Computation Reuse in Statics and Dynamics Problems for Assemblies of Rigid Bodies

The problem of determining the forces among contacting rigid bodies is fundamental to many areas of robotics, including manipulation planning, control, and dynamic simulation. For example, consider the question of how to unstack an assembly, or how to find stable regions of a rubble pile. In considering problems of this type over discrete or continuous time, we often encounter a sequence of problems with similar substructure. The primary contribution of our work is the observation that in many cases, common physical structure can be exploited to solve a sequence of related problems more efficiently than if each problem were considered in isolation. We examine three general problems concerning rigid-body assemblies: dynamic simulation, assembly planning, and assembly stability given limited knowledge of the structure\u27s geometry. To approach the dynamic simulation and assembly planning applications, we have optimized a known method for solving the system dynamics. The accelerations of and forces among contacting rigid bodies may be computed by formulating the dynamics equations and contact constraints as a complementarity problem. Dantzig\u27s algorithm, when applicable, takes n or fewer major cycles to find a solution to the linear complementarity problem corresponding to an assembly with n contacts. We show that Dantzig\u27s algorithm will find a solution in n - k or fewer major cycles if the algorithm is initialized with a solution to the dynamics problem for a subassembly with k internal contacts. Finally, we show that if we have limited knowledge of a structure\u27s geometry, we can still learn about stable regions of its surface by physically pressing on it. We present an approach for finding stable regions of planar assemblies: sample presses on the surface to identify a stable cone in wrench space, partition the space of applicable wrenches into stable and unstable regions, and map these back to the surface of the structure

Automatic decomposition of planned assembly sequences into skill primitives

Abstract-This paper presents a new method to decompose complex sequences of assembly operations into skill primitives. This can be realized by analyzing hyperarcs of the underlying AND/ORgraphs representing automatically generated assembly plans. Features like local depart spaces, symbolic spatial relations, and the necessary tools classify the type of assembly operation (peg in hole, placements, alignments, etc.). Skill primitives are robot movements or commands for grippers and tools. The unified modeling language (UML) is used to model the robot tasks and skill primitives. A robot control system uses the skill primitives as input to select the desired control scheme (position, force, or hybrid). In addition to this, we use an algorithm to identify assembly process states considering static friction under uniform gravity to execute skill primitives. This enables a robot to select and modify its motion strategies adequately according to the state of the assembly operation

Grasp planning for object manipulation by an autonomous robot

L'évolution autonome d'un robot dans un environnement évolutif nécessite qu'il soit doté de capacités de perception, d'action et de décision suffisantes pour réaliser la tâche assignée. Une tâche essentielle en robotique est la manipulation d'objets et d'outils. Elle intervient non seulement pour un robot seul mais également dans des situations d'interaction avec un humain ou un autre robot quand il s’agit d’échanger des objets ou de les manipuler conjointement.\ud Cette thèse porte sur la planification de tâches de manipulation d'objets pour un robot autonome dans un environnement humain. Une architecture logicielle susceptible de résoudre ce type de problèmes au niveau géométrique est proposée. Généralement, une tâche de manipulation commence par une opération de saisie dont la qualité conditionne fortement la réussite de la tâche et pour laquelle nous proposons un planificateur basé sur les propriétés inertielles de l'objet et une décomposition en éléments quasi-convexes tout en prenant en compte les contraintes imposées par le système mobile complet dans un environnement donné.\ud Les résultats sont validés en simulation et sur le robot sur la base d’une extension des outils de planification développés au LAAS-CNRS. Le modèle géométrique 3D de l’objet peut être connu a priori ou bien acquis en ligne. Des expérimentations menées sur un robot manipulateur mobile équipé d'une pince à trois points de contacts, de capteurs de force et d'une paire de caméras stéréoscopiques ont montré la validité de l'approche.\ud The autonomous robot performance in a dynamic environment requires advanced perception, action and decision capabilities. Interaction with the environment plays a key role for a robot and it is well illustrated in object and/or tool manipulation. Interaction with humans or others robots can consist in object exchanges.\ud This thesis deals with object manipulation planning by an autonomous robot in human environments. A software architecture is proposed that is capable to solve such problems at the geometrical level. In general, a manipulation task starts by a grasp operation which quality influences strongly the success of the overall task. We propose a planner based on object inertial properties and an approximate convex decomposition. The whole mobile system taken into account in the planning process.\ud The planner has been completely implemented as an extension of the planning tools developed at LAAS-CNRS. Its results have been tested in simulation and on a robotic platform. Object models may be known a priori or acquired on-line. Experiments have been carried out with a mobile manipulator equipped with a three fingers gripper, a wrist force sensor and a stereo camera system in order to validate the approach.\ud \ud \u

Actuation-Aware Simplified Dynamic Models for Robotic Legged Locomotion

In recent years, we witnessed an ever increasing number of successful hardware implementations of motion planners for legged robots. If one common property is to be identified among these real-world applications, that is the ability of online planning. Online planning is forgiving, in the sense that it allows to relentlessly compensate for external disturbances of whatever form they might be, ranging from unmodeled dynamics to external pushes or unexpected obstacles and, at the same time, follow user commands. Initially replanning was restricted only to heuristic-based planners that exploit the low computational effort of simplified dynamic models. Such models deliberately only capture the main dynamics of the system, thus leaving to the controllers the issue of anchoring the desired trajectory to the whole body model of the robot. In recent years, however, we have seen a number of new approaches attempting to increase the accuracy of the dynamic formulation without trading-off the computational efficiency of simplified models. In this dissertation, as an example of successful hardware implementation of heuristics and simplified model-based locomotion, I describe the framework that I developed for the generation of an omni-directional bounding gait for the HyQ quadruped robot. By analyzing the stable limit cycles for the sagittal dynamics and the Center of Pressure (CoP) for the lateral stabilization, the described locomotion framework is able to achieve a stable bounding while adapting to terrains of mild roughness and to sudden changes of the user desired linear and angular velocities. The next topic reported and second contribution of this dissertation is my effort to formulate more descriptive simplified dynamic models, without trading off their computational efficiency, in order to extend the navigation capabilities of legged robots to complex geometry environments. With this in mind, I investigated the possibility of incorporating feasibility constraints in these template models and, in particular, I focused on the joint torques limits which are usually neglected at the planning stage. In this direction, the third contribution discussed in this thesis is the formulation of the so called actuation wrench polytope (AWP), defined as the set of feasible wrenches that an articulated robot can perform given its actuation limits. Interesected with the contact wrench cone (CWC), this yields a new 6D polytope that we name feasible wrench polytope (FWP), defined as the set of all wrenches that a legged robot can realize given its actuation capabilities and the friction constraints. Results are reported where, thanks to efficient computational geometry algorithms and to appropriate approximations, the FWP is employed for a one-step receding horizon optimization of center of mass trajectory and phase durations given a predefined step sequence on rough terrains. For the sake of reachable workspace augmentation, I then decided to trade off the generality of the FWP formulation for a suboptimal scenario in which a quasi-static motion is assumed. This led to the definition of the, so called, local/instantaneous actuation region and of the global actuation/feasible region. They both can be seen as different variants of 2D linear subspaces orthogonal to gravity where the robot is guaranteed to place its own center of mass while being able to carry its own body weight given its actuation capabilities. These areas can be intersected with the well known frictional support region, resulting in a 2D linear feasible region, thus providing an intuitive tool that enables the concurrent online optimization of actuation consistent CoM trajectories and target foothold locations on rough terrains

Redundant Unilaterally Actuated Kinematic Chains: Modeling and Analysis

Unilaterally Actuated Robots (UAR)s are a class of robots defined by an actuation that is constrained to a single sign. Cable robots, grasping, fixturing and tensegrity systems are certain applications of UARs. In recent years, there has been increasing interest in robotic and other mechanical systems actuated or constrained by cables. In such systems, an individual constraint is applied to a body of the mechanism in the form of a pure force which can change its magnitude but cannot reverse its direction. This uni-directional actuation complicates the design of cable-driven robots and can result in limited performance. Cable Driven Parallel Robot (CDPR)s are a class of parallel mechanisms where the actuating legs are replaced by cables. CDPRs benefit from the higher payload to weight ratio and increased rigidity. There is growing interest in the cable actuation of multibody systems. There are potential applications for such mechanisms where low moving inertia is required. Cable-driven serial kinematic chain (CDSKC) are mechanisms where the rigid links form a serial kinematic chain and the cables are arranged in a parallel configuration. CDSKC benefits from the dexterity of the serial mechanisms and the actuation advantages of cable-driven manipulators. Firstly, the kinematic modeling of CDSKC is presented, with a focus on different types of cable routings. A geometric approach based on convex cones is utilized to develop novel cable actuation schemes. The cable routing scheme and architecture have a significant effect on the performance of the robot resulting in a limited workspace and high cable forces required to perform a desired task. A novel cable routing scheme is proposed to reduce the number of actuating cables. The internal routing scheme is where, in addition to being externally routed, the cable can be re-routed internally within the link. This type of routing can be considered as the most generalized form of the multi-segment pass-through routing scheme where a cable segment can be attached within the same link. Secondly, the analysis for CDSKCs require extensions from single link CDPRs to consider different routings. The conditions to satisfy wrench-closure and the workspace analysis of different multi-link unilateral manipulators are investigated. Due to redundant and constrained actuation, it is possible for a motion to be either infeasible or the desired motion can be produced by an infinite number of different actuation profiles. The motion generation of the CDSKCs with a minimal number of actuating cables is studied. The static stiffness evaluation of CDSKCs with different routing topologies and isotropic stiffness conditions were investigated. The dexterity and wrench-based metrics were evaluated throughout the mechanism's workspace. Through this thesis, the fundamental tools required in studying cable-driven serial kinematic chains have been presented. The results of this work highlight the potential of using CDSKCs in bio-inspired systems and tensegrity robots

Master’s thesis proposal: computation reuse in stacking and unstacking

Algorithms for dynamic simulation and control are fundamental to many applications, including computer games and movies, medical simulation, and mechanical design. I propose to explore efficient algorithms for finding a stable unstacking sequence -- an order in which we can remove every object from a structure without causing the structure to collapse under gravity at any step. We begin with a basic unstacking sequence algorithm: consider the set of all objects in a structure. Collect all possible subsets into a disassembly graph. Search the graph, testing the stability of each node as it is visited. Any path of stable nodes from start to goal is a stable unstacking sequence. I propose to show how we can improve the performance of individual stability tests for three-dimensional structures with Coulomb friction, and give effective methods for searching the disassembly graph. I will also analyze the computational complexity of stable unstacking problems, and explore a classification of structures based on characteristics of their stable unstacking sequences. In preliminary work, I have shown that we can reuse computation from one stability test of a planar subassembly to the next. The implementation, which solves the system dynamics as a linear complementarity problem (LCP), outperforms an implementation that solves the system statics as a linear program (LP). This is surprising because LCPs are more complex than LPs, and dynamics equations are more complex than statics equations

運動計画をフィードバックループに含むヒューマノイドロボットの多点接触全身制御のための計算基盤

学位の種別: 課程博士審査委員会委員 : （主査）東京大学教授 中村 仁彦, 東京大学教授 下山 勲, 東京大学教授 稲葉 雅幸, 東京大学教授 國吉 康夫, 東京大学准教授 高野 渉, LAAS-CNRSSenior Researcher LAUMOND Jean-PaulUniversity of Tokyo(東京大学