

Completeness of Randomized Kinodynamic Planners with State-based Steering

Probabilistic completeness is an important property in motion planning. Although it has been established with clear assumptions for geometric planners, the panorama of completeness results for kinodynamic planners is still incomplete, as most existing proofs rely on strong assumptions that are difficult, if not impossible, to verify on practical systems. In this paper, we focus on an important class of kinodynamic planners, namely those that interpolate trajectories in the state space. We provide a proof of probabilistic completeness for these planners under assumptions that can be readily verified from the system's equations of motion and the user-defined interpolation function. Our proof relies crucially on a property of interpolated trajectories, termed second-order continuity (SOC), which we show is tightly related to the ability of a planner to benefit from denser sampling. We analyze the impact of this property in simulations on a low-torque pendulum. Our results show that a simple RRT using a second-order continuous interpolation swiftly finds solution, while it is impossible for the same planner using standard Bezier curves (which are not SOC) to find any solution.Comment: 21 pages, 5 figure

ZMP support areas for multi-contact mobility under frictional constraints

We propose a method for checking and enforcing multi-contact stability based on the Zero-tilting Moment Point (ZMP). The key to our development is the generalization of ZMP support areas to take into account (a) frictional constraints and (b) multiple non-coplanar contacts. We introduce and investigate two kinds of ZMP support areas. First, we characterize and provide a fast geometric construction for the support area generated by valid contact forces, with no other constraint on the robot motion. We call this set the full support area. Next, we consider the control of humanoid robots using the Linear Pendulum Mode (LPM). We observe that the constraints stemming from the LPM induce a shrinking of the support area, even for walking on horizontal floors. We propose an algorithm to compute the new area, which we call pendular support area. We show that, in the LPM, having the ZMP in the pendular support area is a necessary and sufficient condition for contact stability. Based on these developments, we implement a whole-body controller and generate feasible multi-contact motions where an HRP-4 humanoid locomotes in challenging multi-contact scenarios.Comment: 14 pages, 10 figure

Admissible Velocity Propagation : Beyond Quasi-Static Path Planning for High-Dimensional Robots

Path-velocity decomposition is an intuitive yet powerful approach to address the complexity of kinodynamic motion planning. The difficult trajectory planning problem is solved in two separate, simpler, steps: first, find a path in the configuration space that satisfies the geometric constraints (path planning), and second, find a time-parameterization of that path satisfying the kinodynamic constraints. A fundamental requirement is that the path found in the first step should be time-parameterizable. Most existing works fulfill this requirement by enforcing quasi-static constraints in the path planning step, resulting in an important loss in completeness. We propose a method that enables path-velocity decomposition to discover truly dynamic motions, i.e. motions that are not quasi-statically executable. At the heart of the proposed method is a new algorithm -- Admissible Velocity Propagation -- which, given a path and an interval of reachable velocities at the beginning of that path, computes exactly and efficiently the interval of all the velocities the system can reach after traversing the path while respecting the system kinodynamic constraints. Combining this algorithm with usual sampling-based planners then gives rise to a family of new trajectory planners that can appropriately handle kinodynamic constraints while retaining the advantages associated with path-velocity decomposition. We demonstrate the efficiency of the proposed method on some difficult kinodynamic planning problems, where, in particular, quasi-static methods are guaranteed to fail.Comment: 43 pages, 14 figure

Local density of states and superconducting gap in the iron chalcogenide superconductor Fe1+δ_{1+\delta}Se1−x_{1-x}Tex_{x} observed by scanning tunneling spectroscopy

We report on the first investigation of the quasiparticle local density of states and superconducting gap in the iron chalcogenide superconductor Fe$_{1+\delta}$Se$_{1-x}$Te$_{x}$ ($T_{\mathrm{c}} \sim 14$ K). The surface of a cleaved crystal revealed an atomic square lattice, superimposed on the inhomogeneous background, with a lattice constant of $\sim 3.8$ \AA without any reconstruction. Tunneling spectra measured at 4.2 K exhibit the superconducting gap, which completely disappears at 18 K, with a magnitude of $\sim 2.3$ meV, corresponding to $2\Delta / k_{\mathrm{B}}T_{\mathrm{c}}=3.8$.In stark contrast to the cuprate superconductors, the value of the observed superconducting gap is relatively homogeneous, following a sharp distribution with a small standard deviation of 0.23 meV. Conversely, the normal-state local density of states observed above $T_{\mathrm{c}}$ shows spatial variation over a wide energy range of more than 1 eV, probably due to the excess iron present in the crystal.Comment: 4 pages, 5 figure

Correlated space formation for human whole-body motion primitives and descriptive word labels

AbstractThe motion capture technology has been improved, and widely used for motion analysis and synthesis in various fields, such as robotics, animation, rehabilitation, and sports engineering. A massive amount of captured human data has already been collected. These prerecorded motion data should be reused in order to make the motion analysis and synthesis more efficient. The retrieval of a specified motion data is a fundamental technique for the reuse. Imitation learning frameworks have been developed in robotics, where motion primitive data is encoded into parameters in stochastic models or dynamical systems. We have also been making research on encoding motion primitive data into Hidden Markov Models, which are referred to as “motion symbol”, and aiming at integrating the motion symbols with language. The relations between motions and words in natural language will be versatile and powerful to provide a useful interface for reusing motion data. In this paper, we construct a space of motion symbols for human whole body movements and a space of word labels assigned to those movements. Through canonical correlation analysis, these spaces are reconstructed such that a strong correlation is formed between movements and word labels. These spaces lead to a method for searching for movement data from a query of word labels. We tested our proposed approach on captured human whole body motion data, and its validity was demonstrated. Our approach serves as a fundamental technique for extracting the necessary movements from a database and reusing them

Human motion database with a binary tree and node transition graphs

Abstract — Database of human motion has been widely used for recognizing human motion and synthesizing humanoid motions. In this paper, we propose a data structure for storing and extracting human motion data and demonstrate that the database can be applied to the recognition and motion synthesis problems in robotics. We develop an efficient method for building a binary tree data structure from a set of continuous, multi-dimensional motion clips. Each node of the tree represents a statistical distribution of a set of human figure states extracted from the motion clips. We also identify the valid transitions among the nodes and construct node transition graphs. Similar states in different clips may be grouped into a single node, thereby allowing transitions between different behaviors. Using databases constructed from real human motion data, we demonstrate that the proposed data structure can be used for human motion recognition, state estimation and prediction, and robot motion planning. I