arXiv subjects

Quang-Cuong Pham

Publications and source records attributed to Quang-Cuong Pham.

At least 55 records · Page 3Linked to original sources

arXiv2018

Time-Optimal Path Tracking via Reachability Analysis

Given a geometric path, the Time-Optimal Path Tracking problem consists in finding the control strategy to traverse the path time-optimally while regulating tracking errors. A simple yet effective approach to this problem is to decompose the controller into two components: (i)~a path controller, which modulates the parameterization of the desired path in an online manner, yielding a reference trajectory; and (ii)~a tracking controller, which takes the reference trajectory and outputs joint torques for tracking. However, there is one major difficulty: the path controller might not find any feasible reference trajectory that can be tracked by the tracking controller because of torque bounds. In turn, this results in degraded tracking performances. Here, we propose a new path controller that is guaranteed to find feasible reference trajectories by accounting for possible future perturbations. The main technical tool underlying the proposed controller is Reachability Analysis, a new method for analyzing path parameterization problems. Simulations show that the proposed controller outperforms existing methods.

cs.RO↗

arXiv2018

SCALAR - Simultaneous Calibration of 2D Laser and Robot's Kinematic Parameters Using Three Planar Constraints

Industrial robots are increasingly used in various applications where the robot accuracy becomes very important, hence calibrations of the robot's kinematic parameters and the measurement system's extrinsic parameters are required. However, the existing calibration approaches are either too cumbersome or require another expensive external measurement system such as laser tracker or measurement spinarm. In this paper, we propose SCALAR, a calibration method to simultaneously improve the kinematic parameters of a 6-DoF robot and the extrinsic parameters of a 2D Laser Range Finder (LRF) which is attached to the robot. Three flat planes are placed around the robot, and for each plane the robot moves to several poses such that the LRF's ray intersect the respective plane. Geometric planar constraints are then used to optimize the calibration parameters using Levenberg- Marquardt nonlinear optimization algorithm. We demonstrate through simulations that SCALAR can reduce the average position and orientation errors of the robot system from 14.6mm and 4.05 degrees to 0.09mm and 0.02 degrees.

cs.RO↗

arXiv2017

A New Approach to Time-Optimal Path Parameterization based on Reachability Analysis

Time-Optimal Path Parameterization (TOPP) is a well-studied problem in robotics and has a wide range of applications. There are two main families of methods to address TOPP: Numerical Integration (NI) and Convex Optimization (CO). NI-based methods are fast but difficult to implement and suffer from robustness issues, while CO-based approaches are more robust but at the same time significantly slower. Here we propose a new approach to TOPP based on Reachability Analysis (RA). The key insight is to recursively compute reachable and controllable sets at discretized positions on the path by solving small Linear Programs (LPs). The resulting algorithm is faster than NI-based methods and as robust as CO-based ones (100% success rate), as confirmed by extensive numerical evaluations. Moreover, the proposed approach offers unique additional benefits: Admissible Velocity Propagation and robustness to parametric uncertainty can be derived from it in a simple and natural way.

cs.RO↗

arXiv2017

When to make a step? Tackling the timing problem in multi-contact locomotion by TOPP-MPC

We present a model predictive controller (MPC) for multi-contact locomotion where predictive optimizations are realized by time-optimal path parameterization (TOPP). A key feature of this solution is that, contrary to existing planners where step timings are provided as inputs, here the timing between contact switches is computed as output of a fast nonlinear optimization. This is particularly appealing to multi-contact locomotion, where proper timings depend on terrain topology and suitable heuristics are unknown. We show how to formulate legged locomotion as a TOPP problem and demonstrate the behavior of the resulting TOPP-MPC controller in simulations with a model of the HRP-4 humanoid robot.

cs.RO↗

arXiv2017

RoboTSP - A Fast Solution to the Robotic Task Sequencing Problem

In many industrial robotics applications, such as spot-welding, spray-painting or drilling, the robot is required to visit successively multiple targets. The robot travel time among the targets is a significant component of the overall execution time. This travel time is in turn greatly affected by the order of visit of the targets, and by the robot configurations used to reach each target. Therefore, it is crucial to optimize these two elements, a problem known in the literature as the Robotic Task Sequencing Problem (RTSP). Our contribution in this paper is two-fold. First, we propose a fast, near-optimal, algorithm to solve RTSP. The key to our approach is to exploit the classical distinction between task space and configuration space, which, surprisingly, has been so far overlooked in the RTSP literature. Second, we provide an open-source implementation of the above algorithm, which has been carefully benchmarked to yield an efficient, ready-to-use, software solution. We discuss the relationship between RTSP and other Traveling Salesman Problem (TSP) variants, such as the Generalized Traveling Salesman Problem (GTSP), and show experimentally that our method finds motion sequences of the same quality but using several orders of magnitude less computation time than existing approaches.

cs.RO↗

arXiv2017

Touch-based object localization in cluttered environments

Touch-based object localization is an important component of autonomous robotic systems that are to perform dexterous tasks in real-world environments. When the objects to locate are placed within clutters, this touch-based procedure tends to generate outlier measurements which, in turn, can lead to a significant loss in localization precision. Our first contribution is to address this problem by applying the RANdom SAmple Consensus (RANSAC) method to a Bayesian estimation framework. As RANSAC requires repeatedly applying the (computationally intensive) Bayesian updating step, it is crucial to improve that step in order to achieve practical running times. Our second contribution is therefore a fast method to find the most probable object face that corresponds to a given touch measurement, which yields a significant acceleration of the Bayesian updating step. Experiments show that our overall algorithm provides accurate localization in practical times, even when the measurements are corrupted by outliers.

cs.RO↗

arXiv2017

On the Structure of the Time-Optimal Path Parameterization Problem with Third-Order Constraints

Finding the Time-Optimal Parameterization of a Path (TOPP) subject to second-order constraints (e.g. acceleration, torque, contact stability, etc.) is an important and well-studied problem in robotics. In comparison, TOPP subject to third-order constraints (e.g. jerk, torque rate, etc.) has received far less attention and remains largely open. In this paper, we investigate the structure of the TOPP problem with third-order constraints. In particular, we identify two major difficulties: (i) how to smoothly connect optimal profiles, and (ii) how to address singularities, which stop profile integration prematurely. We propose a new algorithm, TOPP3, which addresses these two difficulties and thereby constitutes an important milestone towards an efficient computational solution to TOPP with third-order constraints.

cs.RO↗

arXiv2017

Robotic manipulation of a rotating chain

This paper considers the problem of manipulating a uniformly rotating chain: the chain is rotated at a constant angular speed around a fixed axis using a robotic manipulator. Manipulation is quasi-static in the sense that transitions are slow enough for the chain to be always in "rotational" equilibrium. The curve traced by the chain in a rotating plane -- its shape function -- can be determined by a simple force analysis, yet it possesses complex multi-solutions behavior typical of non-linear systems. We prove that the configuration space of the uniformly rotating chain is homeomorphic to a two-dimensional surface embedded in $\mathbb{R}^3$. Using that representation, we devise a manipulation strategy for transiting between different rotation modes in a stable and controlled manner. We demonstrate the strategy on a physical robotic arm manipulating a rotating chain. Finally, we discuss how the ideas developed here might find fruitful applications in the study of other flexible objects, such as elastic rods or concentric tubes.

cs.RO↗

arXiv2017

Closed-Chain Manipulation of Large Objects by Multi-Arm Robotic Systems

Closed kinematic chains are created whenever multiple robot arms concurrently manipulate a single object. The closed-chain constraint, when coupled with robot joint limits, dramatically changes the connectivity of the configuration space. We propose a regrasping move, termed "IK-switch", which allows efficiently bridging components of the configuration space that are otherwise mutually disconnected. This move, combined with several other developments, such as a method to stabilize the manipulated object using the environment, a new tree structure, and a compliant control scheme, enables us to address complex closed-chain manipulation tasks, such as flipping a chair frame, which is otherwise impossible to realize using existing multi-arm planning methods.

cs.RO↗

arXiv2017

On the covariance of X in AX = XB

Hand-eye calibration, which consists in identifying the rigid- body transformation between a camera mounted on the robot end-effector and the end-effector itself, is a fundamental problem in robot vision. Mathematically, this problem can be formulated as: solve for X in AX = XB. In this paper, we provide a rigorous derivation of the covariance of the solution X, when A and B are randomly perturbed matrices. This fine-grained information is critical for applications that require a high degree of perception precision. Our approach consists in applying covariance propagation methods in SE(3). Experiments involving synthetic and real calibration data confirm that our approach can predict the covariance of the hand-eye transformation with excellent precision.

cs.RO↗

arXiv2017

A Certified-Complete Bimanual Manipulation Planner

Planning motions for two robot arms to move an object collaboratively is a difficult problem, mainly because of the closed-chain constraint, which arises whenever two robot hands simultaneously grasp a single rigid object. In this paper, we propose a manipulation planning algorithm to bring an object from an initial stable placement (position and orientation of the object on the support surface) towards a goal stable placement. The key specificity of our algorithm is that it is certified-complete: for a given object and a given environment, we provide a certificate that the algorithm will find a solution to any bimanual manipulation query in that environment whenever one exists. Moreover, the certificate is constructive: at run-time, it can be used to quickly find a solution to a given query. The algorithm is tested in software and hardware on a number of large pieces of furniture.

cs.RO↗

arXiv2016

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.

cs.RO↗

arXiv2016

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.

cs.RO↗

arXiv2015

A Single-Query Manipulation Planner

In manipulation tasks, a robot interacts with movable object(s). The configuration space in manipulation planning is thus the Cartesian product of the configuration space of the robot with those of the movable objects. It is the complex structure of such a "Composite Configuration Space" that makes manipulation planning particularly challenging. Previous works approximate the connectivity of the Composite Configuration Space by means of discretization or by creating random roadmaps. Such approaches involve an extensive pre-processing phase, which furthermore has to be re-done each time the environment changes. In this paper, we propose a high-level Grasp-Placement Table similar to that proposed by Tournassoud et al. (1987), but which does not require any discretization or heavy pre-processing. The table captures the potential connectivity of the Composite Configuration Space while being specific only to the movable object: in particular, it does not require to be re-computed when the environment changes. During the query phase, the table is used to guide a tree-based planner that explores the space systematically. Our simulations and experiments show that the proposed method enables improvements in both running time and trajectory quality as compared to existing approaches.

cs.RO↗

arXiv2015

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.

cs.RO↗

arXiv2015

A Framework for Fine Robotic Assembly

Fine robotic assembly, in which the parts to be assembled are small and fragile and lie in an unstructured environment, is still out of reach of today's industrial robots. The main difficulties arise in the precise localization of the parts in an unstructured environment and the control of contact interactions. Our contribution in this paper is twofold. First, we propose a taxonomy of the manipulation primitives that are specifically involved in fine assembly. Such a taxonomy is crucial for designing a scalable robotic system (both hardware and software) given the complexity of real-world assembly tasks. Second, we present a hardware and software architecture where we have addressed, in an integrated way, a number of issues arising in fine assembly, such as workspace optimization, external wrench compensation, position-based force control, etc. Finally, we show the above taxonomy and architecture in action on a highly dexterous task -- bimanual pin insertion -- which is one of the key steps in our long term project, the autonomous assembly of an IKEA chair.

cs.RO↗

arXiv2015

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.

cs.RO↗

arXiv2014

A General, Fast, and Robust Implementation of the Time-Optimal Path Parameterization Algorithm

Finding the Time-Optimal Parameterization of a given Path (TOPP) subject to kinodynamic constraints is an essential component in many robotic theories and applications. The objective of this article is to provide a general, fast and robust implementation of this component. For this, we give a complete solution to the issue of dynamic singularities, which are the main cause of failure in existing implementations. We then present an open-source implementation of the algorithm in C++/Python and demonstrate its robustness and speed in various robotics settings.

cs.RO↗