Quang-Cuong Pham

Shilin Shan, Quang-Cuong Pham

Force Sensing and Force Control are essential to many industrial applications. Typically, a 6-axis Force/Torque (F/T) sensor is mounted between the robot's wrist and the end-effector in order to measure the forces and torques exerted by the environment onto the robot (the external wrench). Although a typical 6-axis F/T sensor can provide highly accurate measurements, it is expensive and vulnerable to drift and external impacts. Existing methods aiming at estimating the external wrench using only the robot's internal signals are limited in scope: for example, wrench estimation accuracy was mostly validated in free-space motions and simple contacts as opposed to tasks like assembly that require high-precision force control. Here we present a Neural Network based method and argue that by devoting particular attention to the training data structure, it is possible to accurately estimate the external wrench in a wide range of scenarios based solely on internal signals. As an illustration, we demonstrate a pin insertion experiment with 100-micron clearance and a hand-guiding experiment, both performed without external F/T sensors or joint torque sensors. Our result opens the possibility of equipping the existing 2.7 million industrial robots with Force Sensing and Force Control capabilities without any additional hardware.

Bing Song, Jean-Jacques Slotine, Quang-Cuong Pham

We propose a novel way to integrate control techniques with reinforcement learning (RL) for stability, robustness, and generalization: leveraging contraction theory to realize modularity in neural control, which ensures that combining stable subsystems can automatically preserve the stability. We realize such modularity via signal composition and dynamic decomposition. Signal composition creates the latent space, within which RL applies to maximizing rewards. Dynamic decomposition is realized by coordinate transformation that creates an auxiliary space, within which the latent signals are coupled in the way that their combination can preserve stability provided each signal, that is, each subsystem, has stable self-feedbacks. Leveraging modularity, the nonlinear stability problem is deconstructed into algebraically solvable ones, the stability of the subsystems in the auxiliary space, yielding linear constraints on the input gradients of control networks that can be as simple as switching the signs of network weights. This minimally invasive method for stability allows arguably easy integration into the modular neural architectures in machine learning, like hierarchical RL, and improves their performance. We demonstrate in simulation the necessity and the effectiveness of our method: the necessity for robustness and generalization, and the effectiveness in improving hierarchical RL for manipulation learning.

Hung Pham, Quang-Cuong Pham

Fast robotics pick-and-place with suction cups is a crucial component in the current development of automation in logistics (factory lines, e-commerce, etc.). By "critically fast" we mean the fastest possible movement for transporting an object such that it does not slip or fall from the suction cup. The main difficulties are: (i) handling the contact between the suction cup and the object, which fundamentally involves kinodynamic constraints; and (ii) doing so at a low computational cost, typically a few hundreds of milliseconds. To address these difficulties, we propose (a) a model for suction cup contacts, (b) a procedure to identify the contact stability constraint based on that model, and (c) a pipeline to parameterize, in a time-optimal manner, arbitrary geometric paths under the identified contact stability constraint. We experimentally validate the proposed pipeline on a physical robot system: the cycle time for a typical pick-and-place task was less than 5 seconds, planning and execution times included. The full pipeline is released as open-source for the robotics community.

Francisco Suárez-Ruiz, Teguh Santoso Lembono, Quang-Cuong Pham

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.

Quang-Cuong Pham

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.

Nicholas Adrian, Van-Thach Do, Quang-Cuong Pham

Classical Visual Servoing (VS) rely on handcrafted visual features, which limit their generalizability. Recently, a number of approaches, some based on Deep Neural Networks, have been proposed to overcome this limitation by comparing directly the entire target and current camera images. However, by getting rid of the visual features altogether, those approaches require the target and current images to be essentially similar, which precludes the generalization to unknown, cluttered, scenes. Here we propose to perform VS based on visual features as in classical VS approaches but, contrary to the latter, we leverage recent breakthroughs in Deep Learning to automatically extract and match the visual features. By doing so, our approach enjoys the advantages from both worlds: (i) because our approach is based on visual features, it is able to steer the robot towards the object of interest even in presence of significant distraction in the background; (ii) because the features are automatically extracted and matched, our approach can easily and automatically generalize to unseen objects and scenes. In addition, we propose to use a render engine to synthesize the target image, which offers a further level of generalization. We demonstrate these advantages in a robotic grasping task, where the robot is able to steer, with high accuracy, towards the object to grasp, based simply on an image of the object rendered from the camera view corresponding to the desired robot grasping pose.

Shohei Fujii, Quang-Cuong Pham

In order to safely and efficiently collaborate with humans, industrial robots need the ability to alter their motions quickly to react to sudden changes in the environment, such as an obstacle appearing across a planned trajectory. In Realtime Motion Planning, obstacles are detected in real time through a vision system, and new trajectories are planned with respect to the current positions of the obstacles, and immediately executed on the robot. Existing realtime motion planners, however, lack the smoothing post-processing step -- which are crucial in sampling-based motion planning -- resulting in the planned trajectories being jerky, and therefore inefficient and less human-friendly. Here we propose a Realtime Trajectory Smoother based on the shortcutting technique to address this issue. Leveraging fast clearance inference by a novel neural network, the proposed method is able to consistently smooth the trajectories of a 6-DOF industrial robot arm within 200 ms on a commercial GPU. We integrate the proposed smoother into a full Vision--Motion Planning--Execution loop and demonstrate a realtime, smooth, performance of an industrial robot subject to dynamic obstacles.

Nicholas Adrian, Quang-Cuong Pham

We introduce a new approach to tackle the mobile manipulator task sequencing problem. We leverage computational geometry, graph theory and combinatorial optimization to yield a principled method to segment the task-space targets into clusters, analytically determine reachable base pose for each cluster, and find task sequences that minimize the number of base movements and robot execution time. By clustering targets first and by doing so from first principles, our solution is more general and computationally efficient when compared to existing methods.

Nghia Vuong, Hung Pham, Quang-Cuong Pham

This paper explores the idea that skillful assembly is best represented as dynamic sequences of Manipulation Primitives, and that such sequences can be automatically discovered by Reinforcement Learning. Manipulation Primitives, such as "Move down until contact", "Slide along x while maintaining contact with the surface", have enough complexity to keep the search tree shallow, yet are generic enough to generalize across a wide range of assembly tasks. Moreover, the additional "semantics" of the Manipulation Primitives make them more robust in sim2real and against model/environment variations and uncertainties, as compared to more elementary actions. Policies are learned in simulation, and then transferred onto a physical platform. Direct sim2real transfer (without retraining in real) achieves excellent success rates on challenging assembly tasks, such as round peg insertion with 0.04 mm clearance or square peg insertion with large hole position/orientation estimation errors.

Huy Nguyen, Nicholas Adrian, Joyce Lim Xin Yan et al.

With the rapid rise of 3D-printing as a competitive mass manufacturing method, manual "decaking" - i.e. removing the residual powder that sticks to a 3D-printed part - has become a significant bottleneck. Here, we introduce, for the first time to our knowledge, a robotic system for automated decaking of 3D-printed parts. Combining Deep Learning for 3D perception, smart mechanical design, motion planning, and force control for industrial robots, we developed a system that can automatically decake parts in a fast and efficient way. Through a series of decaking experiments performed on parts printed by a Multi Jet Fusion printer, we demonstrated the feasibility of robotic decaking for 3D-printing-based mass manufacturing.

Ying Jun Wilson Lee, Quang-Cuong Pham

Active Force Control (AFC) is an important scheme for tackling high-precision robotic assembly. Classical force controllers are highly surface-dependent: the controller must be carefully tuned for each type of surface in contact, in order to avoid instabilities and to achieve a reasonable performance level. Here, we build upon the recently-developed Convex Controller Synthesis (CCS) to enable high-precision assembly across a wide range of surface stiffnesses without any surface-dependent tuning. Specifically, we demonstrate peg-in-hole assembly with 100 micron clearance, initial position uncertainties up to 2 cm, and for four types of peg and hole materials -- rubber, plastic, wood, aluminum -- whose stiffnesses range from 10 to 100 N/mm, using a single controller.

Hung Pham, Quang-Cuong Pham

Controlling contacts is truly challenging, and this has been a major hurdle to deploying industrial robots into unstructured/human-centric environments. More specifically, the main challenges are: (i) how to ensure stability at all times; (ii) how to satisfy task-specific performance specifications; (iii) how to achieve (i) and (ii) under environment uncertainty, robot parameters uncertainty, sensor and actuator time delays, external perturbations, etc. Here, we propose a new approach -- Convex Controller Synthesis (CCS) -- to tackle the above challenges based on robust control theory and convex optimization. In two physical interaction tasks -- robot hand guiding and sliding on surfaces with different and unknown stiffnesses -- we show that CCS controllers outperform their classical counterparts in an essential way.

Joyce Xin-Yan Lim, Dasheng Leow, Quang-Cuong Pham et al.

Automated chemical synthesis carries great promises of safety, efficiency and reproducibility for both research and industry laboratories. Current approaches are based on specifically-designed automation systems, which present two major drawbacks: (i) existing apparatus must be modified to be integrated into the automation systems; (ii) such systems are not flexible and would require substantial re-design to handle new reactions or procedures. In this paper, we propose a system based on a robot arm which, by mimicking the motions of human chemists, is able to perform complex chemical reactions without any modifications to the existing setup used by humans. The system is capable of precise liquid handling, mixing, filtering, and is flexible: new skills and procedures could be added with minimum effort. We show that the robot is able to perform a Michael reaction, reaching a yield of 34%, which is comparable to that obtained by a junior chemist (undergraduate student in Chemistry).

Xu Zhang, Quang-Cuong Pham

This paper considers the motion planning problem for multiple tethered planar mobile robots. Each robot is attached to a fixed base by a flexible cable. Since the robots share a common workspace, the interactions amongst the robots, cables, and obstacles pose significant difficulties for planning. Previous works have studied the problem of detecting whether a target cable configuration is intersecting (or entangled). Here, we are interested in the motion planning problem: how to plan and coordinate the robot motions to realize a given non-intersecting target cable configuration. We identify four possible modes of motion, depending on whether (i) the robots move in straight lines or following their cable lines; (ii) the robots move sequentially or concurrently. We present an in-depth analysis of Straight & Concurrent, which is the most practically-interesting mode of motion. In particular, we propose algorithms that (a) detect whether a given target cable configuration is realizable by a Straight & Concurrent motion, and (b) return a valid coordinated motion plan. The algorithms are analyzed in detail and validated in simulations and in a hardware experiment.

Teguh Santoso Lembono, Francisco Suárez-Ruiz, Quang-Cuong Pham

In this paper, we propose SCALAR, a calibration method to simultaneously calibrate the kinematic parameters of a 6-DoF robot and the extrinsic parameters of a 2D Laser Range Finder (LRF) attached to the robot's flange. The calibration setup requires only a flat plate with two small holes carved on it at a known distance from each other, and a sharp tool-tip attached to the robot's flange. The calibration is formulated as a nonlinear optimization problem where the laser and the tool-tip are used to provide planar and distance constraints, and the optimization problem is solved using Levenberg-Marquardt algorithm. We demonstrate through experiments that SCALAR can reduce the mean and the maximum tool position error from 0.44 mm to 0.19 mm and from 1.41 mm to 0.50 mm, respectively.

Cunjun Yu, Zhongang Cai, Hung Pham et al.

Visual Servoing (VS), where images taken from a camera typically attached to the robot end-effector are used to guide the robot motions, is an important technique to tackle robotic tasks that require a high level of accuracy. We propose a new neural network, based on a Siamese architecture, for highly accurate camera pose estimation. This, in turn, can be used as a final refinement step following a coarse VS or, if applied in an iterative manner, as a standalone VS on its own. The key feature of our neural network is that it outputs the relative pose between any pair of images, and does so with sub-millimeter accuracy. We show that our network can reduce pose estimation errors to 0.6 mm in translation and 0.4 degrees in rotation, from initial errors of 10 mm / 5 degrees if applied once, or of several cm / tens of degrees if applied iteratively. The network can generalize to similar objects, is robust against changing lighting conditions, and to partial occlusions (when used iteratively). The high accuracy achieved enables tackling low-tolerance assembly tasks downstream: using our network, an industrial robot can achieve 97.5% success rate on a VGA-connector insertion task without any force sensing mechanism.

Nicholas Adrian, Quang-Cuong Pham

Transparent surfaces, such as glass, transmit most of the visible light that falls on them, making accurate pose estimation challenging. We propose a method to locate glass objects to millimetre accuracy using a simple Laser Range Finder (LRF) attached to the robot end-effector. The method, derived from a physical understanding of laser-glass interactions, consists of (i) sampling points on the glass border by looking at the glass surface from an angle of approximately 45 degrees, and (ii) performing Iterative Closest Point registration on the sampled points. We verify experimentally that the proposed method can locate a transparent, non-planar, side car glass to millimetre accuracy.

Huy Nguyen, Quang-Cuong Pham

Precisely tracking uncertainties is crucial for robots to successfully and safely operate in unstructured and dynamic environments. We present a probabilistic framework to precisely keep track of uncertainties throughout the entire manipulation process. In agreement with common manipulation pipelines, we decompose the process into two subsequent stages, namely perception and physical interaction. Each stage is associated with different sources and types of uncertainties, requiring different techniques. We discuss which representation of uncertainties is the most appropriate for each stage (e.g. as probability distributions in SE(3) during perception, as weighted particles during physical interactions), how to convert from one representation to another, and how to initialize or update the uncertainties at each step of the process (camera calibration, image processing, pushing, grasping, etc.). Finally, we demonstrate the benefit of this fine-grained knowledge of uncertainties in an actual assembly task.

Zhongang Cai, Cunjun Yu, Quang-Cuong Pham

The conventional pose estimation of a 3D object usually requires the knowledge of the 3D model of the object. Even with the recent development in convolutional neural networks (CNNs), a 3D model is often necessary in the final estimation. In this paper, we propose a two-stage pipeline that takes in raw colored point cloud data and estimates an object's translation and rotation by running 3D convolutions on voxels. The pipeline is simple yet highly accurate: translation error is reduced to the voxel resolution (around 1 cm) and rotation error is around 5 degrees. The pipeline is also put to actual robotic grasping tests where it achieves above 90% success rate for test objects. Another innovation is that a motion capture system is used to automatically label the point cloud samples which makes it possible to rapidly collect a large amount of highly accurate real data for training the neural networks.

Mehmet Efe Tiryaki, Xu Zhang, Quang-Cuong Pham

Building and Construction have recently become an exciting application ground for robotics. In particular, rapid progress in materials formulation and in robotics technology has made robotic 3D Printing of concrete a promising technique for in-situ construction. Yet, scalability remains an important hurdle to widespread adoption: the printing systems (gantry- based or arm-based) are often much larger than the structure to be printed, hence cumbersome. Recently, a mobile printing system - a manipulator mounted on a mobile base - was proposed to alleviate this issue: such a system, by moving its base, can potentially print a structure larger than itself. However, the proposed system could only print while being stationary, imposing thereby a limit on the size of structures that can be printed in a single take. Here, we develop a system that implements the printing-while-moving paradigm, which enables printing single-piece structures of arbitrary sizes with a single robot. This development requires solving motion planning, localization, and motion control problems that are specific to mobile 3D Printing. We report our framework to address those problems, and demonstrate, for the first time, a printing-while-moving experiment, wherein a 210 cm x 45 cm x 10 cm concrete structure is printed by a robot arm that has a reach of 87 cm.

Teguh Santoso Lembono, Fransisco Suarez-Ruiz, Quang-Cuong Pham

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.

Huy Nguyen, Quang-Cuong Pham

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.

Hung Pham, Quang-Cuong Pham

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.

Hung Pham, Quang-Cuong Pham

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.

Huy Nguyen, Quang-Cuong Pham

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.

Puttichai Lertkultanon, Quang-Cuong Pham

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.

Xian Zhou, Puttichai Lertkultanon, Quang-Cuong Pham

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.

Hung Pham, Quang-Cuong Pham

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.

Stéphane Caron, Quang-Cuong Pham

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.

Hung Pham, Quang-Cuong Pham

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.

Stéphane Caron, Quang-Cuong Pham, Yoshihiko Nakamura

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.

Stéphane Caron, Quang-Cuong Pham, Yoshihiko Nakamura

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.

Francisco Suárez-Ruiz, Quang-Cuong Pham

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.

Puttichai Lertkultanon, Quang-Cuong Pham

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.

Stéphane Caron, Quang-Cuong Pham, Yoshihiko Nakamura

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.

Quang-Cuong Pham, Stéphane Caron, Puttichai Lertkultanon et al.

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.