International audience

This work aims at leveraging instructional video to guide the solving of complex multi-contact task-and-motion planning tasks in robotics. Towards this goal, we propose an extension of the well-established Rapidly-Exploring Random Tree (RRT) planner, which simultaneously grows multiple trees around grasp and release states extracted from the guiding video. Our key novelty lies in combining contact states, and 3D object poses extracted from the guiding video with a traditional planning algorithm that allows us to solve tasks with sequential dependencies, for example, if an object needs to be placed at a specific location to be grasped later. To demonstrate the benefits of the proposed video-guided planning approach, we design a new benchmark with three challenging tasks: (i) 3D re-arrangement of multiple objects between a table and a shelf, (ii) multi-contact transfer of an object through a tunnel, and (iii) transferring objects using a tray in a similar way a waiter transfers dishes. We demonstrate the effectiveness of our planning algorithm on several robots, including the Franka Emika Panda and the KUKA KMR iiwa.

This article presents a software platform tailored for prehensile manipulation planning named humanoid path planner. The platform implements an original way of modeling manipulation planning through a constraint graph that represents the numerical constraints that define the manipulation problem. We propose an extension of the RRT algorithm to manipulation planning that is able to solve a large variety of problems. We provide replicable experimental results via a docker image that readers may download to run the experimental results by themselves.

This paper deals with continuous tension validation for Cable-Driven Parallel Robots (CDPRs). The proposed method aims at determining whether or not a quasi-static path is feasible regarding cable tension limits. The available wrench set (AWS) is the set of wrenches that can be generated with cable tensions within given minimum and maximum limits. A pose of the robot is considered valid regarding the tensions if and only if the wrench induced by the platform weight is inside the AWS. The hyperplane shifting method gives a geometric representation of the AWS as the intersection of half-spaces. For each facet-defining hyperplane of the AWS, we define a value which is positive when the pose is valid, i.e. when the corresponding wrench lies on the proper side of the hyperplane. Using this value and an upper bound on its time derivative along the path, the half-length of a valid time interval is obtained. Intervals are repeatedly validated for each hyperplane until either the whole path is validated or a non-valid pose is found. The presented method is integrated within the open-source software Humanoid Path Planner (HPP) and implementation results using the configuration of the CDPR CoGiRo are presented.

A continuous collision checking method for a cable-driven parallel robot with an embarked robotic arm is proposed in this paper. The method aims at validating paths by checking for collisions between any pair of robot bodies (mobile platform, cables, and arm links). For a pair of bodies, an upper bound on their relative velocity and a lower bound on the distance between the bodies are computed and used to validate a portion of the path. These computations are done repeatedly until a collision is found or the path is validated. The method is integrated within the Humanoid Path Planner (HPP) software, tested with the cable-driven parallel robot CoGiRo, and compared to a discretized validation method.

The dynamics of a humanoid robot cannot be correctly described independently from the external forces acting on it. These forces have to be reconstructed to enable the robot to control them or to compensate for them. Force sensors are usually used to measure these forces, but because of their cost, they are often put only on the ankle/feet and possibly the wrists. This paper addresses the issue of the estimation of external forces and moments that apply at any part of a robot without direct force measurements and without torque measurements. The sensors used are the regular force sensors and the IMUs of the robot. The method relies on a model-based estimator able to make the fusion between these sensors and the whole body dynamics. The estimator reconstructs a single state vector containing the floating-base kinematics, a filtered measurement of contact force and an additional estimation external force that we evaluate in this paper. Validation is performed on HRP-2 in a multi-contact motion.

International audience

This paper deals with manipulation planning. First, we propose a new tool called the constraint graph to describe the various motion constraints relative to a manipulation planning problem. Then, we describe a problem arising for some manipulation planning problems called the crossed foliation issue. We propose a extension of RRT algorithm that explores the leaves of the foliations generated by motion constraints and that solves the crossed foliation problem. Finally, we show a wide variety of problem that our approach can solve.

While only continuous motions are possible, the way in which contacts appear and disappear confers to legged locomotion a characteristic discontinuous nature that is traditionally shared by the algorithms used for legged locomotion planning. In this paper, we show that this discontinuous nature can disappear if the notion of collision is well redefined and we efficiently solve two different practical problems of legged locomotion planning with algorithms based on an approach that establishes a bridge between discrete and continuous planning. The first problem consists of reactive footstep planning with a biped robot and the second one consists of nongaited locomotion planning with a hexapod.

To guarantee its balance, a humanoid robot has to respect some contact force constraints. Therefore, traditional controllers generate motions complying with these constraints, but they usually consider the robot as stiff and the joint position perfectly known. However, several robots contain compliant parts in their structure. This flexibility modifies the forces at contacts and endangers balance. However, most solutions to stabilize the robot rely on force sensors. But several humanoid robots aren't equipped with these sensors. This paper has two aims. The first one is to develop a compliance stabilizer using the center of mass position and upper-body orientation through a viscoelastic reaction mass pendulum model. The second objective is to show the performances of such a stabilizer when relying only on an IMU-based state observer. Experimental results on HRP-2 robot show that the stabilization successfully rejects perturbations with high gains using only these IMU signals. Moreover, the actuation of the upper-body orientation provides redundancy, robustness and finally improved performances to the stabilizer.

We present HPP, a software designed for complex classes of motion planning problems, such as navigation among movable objects, manipulation, contact-rich multiped locomotion, or elastic rods in cluttered environments. HPP is an open-source answer to the lack of a standard framework for these important issues for robotics and graphics communities.

We introduce a novel notion for lowering the dimensionality of motion planning problems: Irreducibility. Irreducibility of a configuration space trajectory τ means: We cannot find another configuration space trajectory τ', such that the swept volume of τ' is included in the swept volume of τ. The main contribution of our work is twofold: First, we show that motion planning in the space of irreducible trajectories is complete. Second, we show that we can construct reducible subspaces by reasoning about the inherent hierarchical structure of open kinematic chains. Using those theoretical results, we proceed by analytically defining a 7-dimensional irreducible configuration subspace for the humanoid robot HRP-2 under some assumptions. To show its practical importance, we solve a high-dimensional pin-hole problem for HRP-2 from the scratch.

A humanoid robot is underactuated and only relies on contacts with environment to move in the space. The ability to measure contact forces and torques enables then to predict the robot dynamics including balance. In classical cases, a humanoid robot is considered as a multi-body system with rigid limbs and joints and interactions with the environment are modeled as stiff contacts. Forces and torques at contacts are generally estimated with sensors which are expensive and sensitive to calibration errors. However, a robot is not perfectly rigid and contacts may have flexibilities. Therefore, external forces create geometric deformations of the body or its environment. These deformations may modify the robot dynamics and produce unwanted and unbalanced motions. Nonetheless, if we have a model of contact stiffness and are able to reconstruct reliably the geometric deformation, we can reconstruct forces and torques at contact. This study aims at estimating contact forces and torques and to observe the body kinematics of the robot with only an Inertial Measurements Unit (IMU). We show that we are able to reconstruct efficiently the position of the Center of Pressure (CoP) of the robot with only the IMU and proprioceptive data from the robot.

This paper aims at combining state of the art developments of path planning and optimal control and to create the algorithmic foundations to tackle optimal control problems in cluttered environments. Our contribution is three-fold: first, we describe a simple method to automatically generate minimum bounding capsules around exact robot body geometries represented by meshes. Second, we use the bounding capsules to implement distance constraints for an optimal control problem solver and achieve (self-)collision avoidance. Finally, we propose a complete two-stage framework for optimal motion planning on complex robots. This framework is successfully applied to generate optimal collision-free trajectories both in simulation and on the humanoid robot HRP-2.

In this paper we introduce a new bounding box method for footstep planning for humanoid robots. Similar to the classic bounding box method (which uses a single rectangular box to encompass the robot) it is computationally efficient, easy to implement and can be combined with any rigid body motion planning library. However, unlike the classic bounding box method, our method takes into account the stepping over capabilities of the robot, and generates precise leg trajectories to avoid obstacles on the ground. We demonstrate that this method is well suited for footstep planning in cluttered environments.

In this paper, we propose a novel and coherent framework for fast footstep planning for legged robots on a flat ground with 3-D obstacle avoidance. We use swept volume approximations that are computed offline in order to considerably reduce the time spent in collision checking during the online planning phase, in which a rapidly exploring random tree variant is used to find collision-free sequences of half-steps (which are produced by a specific walking pattern generator). Then, an original homotopy is used to smooth the sequences into natural motions, gently avoiding the obstacles. The results are experimentally validated on the robot HRP-2.

We present a new biped walking pattern generator based on "half-steps". Its key features are a) a 3-dimensional parametrization of the input space, and b) a simple homotopy that efficiently smooths the walking trajectory corresponding to a fixed sequence of steps. We show how these features can be ideally combined in the framework of sampling-based footstep planning. We apply our approach to the robot HRP-2 and are able to quickly produce smooth and dynamically stable trajectories that are solutions to a difficult problem of footstep planning.

In this paper we demonstrate an original equivalence between footstep planning problems, where discrete sequences of steps are searched for, and the more classical problem of motion planning for a 2D rigid shape, where a continuous collision-free path has to be found. This equivalence enables a lot of classical motion planning techniques (such as PRM, RRT, etc.) to be applied almost effortlessly to the specific problem of footstep planning for a humanoid robot.

Redundant mechanical systems like humanoid robots are designed to fulfill multiple tasks at a time. A task, in velocity-resolved inverse kinematics, is a desired value for a function of the robot configuration that can be regulated with an ordinary differential equation (ODE). When facing simultaneous tasks, the corresponding equations can be grouped in a single system or, better, sorted in priority and solved each in the solutions set of higher priority tasks. This elegant framework for hierarchical task regulation has been implemented as a sequence of least-squares problems. Its limitation lies in the handling of inequality constraints, which are usually transformed into more restrictive equality constraints through potential fields. In this paper, we propose a new prioritized task-regulation framework based on a sequence of quadratic programs (QP) that removes the limitation. At the basis of the proposed algorithm, there is a study of the optimal sets resulting from the sequence of QPs. The algorithm is implemented and illustrated in simulation on the humanoid robot HRP-2.

We present here an original approach to test the feasibility of footsteps for a given walking pattern generator. It is based on a new approximation algorithm intended to cope with this specific problem. The result obtained is used on the robot HRP-2, and enables it to guess a step feasibility 40,000 times faster (in 9μs) than with the normal verification process. As a consequence some advance is made towards fast online motion (re)planning based on a continuous set of possible steps.

We present a motion planning algorithm that computes rough trajectories used by a contact-points planner as a guide to grow its search graph. We adapt collision-free motion planning algorithms to plan a path within the guide space, a submanifold of the configuration space included in the free space in which the configurations are subject to static stability constraint. We first discuss the definition of the guide space. Then we detail the different techniques and ideas involved: relevant C-space sampling for humanoid robot, task-driven projection process, static stability test based on polyhedral convex cones theory's double description method. We finally present results from our implementation of the algorithm.

We present a novel method for prioritizing both linear equality and inequality systems and provide one algorithm for its resolution. This algorithm can be summarized as a sequence of optimal resolutions for each linear system following their priority order. We propose an optimality criterion that is adapted to linear inequality systems and characterize the resulting optimal sets at every priority level. We have successfully applied our method to plan local motions for the humanoid robot HPR-2. We will demonstrate the validity of the method using an original scenario where linear inequality constraints are solved at lower priority than equality constraints.

A method of regrasp planning for humanoid robot manipulation is proposed. We adopt pivoting manipulation for the humanoid robot to move a bulky object without lifting in a stable and dexterous manner. In order to carry the object to a desired place, the humanoid should sometimes move through narrow areas surrounded by obstacles. We propose a roadmap multiplexing planning to allow the robot to leave the object near narrow places and to regrasp it from another position to continue carrying. We utilize visibility probabilistic roadmap (PRM) method as a preprocessing to capture the critical configurations for regrasping. Then a diffusion method is employed to plan the overall manipulation path including regrasping. The proposed method is verified through planning simulation including whole-body motions.

Many collision detection methods exist, each specialized for certain data types under certain constraints. In order to enable rapid development of efficient collision detection procedures, we propose an extensible software architecture that allows for cross-queries between data types, while permitting the time and memory optimizations needed for high-performance. By decomposing collision detection into well-defined algorithmic and data components, we can use the same tree-descent algorithm to execute proximity queries, regardless the data type. We validate our implementation on a path planning problem in which a vision guided humanoid represented by an OBB tree explores a dynamic environment composed of voxel maps.

In this paper we propose a framework for motion planning in stochastic map. Most of the recent planners are good enough to solve motion planning problems. However, they need a complete and accurate model of the environment and such an assumption may cause a collision in executing the results in a real world with its uncertainties. Considering uncertainties in the model of environment, we reformulate the path planning problem in a stochastic map and then propose a way to modify classical path planning methods in order to fit into this new framework. Our work shares ideas with previous work in this area but follows a different approach. In this framework, sensors and landmarks need to be taken into account. The core computations lie in the evaluation of the probability of collision of configurations with the map.

This paper emphasizes on the capacity of a humanoid robot to perform tasks that are difficult for other types of robots. It deals with manipulation of bulky objects. Such tasks require complicated manipulations involving the whole-body and fine coordination between legs, arms and torso motions. We introduce here a whole-body motion planner that allows a humanoid robot to autonomously plan a pivoting strategy that accounts for the various constraints: collision avoidance, legs-arms coordination and stability control. Based on a previous result by the authors [1] proving the small-time controllability of a pivoting system, the planner is proven to inherit from the probabilistic completeness of the samplingbased motion planning method it is built on. The geometric and kinematic capacity of the proposed planner is mainly demonstrated through simulations and experiments.

This paper proposes an whole body motion planning method for humanoid robots in which dynamics is integrated. The method consists of two stages. A collision-free and statically stable path is planned in the first stage and it is transformed into a dynamically stable trajectory in the second stage. Contributions of the method is summarized as follows. (1) A local method plans a C1path while avoiding collisions between non-strictly convex objects. (2) The second stage gives the minimum time trajectory by time parameterization under dynamic balance constraints. (3) Any path reshaping for recovering collision-freeness is not required since the second stage doesnpsilat change shape of the path. Effectiveness of the method is examined by applying it to scenarios of a humanoid robot HRP-2.

This paper deals with the problem of autonomous navigation for nonholonomic mobile robots. To avoid obstacles while executing a planned motion, we use a nonholonomic trajectory deformation method. Initially, this method did not take into account the velocity and acceleration bounds of the robot. The contribution of this paper is a significant improvement of the method to take into account these kinematic bounds. The idea consists in applying zero input perturbation on intervals on which the kinematic bounds are not satisfied and to reparameterize the trajectory in order to remove bound overflows. Experimental results illustrate and validate the improvement.

Autonomous navigation for wheeled mobile robots generally requires to plan a trajectory and to follow it while performing localization in the environment. In order to execute long-range motion, dead-reckoning localization is not precise enough and the robot must use landmark-based localization. Landmark-based localization can produce discontinuities in the robot position estimation, as it is well known with GPS systems, and perturb the trajectory following. If the robot is able to converge smoothly towards the trajectory, then these perturbations are easily managed. Otherwise, if the robot is more complex (for instance a multi-body mobile robot subject to several nonholonomic constraints) and navigates in a cluttered environment, we show that these perturbations can lead to collisions. The contribution of this paper is to state theoretically the problem and to propose a practical solution to trajectory following for multi-body wheeled mobile robots using landmark-based localization. This solution has been tested on a real robot towing a trailer.

Providing a safe behavior of a vehicle in every situation is a critical mission in the design of a modern car. To measure this ability, the standard ISO double lane change test was a designed by consumer unions. The detailed simulation of such an active safety issue would contribute to shorten the design cycle time of a vehicle by reducing the number of real world tests. In this paper we discuss the use of a trajectory deformation algorithm to determine a possible motion for a realistic dynamic car model going through such a test, and the way to determine the maximum passage speed. The main idea of this method is to iteratively deform the inputs of the system to progressively reduce the number of collisions while respecting the dynamic constraints. This deformation is calculated for each iteration by taking into account a locally linearized dynamic model of the system. Consequently, this algorithm can anticipate correctly the inputs needed to solve the future collisions

This paper presents a framework for precise parking for nonholonomic mobile robots: the docking task. It consists in following a planned trajectory and reaching a docking configuration, defined relatively to the environment. The trajectory is deformed in order to reach the docking configuration, to avoid obstacles and to keep the nonholonomic constraints satisfied. A generic framework to compute the docking configuration is presented. Then we give the principle of a nonholonomic path deformation method that was used to deform the planned trajectory towards the docking configuration. This framework has been tested on a real robot with a trailer in a realistic scenario

This paper addresses the scan matching problem for mobile robot displacement estimation. The contribution is a new metric distance and all the tools necessary to be used within the iterative closest point framework. The metric distance is defined in the configuration space of the sensor, and takes into account both translation and rotation error of the sensor. The new scan matching technique ameliorates previous methods in terms of robustness, precision, convergence, and computational load. Furthermore, it has been extensively tested to validate and compare this technique with existing methods

This paper deals with the optimization of Robot-Obstacle interaction computations, in the context of non-holonomic trajectory deformation for mobile robots. We first recall the principle of the trajectory deformation and the role of the potential field gradient in the configuration space. The contribution of the paper is twofold. First we show that the potential field gradient can be computed without any closed-form expression of the potential function if this latter depends only on the distance between the robot and the obstacles. Then an algorithm to filter obstacles that have no influence in Robot-Obstacle interactions is presented. This algorithm takes advantage of the spatial coherence of the planned trajectory, and has been evaluated by experiments on mobile robot Hilare2 towing a trailer.

This paper presents a metric-based matching algorithm to estimate the robot planar displacement by matching dense two-dimensional range scans. The contribution is a geometric distance that takes into account the translation and orientation of the sensor at the same time. This result is used in the two steps of the matching - estimation process. The correspondences between scans are established with this measure and the minimization of the error is also carried out in terms of this distance. As a result, the translation and rotation are compensated in this framework simultaneously. In fact, this is the contribution with respect to previous work that addressed only translation or translation and rotation but separately. The new technique has been implemented and tested on a real vehicle. The experiments illustrate how it is more robust and accurate than prior techniques. At the end of the paper, we give an extension of our distance measure to 3D range-data matching problems.

In this paper we consider the problem of maintaining surveillance of a moving the target by a nonholonomic mobile observer. The observer's goal is to maintain visibility of the target from a predefined, fixed distance, l. The target escapes if (a) it moves behind an obstacle to occlude the observer's view, (b) it causes the observer to collide with an obstacle, or (c) it exploits the nonholonomic constraints on the observer motion to increase its distance from the observer beyond the surveillance distance l. We deal specifically with the situation in which the only constraint on the target's velocity is a bound on speed (i.e., there are no nonholonomic constraints on the target's motion), and the observer is a nonholonomic, differential drive system having bounded speed. We develop the system model, from which we derive a lower bound for the required observer speed. Finally, we consider the effect of obstacles on the observer's ability to successfully track the target.

Motion planning for complex dynamic systems as well as kinodynamic motion planning are still problems difficult to solve in their generic formulation. For systems for which no steering method is known, the only existing algorithms consist in building an exploration tree in the configuration space by exploring the input space of the system. The main drawback of this type of methods is that they never reach exactly the goal but stops the search when a small neighborhood of the goal has been reached. If the neighborhood is small, the exploration method needs to produce a lot of nodes. In this paper, we propose a solution to cope with this complexity issue. We run a tree exploration method with a big neighborhood and then we locally modify the trajectory in order to make it reach exactly the goal. Our solution is based on a trajectory optimization method we have developed earlier in a mobile robot context and that we have adapted for the problem raised here. The method is generic and can be applied to any dynamic system. A few experimental results are given at the end of the paper.

In this paper we address the problem of obstacles avoidance for car-like robots. We present a generic nonholonomic path deformation method that has been applied on two robots. The principle is to perturb the inputs of the system in order to move away from obstacles and to keep the nonholonomic constraints satisfied. We present an extension of the method to car-like robots. We have integrated the method on two robots (Dala and CyCab) and carried out experiments that show the portability and genericity of the approach.

The robust execution of a planned trajectory is a critical issue in robotics. In this paper, we set the formal basis for a sensor-landmark-based motion planning approach. Our approach deals with inaccuracy of the map of the environment by producing motion features composed of a reference trajectory and of a set of pair sensor landmark over which the robot would control its motion. These motion features define along the trajectory closed-loop motion strategies for the robot. This approach enables us to produce secure motions by putting emphasis on landmarks that can represent a danger of collision. Our contribution is to state the problem in a generic formalism and to propose some simulations that show the relevance of our resolution approach.

This paper presents a novel and generic approach of path optimization for nonholonomic systems. The approach is applied to the problem of reactive navigation for nonholonomic mobile robots in highly cluttered environments. This is a collision-free initial path being given for a robot, and obstacles detected while following this path can make it in collision. The current path is iteratively deformed in order to get away from obstacles and satisfy the nonholonomic constraints. The core idea of the approach is to perturb the input functions of the system along the current path in order to modify this path, making an optimization criterion decrease.

In this paper, we present a method to follow a planned trajectory in a highly cluttered environment for complex nonholonomic systems. This method ensures, under some hypotheses, that the robot never collides. When a collision is detected on the trajectory, we compute a deceleration interval to stop the robot while decelerating, we deform the trajectory in such a way that the trajectory is always feasible.

In this paper, we propose a novel approach to reactive obstacle avoidance for nonholonomic systems. The method is based on the deformation of an initial trajectory computed by a motion planner. The deformation we perform keeps the nonholonomic constraints of the system satisfied. The deformation algorithm is based on a potential field generated by obstacles. We applied this approach to the mobile robot Hilare 2 towing a trailer and we carried out some experiments.

We propose a generic scheme to solve the kinematic control problem of wheeled mobile manipulators when the operational motion is imposed. We generalize the Additional Task Method to solve the control problem of these redundant nonholonomic systems.

Presents a steering method for a car-like vehicle providing smooth paths subjected to curvature constraints. We show how to integrate this steering method in a global motion planning scheme taking obstacles into account. The main idea of the paper is to consider the car as a 4-D system from a kinematic point of view and as a 3-D system from a geometric point of view of collision checking. The resulting planned motions are guaranteed to be collision-free and C/sup 2/ between two cusp points.

This paper addresses the problem of path planning for a class of deformable volumes under fairly general manipulation constraints. The underlying geometric model for the volume is provided by a mass-spring representation. It is augmented by a realistic mechanical model. The latter permits the computation of the shape of the considered object with respect to the grasping constraints by minimizing the energy function of the deformation of the object. Previous research in planning for deformable objects considered the case of elastic plates and proposed a randomized framework for planning paths for plates under manipulation constraints. The present paper modifies and extends the previously proposed framework to handle simple volumes. Our planner builds a roadmap in the configuration space. The nodes of the roadmap are equilibrium configurations of the considered volume under the manipulation constraints, while its edges correspond to quasi-static equilibrium paths. Paths are found by searching the roadmap. We present experimental results that illustrate our approach.

Part positioning and orientation is a key issue in manufacturing. Extensive recent work has investigated a series of force fields for part positioning and orientation. Typically, a strategy that brings a part to a unique equilibrium consists of several force fields that are employed in sequence. Bohringer and Donald conjectured a few years ago that the combination of a unit radial field with a constant field would give rise to a unique equilibrium. Such a field is extremely interesting as it positions and orients parts without the need of sensing or a clock. We (2000) have proved this conjecture for nonsymmetric parts. In this paper, we focus our attention on symmetric parts and show that some of them can be uniquely positioned and oriented using the same field. Our work further explores the capabilities and limits of force fields and provides additional evidence that force fields are a powerful tool for parts manipulation.

Programmable force fields are a representation of a class of devices for distributed, nonprehensile manipulation for applications in parts feeding, sorting, positioning, and assembly. They generate force vector fields in which the parts move until they reach a stable equilibrium pose. Research has yielded open-loop strategies to uniquely position, orient, and sort parts. These strategies typically consist of several fields employed in sequence to achieve a desired final pose. The length of the sequence depends on the complexity of the part. We show that unique part poses can be achieved with just one field. First, we exhibit a single field that positions and orients any part (except certain symmetric parts) into two stable equilibrium poses. Then, we show that for any part there exists a field in which the part reaches a unique stable equilibrium pose (again, except for symmetric parts). Besides giving an optimal upper bound for unique parts positioning and orientation, our work gives further evidence that programmable force fields are a powerful tool for parts manipulation. Our second result also leads to the design of "universal parts feeders", proving an earlier conjecture about their existence. We argue that universal parts feeders are relatively easy to build, and we report on extensive simulation results which indicate that these devices may work very well in practice. We believe that the results in this paper could be the basis for a new generation of efficient, open-loop, parallel parts feeders.

Addresses the problem of path planning for a thin elastic metal plate under fairly general manipulation constraints. The underlying geometric model for the plate is provided by a Bezier representation. The geometric model is augmented by a realistic mechanical model. We assume that the plate is manipulated in accordance with a set of user-defined grasping constraints that specify the position and orientation of two opposite edges. Our mechanical model permits the computation of the shape of the plate with respect to the grasping constraints by minimizing the energy function of the deformation of the plate. Paths are computed by a planner that is based on the principle of probabilistic roadmaps. The planner builds a roadmap in the configuration space. The nodes of the roadmap are equilibrium configurations of the plate under the grasping constraints, while its edges correspond to quasi-static equilibrium paths. Paths are found by searching the roadmap. Several experimental results illustrate our approach.

This paper deals with motion planning and control for mobile robots. The various components of an integrated architecture for the mobile robot Hilare pulling a trailer are presented. The nonholonomic path planner is based on an original steering method accounting for the small-time controllability of the system. Then the path is transformed into a trajectory by including the dynamical constraints of the system (bounded velocity and bounded acceleration). Finally, the motion control is addressed. Due to the geometric transformation for a virtual robot, we show how to reduce the problem to a classical approach of trajectory tracking for a mobile robot moving forward only. The experimental results presented include two types of robot-trailer connection systems.

This paper presents a robust method to control a mobile robot towing a trailer. Both problems of trajectory tracking and steering to a given configuration are addressed. This second issue is solved by an iterative trajectory tracking. Perturbations are taken into account along the motions. Experimental results on the mobile robot Hilare illustrate the validity of our approach.

This paper describes a real experiment in nonholonomic motion planning and control. It was performed on the mobile robot Hilare-2-bis pulling a trailer.

This paper gives an account of the convergence property of potential field based path planning algorithms that use random motions to escape local minima. Their probabilistic convergence is proved and we provide a finite estimate of the convergence time. The proof is based on the study of Markov chains and diffusion processes.