This paper presents a fast and accurate model of a deformable linear object (DLO) – e.g., a rope, wire, or cable – integrated into an established robot physics simulator, MuJoCo. Most accurate DLO models with low computational times exist in standalone numerical simulators, which are unable or require tedious work to handle external objects. Based on an existing state-of-the-art DLO model – Discrete Elastic Rods (DER) – our implementation provides an improvement in accuracy over MuJoCo’s own native cable model. To minimize computational load, our model utilizes force-lever analysis to adapt the Cartesian stiffness forces of the DER into its generalized coordinates. As a key contribution, we introduce a novel parameter identification pipeline designed for both simplicity and accuracy, which we utilize to determine the bending and twisting stiffness of three distinct DLOs. We then evaluate the performance of each model by simulating the DLOs and comparing them to their real-world counterparts and against theoretically proven validation tests.

This paper studies the problem of using a robot arm to manipulate a uniformly rotating chain with its bottom end fixed. Existing studies have investigated ideal rotational shapes for practical applications, yet they do not discuss how these shapes can be consistently achieved through manipulation planning. Our work presents a manipulation strategy for stable and consistent shape transitions. We find that the configuration space of such a chain is homeomorphic to a three-dimensional cube. Using this property, we suggest a strategy to manipulate the chain into different configurations, specifically from one rotation mode to another, while taking stability and feasibility into consideration. We demonstrate the effectiveness of our strategy in physical experiments by successfully transitioning from rest to the first two rotation modes. The concepts explored in our work have critical applications in ensuring safety and efficiency of drill string and yarn spinning operations.

In human-robot collaboration, there has been a trade-off relationship between the speed of collaborative robots and the safety of human workers. In our previous paper, we introduced a time-optimal path tracking algorithm designed to maximize speed while ensuring safety for human workers [1]. This algorithm runs in real-time and provides the safe and fastest control input for every cycle with respect to ISO standards [2]. However, true optimality has not been achieved due to inaccurate distance computation resulting from conservative model simplification. To attain true optimality, we require a method that can compute distances 1. at many robot configurations to examine along a trajectory 2. in realtime for online robot control 3. as precisely as possible for optimal control. In this paper, we propose a batched, fast and precise distance checking method based on precomputed link-local SDFs. Our method can check distances for 500 waypoints along a trajectory within less than 1 millisecond using a GPU at runtime, making it suited for time-critical robotic control. Additionally, a neural approximation has been proposed to accelerate preprocessing by a factor of 2. Finally, we experimentally demonstrate that our method can navigate a 6-DoF robot earlier than a geometric-primitives-based distance checker in a dynamic and collaborative environment.

Mobile manipulators have been employed in many applications that are traditionally performed by either multiple fixed-base robots or a large robotic system. This capability is enabled by the mobility of the mobile base. However, the mobile base also brings redundancy to the system, which makes mobile manipulator motion planning more challenging. In this paper, we tackle the mobile manipulator motion planning problem under the end-effector trajectory continuity constraint in which the end-effector is required to traverse a continuous task-space trajectory (time-parametrized path), such as in mobile printing or spraying applications. Our method decouples the problem into: (1) planning an optimal base trajectory subject to geometric task constraints, end-effector trajectory continuity constraint, collision avoidance, and base velocity constraint; which ensures that (2) a manipulator trajectory is computed subsequently based on the obtained base trajectory. To validate our method, we propose a discrete optimal base trajectory planning algorithm to solve several mobile printing tasks in hardware experiment and simulations.

Physical human-robot interaction has been an area of interest for decades. Collaborative tasks, such as joint compliance, demand high-quality joint torque sensing. While external torque sensors are reliable, they come with the drawbacks of being expensive and vulnerable to impacts. To address these issues, studies have been conducted to estimate external torques using only internal signals, such as joint states and current measurements. However, insufficient attention has been given to friction hysteresis approximation, which is crucial for tasks involving extensive dynamic to static state transitions. In this paper, we propose a deep-learning-based method that leverages a novel long-term memory scheme to achieve dynamics identification, accurately approximating the static hysteresis. We also introduce modifications to the well-known Residual Learning architecture, retaining high accuracy while reducing inference time. The robustness of the proposed method is illustrated through a joint compliance and task compliance experiment.

Mobile manipulators have gained attention for the potential in performing large-scale tasks which are beyond the reach of fixed-base manipulators. The Robotic Task Sequencing Problem for mobile manipulators often requires optimizing the motion sequence of the robot to visit multiple targets while reducing the number of base placements. A two-step approach to this problem is clustering the task-space into clusters of targets before sequencing the robot motion. In this paper, we propose a task-space clustering method which formulates the clustering step as a Set Cover Problem using bipartite graph and reachability analysis, then solves it to obtain the minimum number of target clusters with corresponding base placements. We demonstrated the practical usage of our method in a mobile drilling experiment containing hundreds of targets. Multiple simulations were conducted to benchmark the algorithm and also showed that our proposed method found, in practical time, better solutions than the existing state-of-the-art methods.

One way of ensuring operator's safety during human-robot collaboration is through Speed and Separation Monitoring (SSM), as defined in ISO standard ISO/TS 15066. In general, it is impossible to avoid all human-robot collisions: consider for instance the case when the robot does not move at all, a human operator can still collide with it by hitting it of her own voluntary motion. In the SSM framework, it is possible however to minimize harm by requiring this: if a collision ever occurs, then the robot must be in a stationary state (all links have zero velocity) at the time instant of the collision. In this paper, we propose a time-optimal control policy based on Time-Optimal Path Parameterization (TOPP) to guarantee such a behavior. Specifically, we show that: for any robot motion that is strictly faster than the motion recommended by our policy, there exists a human motion that results in a collision with the robot in a non-stationary state. Correlatively, we show, in simulation, that our policy is strictly less conservative than state-of-the-art safe robot control methods. Additionally, we propose a parallelization method to reduce the computation time of our pre-computation phase (down to about 0.5 sec, practically), which enables the whole pipeline (including the pre-computation) to be executed at runtime, nearly in real-time. Finally, we demonstrate the application of our method in a scenario: time-optimal, safe control of a 6-dof industrial robot.

Symbolic task planning for robots is computationally challenging due to the combinatorial complexity of the possible action space. This fact is amplified if there are several sub-goals to be achieved due to the increased length of the action sequences. In this work, we propose a multi-goal symbolic task planner for deterministic decision processes based on Monte Carlo Tree Search. We augment the algorithm by prioritized node expansion which prioritizes nodes that already have fulfilled some sub-goals. Due to its linear complexity in the number of sub-goals, our algorithm is able to identify symbolic action sequences of 145 elements to reach the desired goal state with up to 48 sub-goals while the search tree is limited to under 6500 nodes. We use action reduction based on a kinematic reachability criterion to further ease computational complexity. We combine our algorithm with object localization and motion planning and apply it to a real-robot demonstration with two manipulators in an industrial bearing inspection setting.

Least-squares programming is a popular tool in robotics due to its simplicity and availability of open-source solvers. However, certain problems like sparse programming in the$\ell_{0}$- or$\ell_{0}-\mathbf{norm}$for time-optimal control are not equivalently solvable. In this work, we propose a non-linear hierarchical least-squares programming (NL-HLSP) for time-optimal control of non-linear discrete dynamic systems. We use a continuous approximation of the heaviside step function with an additional term that avoids vanishing gradients. We use a simple discretization method by keeping states and controls piece-wise constant between discretization steps. This way, we obtain a comparatively easily implementable NL-HLSP in contrast to direct transcription approaches of optimal control. We show that the NL-HLSP indeed recovers the discrete time-optimal control in the limit for resting goal points. We confirm the results in simulation for linear and non-linear control scenarios.

In sim-to-real Reinforcement Learning (RL), a policy is trained in a simulated environment and then deployed on the physical system. The main challenge of sim-to-real RL is to overcome the reality gap - the discrepancies between the real world and its simulated counterpart. Using generic geometric representations, such as convex decomposition, triangular mesh, signed distance field can improve simulation fidelity, and thus potentially narrow the reality gap. Common to these approaches is that many contact points are generated for geometrically-complex objects, which slows down simulation and may cause numerical instability. Contact reduction methods address these issues by limiting the number of contact points, but the validity of these methods for sim-to-real RL has not been confirmed. In this paper, we present a contact reduction method with bounded stiffness to improve the simulation accuracy. Our experiments show that the proposed method critically enables training RL policy for a tight-clearance double pin insertion task and successfully deploying the policy on a rigid, position-controlled physical robot.

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.

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 0.04mm clearance or square peg insertion with large hole position/orientation estimation errors.

Automated chemical synthesis has 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: 1) existing apparatus must be modified to be integrated into the automation systems and 2) such systems are not flexible and would require substantial redesign to handle new reactions or procedures. In this article, we propose a system based on a robot arm that mimics motions of human chemists, performs complex chemical reactions with no modifications to the existing setup used by humans, and thus removes human interventions. The automated system is capable of precise liquid handling, mixing, and filtering and is flexible; new skills and procedures could be added with minimum effort. The production sequence is customizable by chaining tasks together. 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).Note to Practitioners—This article explored methods to reduce the need of additional modifications on structured environments to implement automation. Existing approaches in chemical synthesis automation require substantial modifications on apparatus to incorporate automation, and hence, they are inflexible to changes in the procedures or reactions. This article suggested a new system that performed chemical reactions in an existing setup used by human chemist and was flexible in the production sequence or addition of tasks. We showed how the robot arm was capable of automating a Michael reaction and repeating the experiment again, which could be further extended multiple times. The yield obtained by the robot was comparable to junior chemist and consistent but lower than a senior chemist. Hence, we could improve the yield by understanding skills of a senior chemist and transferring them to the robot.

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.

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 opensource for the robotics community.

Building and Construction have recently become an exciting application ground for robotics. In particular, rapid progress in material 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 × 45 cm × 10 cm concrete structure is printed by a robot arm that has a reach of 87 cm.

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.

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 2-D 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 the planar and distance constraints, and the optimization problem is solved using the Levenberg-Marquardt algorithm. We demonstrate through experiments that SCALAR can reduce the mean and the maximum tool position error from 0.44 to 0.19 mm and from 1.41 to 0.50 mm, respectively.

This paper addresses the problem of multi-robot path coordination, considering specific features that arise in applications such as automatic aircraft taxiing or driver-less cars coordination. The first feature is departure events: when robots arrive at their destinations (e.g. the runway for takeoff), they can be removed from the coordination diagram. The second feature is the “no-backward-movement” constraint: the robots can only move forward on their assigned paths. These features can interact to give rise to complex conflict situations, which existing planners are unable to solve in practical time. We propose a set of algorithms to efficiently account for these features and validate these algorithms on a realistic model of Charles de Gaulle airport.

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.

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.

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) that 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 14.6 mm and 4.05° to 0.09 mm and 0.02°.

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 a support surface) toward 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.

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 Bare randomly perturbed matrices. This line-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.

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). The 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. The key insight is to recursively compute reachable and controllable sets at discretized positions on the path by solving small linear programs. 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.

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.

We propose a method for checking and enforcing multicontact 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: 1) frictional constraints and 2) multiple noncoplanar 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 by 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 the 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 multicontact motions where an HRP-4 humanoid locomotes in challenging multicontact scenarios.

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 a ready-to-assemble chair.

Humanoids locomote by making and breaking contacts with their environment. Thus, a crucial question for them is to anticipate whether a contact will hold or break under effort. For rigid surface contacts, existing methods usually consider several point-contact forces, which has some drawbacks due to the underlying redundancy. We derive a criterion, the Contact Wrench Cone (CWC), which is equivalent to any number of applied forces on the contact surface, and for which we provide a closed-form formula. It turns out that the CWC can be decomposed into three conditions: (i) Coulomb friction on the resultant force, (ii) CoP inside the support area, and (iii) upper and lower bounds on the yaw torque. While the first two are well-known, the third one is novel. It can, for instance, be used to prevent the undesired foot yaws observed in biped locomotion. We show that our formula yields simpler and faster computations than existing approaches for humanoid motions in single support, and assess its validity in the OpenHRP simulator.

Various control approaches have been developed for micro/nanomanipulations using optical tweezers. Most existing methods assume that the micro/nanoparticles stay trapped during manipulations, and stochastic perturbations (Brownian motion) are usually ignored for the simplification of model dynamics. However, the trapped particles could escape from the optical traps especially in motion due to several possible reasons: small trapping stiffness, stochastic perturbations, and kinetic energy gained during manipulation. This paper investigates the conditions under which micro/nanoparticles will stay trapped while in motion. The dynamics of the trapped particles subject to stochastic perturbations is analyzed. Dynamic trapping is considered and the maximum manipulation velocity is determined from a probabilistic perspective. A controller with certain velocity bound is proposed, the stability of the system is analysed in presence of stochastic perturbation. Experimental results are presented to show the effectiveness of the proposed control approach.

We propose a new approach to deform robot trajectories based on affine transformations. At the heart of our approach is the concept of affine invariance: Trajectories are deformed in order to avoid unexpected obstacles or to achieve new objectives but, at the same time, certain definite features of the original motions are preserved. Such features include, for instance, trajectory smoothness, periodicity, affine velocity, or more generally, all affine-invariant features, which are of particular importance in human-centered applications. Furthermore, this approach enables one to “convert” the constraints and optimization objectives regarding the deformed trajectory into constraints and optimization objectives regarding the matrix of the deformation in a natural way, making constraints satisfaction and optimization substantially easier and faster in many cases. As illustration, we present an application to the transfer of human movements to humanoid robots while preserving equiaffine velocity, a well-established invariant of human hand movements. Building on the presented affine deformation framework, we finally revisit the concept of trajectory redundancy from the viewpoint of group theory.

When possible, non-prehensile transportation (i.e. transporting objects without grasping them) can be faster and more efficient than prehensile transportation. However, the need to explicitly consider reaction and friction forces yields kino-dynamic constraints that are difficult to take into account by traditional planning algorithms. Based on the recently developed Admissible Velocity Propagation algorithm, we propose here a fast and general non-prehensile transportation scheme. Our contribution is twofold. First we show how to cast the dynamic balance constraints of a 3D object (e.g. a bottle) into a form compatible with the AVP algorithm. Second, we extend the AVP-RRT algorithm into a more efficient AVP-biRRT algorithm, which makes use of the idea of concurrently growing two trees, one rooted at the starting configuration and one rooted at the goal configuration. We also show both in simulations and on a real robot how our algorithm allows planning fast and dynamic trajectories for the non-prehensile transportation of a bottle.

The panorama of probabilistic completeness results for kinodynamic planners is still confusing. Most existing completeness proofs require strong assumptions that are difficult, if not impossible, to verify in practice. To make completeness results more useful, it is thus sensible to establish a classification of the various types of constraints and planning methods, and then attack each class with specific proofs and hypotheses that can be verified in practice. We propose such a classification, and provide a proof of probabilistic completeness for an important class of planners, namely those whose steering method is based on the interpolation of system trajectories in the state space. We also provide design guidelines for the interpolation function and discuss two criteria arising from our analysis: local boundedness and acceleration compliance.

Finding the time-optimal parameterization of a given path subject to kinodynamic constraints is an essential component in many robotic theories and applications. The objective of this paper 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.

The algorithm for finding the time-optimal parameterization of a given path subject to dynamics constraints developed mostly in the 80's and 90's plays a central role in a number of important robotic theories and applications. A critical issue in its implementation is associated with the so-called dynamic singularities, i.e. the points where the maximum velocity curve is continuous but undifferentiable and where the minimum and maximum accelerations are not naturally defined. Since such singularities arise in most real-world problem instances, characterizing and addressing them appropriately is of particular interest. Yet, from original articles to reference textbooks, this has not yet been done completely correctly. The contribution of the present article is two-fold. First, we derive a complete characterization of dynamic singularities. In particular, we show that not all zero-inertia points are dynamically singular. Second, we suggest how to appropriately address these singularities. In particular, we derive the analytic expressions of the correct optimal backward and forward accelerations from such points.

Our contribution in this article is twofold. First, we identify the regularity properties of the trajectories of planar wheeled mobile robots. By regularity properties of a trajectory we mean whether this trajectory, or a function computed from it, belongs to a certain class Cn(the class of functions that are differentiable n times with a continuous nthderivative). We show that, under some generic assumptions about the rotation and steering velocities of the wheels, any non-degenerate wheeled robot belongs to one of the two following classes. Class I comprises those robots whose admissible trajectories in the plane are C1and piecewise C2; and class II comprises those robots whose admissible trajectories are C1, piecewise C2and, in addition, curvature-continuous. Second, based on this characterization, we derive new feedback control and gap-filling algorithms for wheeled mobile robots using the recently-developed affine trajectory deformation framework.

To identify the joint parameters (e.g. the position of the joint center for a spherical joint, the position and the orientation of the joint axis for a revolute joint, etc.) from motion capture data, existing provably-correct algorithms require that at least three markers be attached to either of the two links adjacent to the joint. However, as shown in this article, it turns out that the identification of the joint parameters requires, for most types of joints, strictly less than three markers on any link. More precisely, we prove the structural identifiability of joint parameters in the following cases: (a) a spherical joint with two markers attached to each of the two adjacent links; (b) a revolute joint with two markers attached to one of the two links, and one marker attached to the other. We provide a practical algorithm to do the identification in case (a). Finally, we show that identification cannot be achieved with strictly fewer markers than listed in (a) and (b).

THE FUNCTIONAL ROLE OF SYNCHRONIZATION HAS ATTRACTED MUCH INTEREST AND DEBATE: in particular, synchronization may allow distant sites in the brain to communicate and cooperate with each other, and therefore may play a role in temporal binding, in attention or in sensory-motor integration mechanisms. In this article, we study another role for synchronization: the so-called "collective enhancement of precision". We argue, in a full nonlinear dynamical context, that synchronization may help protect interconnected neurons from the influence of random perturbations-intrinsic neuronal noise-which affect all neurons in the nervous system. More precisely, our main contribution is a mathematical proof that, under specific, quantified conditions, the impact of noise on individual interconnected systems and on their spatial mean can essentially be cancelled through synchronization. This property then allows reliable computations to be carried out even in the presence of significant noise (as experimentally found e.g., in retinal ganglion cells in primates). This in turn is key to obtaining meaningful downstream signals, whether in terms of precisely-timed interaction (temporal coding), population coding, or frequency coding. Similar concepts may be applicable to questions of noise and variability in systems biology.

We investigate the stability properties of discrete and hybrid stochastic nonlinear dynamical systems. More precisely, we extend the stochastic contraction theorems (which were formulated for continuous systems) to the case of discrete and hybrid resetting systems. In particular, we show that the mean square distance between any two trajectories of a discrete (or hybrid resetting) contracting stochastic system is upper-bounded by a constant after exponential transients. Using these results, we study the synchronization of noisy nonlinear oscillators coupled by discrete noisy interactions.