This article introduces a computationally efficient robust model predictive control (MPC) scheme for controlling nonlinear systems affected by parametric uncertainties in their models. The approach leverages the recent notion ofclosed-loop state sensitivityand the associated ellipsoidal tubes of perturbed trajectories for taking into account online time-varying restrictions on state and input constraints. This makes the MPC controller “aware” of potential additional requirements needed to cope with parametric uncertainty, thus significantly improving the tracking performance and success rates during navigation in constrained environments. One key contribution lies in the introduction of a computationally efficient robust MPC formulation with acomparable computational complexityto a standard MPC (i.e., an MPC not explicitly dealing with parametric uncertainty). An extensive simulation campaign is presented to demonstrate the effectiveness of the proposed approach in handling parametric uncertainties and enhancing task performance, safety, and overall robustness. Furthermore, we also provide an experimental validation that shows the feasibility of the approach in real-world conditions and corroborates the statistical findings of the simulation campaign. The versatility and efficiency of the proposed method make it therefore a valuable tool for real-time control of robots subject to nonnegligible uncertainty in their models.

This paper presents a novel method to maintain the dynamic balance of a Mobile Manipulator (MM) during the pick-up of heavy objects. The approach entails the generation of a preliminary reach-to-grasp trajectory, which is subsequently refined by an Optimization-Based Controller (OBC) formulated as a Quadratic Program (QP). The trajectory is modified in a minimal fashion to ensure that the robot maintains balance during the reaching phase and remains balanced when the payload is grasped. This is accomplished by incorporating a balance constraint into the OBC that predicts the Zero Moment Point (ZMP) position of the robot at the beginning of the pick-up phase. This accounts for the gravitational and inertial effects that the object has on the robot. The method is validated through simulations conducted with the TIAGo robot in Gazebo. The results demonstrate that the proposed approach effectively prevents the robot from tipping over when the payload is considered.

We propose an effective whole-body MPC controller for locomotion of humanoid robots. Our method generates motions using the full kinematics, allowing it to account for joint limits and to exploit upper-body motions to reject disturbances. Each MPC iteration solves a single QP that considers the interplay between dynamic and kinematic features of the robot. Thanks to our special formulation, we are able to perform a feasibility analysis, which opens the door to future enhancements of functionality and performance, e.g., step adaptation in complex environments. We demonstrate its effectiveness through a campaign of dynamic simulations aimed at highlighting how the joint limits and the use of the angular momentum through upper-body motions are fundamental for maximizing performance, robustness, and ultimately make the robot able to execute more challenging gaits.

We present a whole-body control architecture for the generation of stable task-oriented motions in Wheeled Inverted Pendulum (WIP) robots. Controlling WIP systems is challenging because the successful execution of tasks is subordinate to the ability to maintain balance. Our feedback control approach relies both on partial feedback linearization and Model Predictive Control (MPC). The partial feedback linearization reshapes the system into a convenient form, while the MPC computes inputs to execute the desired task by solving a constrained optimization problem. Input constraints account for actuation limits and a stability constraint is in charge of stabilizing the unstable body pitch angle dynamics. The proposed approach is validated by simulations on an ALTER-EGO robot performing navigation and loco-manipulation tasks.

In most MPC-based schemes used for humanoid gait generation, simple Quadratic Programming (QP) problems are considered for real-time implementation. Since these only allow for convex constraints, the generated gait may be conservative. In this paper we focus on the non-convex reachable region of the swinging foot, also known as Kinematic Admissible Region (KAR), and the corresponding constraint. We represent an approximation of such non-convex region as the union of multiple non-overlapping convex sub-regions. By leveraging the concept of feasibility region, i.e., the subset of the state space for which a QP problem is feasible, and introducing a proper selection criterion, we are able to maintain linearity of the constraints and thus use our Intrinsically Stable Model Predictive Control (IS-MPC) scheme with a negligible additional computational load. This approach allows for a wider range of possible generated motions and is very effective when reacting to a push or avoiding an obstacle, as illustrated in dynamically simulated scenarios.

The advances in computer processor technology have enabled the application of nonlinear model predictive control (NMPC) to agile systems, such as quadrotors. These systems are characterized by their underactuation, nonlinearities, bounded inputs, and time-delays. Classical control solutions fall short in overcoming these difficulties and fully exploiting the capabilities offered by such platforms. This paper presents the design and implementation of an efficient position controller for quadrotors based on real-time NMPC with time-delay compensation and bounds enforcement on the actuators. To deal with the limited computational resources onboard, an offboard control architecture is proposed. It is implemented using the high-performance software package acadoff, which solves optimal control problems and implements a real-time iteration (RTI) variant of a sequential quadratic programming (SQP) scheme with Gauss-Newton Hessian approximation. The quadratic subproblems (QP) in the SQP scheme are solved with HPIPM, an interior-point method solver, built on top of the linear algebra library BLASFEO, finely tuned for multiple CPU architectures. Solution times are further reduced by reformulating the QPs using the efficient partial condensing algorithm implemented in HPIPM. We demonstrate the capabilities of our architecture using the Crazyflie 2.1 nano-quadrotor.

It is common knowledge that tractor-trailer vehicles are affected by jackknifing, a phenomenon that consists in the divergence of the trailer hitch angle and ultimately causes the vehicle to fold up. For the case of backwards motion, in which jackknifing can also occur at low speeds, we present a control method that drives the vehicle along a reference Cartesian trajectory while avoiding the divergence of the hitch angle. In particular, a feedback control law is obtained by combining two actions: a tracking term, computed using input-output linearization, and a corrective term, generated via IS-MPC, an intrinsically stable MPC scheme which is effective for stable inversion of nonminimum-phase systems. The proposed method has been verified in simulation and experimentally validated on a purposely built prototype.

We present an extension of our previously proposed IS-MPC method for humanoid gait generation aimed at obtaining robust performance in the presence of disturbances. The considered disturbance signals vary in a range of known amplitude around a mid-range value that can change at each sampling time, but whose current value is assumed to be available. The method consists in modifying the stability constraint that is at the core of IS-MPC by incorporating the current mid-range disturbance, and performing an appropriate restriction of the ZMP constraint in the control horizon on the basis of the range amplitude of the disturbance. We derive explicit conditions for recursive feasibility and internal stability of the IS-MPC method with constraint modification. Finally, we illustrate its superior performance with respect to the nominal version by performing dynamic simulations on the NAO robot.

In this article, we present an intrinsically stable Model Predictive Control (IS-MPC) framework for humanoid gait generation that incorporates a stability constraint in the formulation. The method uses as prediction model a dynamically extended Linear Inverted Pendulum with Zero Moment Point (ZMP) velocities as control inputs, producing in real time a gait (including footsteps with timing) that realizes omnidirectional motion commands coming from an external source. The stability constraint links future ZMP velocities to the current state so as to guarantee that the generated Center of Mass (CoM) trajectory is bounded with respect to the ZMP trajectory. Being the MPC control horizon finite, only part of the future ZMP velocities are decision variables; the remaining part, called tail, must be either conjectured or anticipated using preview information on the reference motion. Several options for the tail are discussed, each corresponding to a specific terminal constraint. A feasibility analysis of the generic MPC iteration is developed and used to obtain sufficient conditions for recursive feasibility. Finally, we prove that recursive feasibility guarantees stability of the CoM/ZMP dynamics. Simulation and experimental results on NAO and HRP-4 are presented to highlight the performance of IS-MPC.

Walking gaits generated using Model Predictive Control (MPC) is widely used due to its capability to handle several constraints that characterize humanoid locomotion. The use of simplified models such as the Linear Inverted Pendulum allows to perform computations in real-time, giving the robot the fundamental capacity to replan its motion to follow external inputs (e.g. reference velocity, footstep plans). However, usually the MPC does not take into account the current state of the robot when computing the reference motion, losing the ability to react to external disturbances. In this paper a closed-loop MPC scheme is proposed to estimate the robot's real state through Simultaneous Localization and Mapping (SLAM) and proprioceptive sensors (force/torque). With the proposed control scheme it is shown that the robot is able to react to external disturbances (push), by stepping to recover from the loss of balance. Moreover the localization allows the robot to navigate to target positions in the environment without being affected by the drift generated by imperfect open-loop control execution. We validate the proposed scheme through two different experiments with a HRP-4 humanoid robot.

In this paper we present a real-time collision check algorithm based on the parallel computation capabilities of recent graphics card's GPUs. We show an effective application of the proposed algorithm to solve the task-constrained real-time motion planning problem for a redundant manipulator. We propose a proof-of-concept motion planner based on fast collision check of predicted robot motion over a given planning horizon. Obstacles are avoided exploiting the redundancy of the robot. Reactive velocities are computed for some control points placed on the robot and projected in the null space of the task Jacobian. The approach is validated through simulations in V-Rep environments and experiments on the KUKA LWR-IV 7-DoF manipulator.

We consider a pursuit-evasion problem between humanoids. In our scenario, the pursuer enters the safety area of the evader headed for collision, while the latter executes a fast evasive motion. Control schemes are designed for both the pursuer and the evader. They are structurally identical, although the objectives are different: the pursuer tries to align its direction of motion with the line-of-sight to the evader, whereas the evader tries to move in a direction orthogonal to the line-of-sight to the pursuer. At the core of the control scheme is a maneuver planning module which makes use of closed-form expressions exclusively. This allows its use in a replanning framework, where each robot updates its motion plan upon completion of a step to account for the perceived motion of the other. Simulation and experimental results on NAO humanoids reveal an interesting asymptotic behavior which was predicted using unicycle as template models for trajectory generation.

We consider the problem of planning whole-body motions for humanoids that must execute loco-manipulation tasks, i.e., manipulation tasks that implicitly require a locomotion phase. The proposed planner builds a tree in configuration-time space by concatenating feasible, collision-free whole-body motions that realize a succession of CoM movement primitives and, at the same time, the assigned manipulation task. To obtain fluid, natural motions we identify three zones of operation, i.e, locomotion, loco-manipulation and manipulation, and we carefully design a mechanism that allows to synchronize the two tasks. The proposed method has been implemented in V-REP for the NAO humanoid and successfully tested in various scenarios of increasing complexity.

We consider a pursuit-evasion problem between humanoids in the presence of obstacles. In our scenario, the pursuer enters the safety area of the evader headed for collision, while the latter executes a fast evasive motion. Control schemes are designed for both the pursuer and the evader. They are structurally identical, although the objectives are different: the pursuer tries to align its direction of motion with the line-of-sight to the evader, whereas the evader tries to move in a direction orthogonal to the line-of-sight to the pursuer. At the core of the control architecture is a Model Predictive Control scheme for generating a stable gait. This allows for the inclusion of workspace obstacles, which we take into account at two levels: during the determination of the footsteps orientation and as an explicit MPC constraint. We illustrate the results with simulations on NAO humanoids.

We consider the problem of repeatable motion planning for redundant robotic systems performing cyclic tasks in the presence of obstacles. For this open problem, we present a control-based randomized planner, which produces closed collision-free paths in configuration space and guarantees continuous satisfaction of the task constraints. The proposed algorithm, which relies on bidirectional search and loop closure in the task-constrained configuration space, is shown to be probabilistically complete. A modified version of the planner is also devised for the case in which configuration-space paths are required to be smooth. Finally, we present planning results in various scenarios involving both free-flying and nonholonomic robots to show the effectiveness of the proposed method.

This paper addresses the problem of generating whole-body motions for a humanoid robot that must execute a certain task in an environment containing obstacles. The assigned task trajectory is deformable, and the planner may exploit this feature for finding a solution. Our framework consists of two main components: a constrained motion planner and a deformation mechanism. The basic idea is that the constrained motion planner attempts to solve the problem for the original task. If this proves to be too difficult, the deformation mechanism modifies the task using appropriate heuristic functions. Then, the constrained motion planner is invoked again on the deformed task. If needed, this procedure is iterated. The proposed algorithm has been successfully implemented for the NAO humanoid in V-REP.

We present a method for performing evasive motions with a humanoid robot. In the considered scenario, the robot is standing in a workspace, when a moving obstacle (e.g., a human, or another robot) enters its safety area and heads towards it; the humanoid must plan and execute in real-time a maneuver that avoids the collision. The proposed method goes through several conceptual steps. Once the entrance of the moving obstacle in the safety area is detected, its approach direction relative to the robot is determined. On the basis of this information, a suitable evasion maneuver represented by footsteps is generated. From these, an appropriate trajectory is computed for the Center of Mass of the humanoid. Finally, joint motion commands are generated so as to track such trajectory. All computations make use of closed-form expressions and are therefore suitable for real-time implementation. The proposed approach is validated via simulations and experiments on a NAO humanoid. The possibility of adapting the basic method so as to be used in a replanning framework is also investigated.

One of the key problems in planning and control of redundant robots is the fast generation of controls when multiple tasks and constraints need to be satisfied. In the literature, this problem is classically solved by multi-task prioritized approaches, where the priority of each task is determined by a weight function, describing the task strict/soft priority. In this paper, we propose to leverage machine learning techniques to learn the temporal profiles of the task priorities, represented as parametrized weight functions: we automatically determine their parameters through a stochastic optimization procedure. We show the effectiveness of the proposed method on a simulated 7 DOF Kuka LWR and both a simulated and a real Kinova Jaco arm. We compare the performance of our approach to a state-of-the-art method based on soft task prioritization, where the task weights are typically hand-tuned.

We present a decentralized algorithm for estimating mutual poses (relative positions and orientations) in a group of mobile robots. The algorithm uses relative-bearing measurements, which, for example, can be obtained from onboard cameras, and information about the motion of the robots, such as inertial measurements. It is assumed that all relative-bearing measurements are anonymous; i.e., each specifies a direction along which another robot is located but not its identity. This situation, which is often ignored in the literature, frequently arises in practice and remarkably increases the complexity of the problem. The proposed solution is based on a two-step approach: in the first step, the most likely unscaled relative configurations with identities are computed from anonymous measurements by using geometric arguments, while in the second step, the scale is determined by numeric Bayesian filtering based on the motion model. The solution is first developed for ground robots in SE (2) and then for aerial robots in SE (3). Experiments using Khepera III ground mobile robots and quadrotor aerial robots confirm that the proposed method is effective and robust w.r.t. false positives and negatives of the relative-bearing measuring process.

This paper addresses the motion planning problem in the presence of obstacles for underactuated robots that are assigned a geometric task. It is assumed that the robot is subject to kinematic (joint limits, joint velocity bounds) as well as dynamic (torque bounds) constraints. Building on our previous work on task-constrained motion planning, we describe a randomized planner that works directly at the torque level and generates solutions by separating geometric motions from time history. The effectiveness of the proposed approach is shown by planning collision-free swing-up maneuvers for a Pendubot system.

We present a randomized algorithm for planning dynamically feasible motions of robots subject to geometric task constraints in the presence of moving obstacles. The proposed method builds upon our previous results on task-constrained motion planning with moving obstacles. With respect to our previous formulation, the inclusion of bounds on the available actuator torques leads to the adoption of an acceleration-level motion generation scheme. Therefore, the new planner must operate in a task-constrained state space extended with time. The generated trajectories are collision-free, obey velocity and torque bounds, and satisfy the task constraint with arbitrary accuracy. The effectiveness of the proposed approach is shown by results on various scenarios involving a 7-dof manipulator.

This paper considers the problem of planning the motion of a humanoid robot that must execute a manipulation task, possibly requiring stepping, in environments cluttered by obstacles. The proposed method explores the submanifold of the configuration space that is admissible with respect to the assigned task and at the same time satisfies other constraints, including humanoid equilibrium. The exploration tree is expanded using a hybrid scheme that simultaneously generates footsteps and whole-body motions. The algorithm has been implemented for the humanoid robot NAO and validated through planning experiments and dynamic playback in V-REP.

We propose a cooperative control scheme for a heterogeneous multi-robot system, consisting of an Unmanned Aerial Vehicle (UAV) equipped with a camera and multiple identical Unmanned Ground Vehicles (UGVs). Our control scheme takes advantage of the different capabilities of the robots. Since the system is highly redundant, the execution of multiple different tasks is possible. The primary task is aimed at keeping the UGVs well inside the camera field of view, so as to allow our localization system to reconstruct the identity and relative pose of each UGV with respect to the UAV. Additional tasks include formation control, navigation and obstacle avoidance. We thoroughly discuss the feasibility of each task, proving convergence when possible. Simulation results are presented to validate the proposed method.

Minimally invasive surgery assisted by robots is characterized by the restriction of feasible motions of the manipulator link constrained to move through the entry port to the patient's body. In particular, the link is only allowed to translate along its axis and rotate about the entry point. This requires constraining the manipulator motion with respect to a point known as Remote Center of Motion (RCM). The achievement of any surgical task inside the patient's body must take into account this constraint. In this paper we provide a new, general characterization of the RCM constraint useful for task control in the minimally invasive robotic surgery context. To show the effectiveness of our formalization, we consider first a visual task for a manipulator with 6 degrees of freedom holding an endoscopic camera and derive the kinematic control law allowing to achieve the visual task while satisfying the RCM constraint. An example of application of the proposed kinematic modeling to a motion planning problem for a 9 degrees of freedom manipulator with assigned path for the surgical tool is then proposed to illustrate the generality of the approach.

We consider motion planning in the presence of obstacles for redundant robotic systems subject to repetitive task constraints. For this open problem, we present a novel control-based randomized planner which produces cyclic, collision-free paths in configuration space and guarantees continuous satisfaction of the task constraints. In particular, the proposed algorithm relies on bidirectional search and loop closure in the task-constrained configuration space. Planning experiments on a simple 3R planar robot and the KUKA LWR-IV 7-dof manipulator are reported to show the effectiveness of the proposed method.

We present a control-based approach for visual navigation of humanoid robots in office-like environments. In particular, the objective of the humanoid is to follow a maze of corridors, walking as close as possible to their center to maximize motion safety. Our control algorithm is inspired by a technique originally designed for unicycle robots and extended here to cope with the presence of turns and junctions. The feedback signals computed for the unicycle are transformed to inputs that are suited for the locomotion system of the humanoid, producing a natural, human-like behavior. Experimental results for the humanoid robot NAO are presented to show the validity of the approach, and in particular the successful extension of the controller to turns and junctions.

In this paper, a novel decentralized swarm aggregation algorithm for multi-robot systems with an integrated obstacle avoidance is proposed. In this framework, the interaction among robots is limited to their visibility neighborhood, i.e., robots that are within the visibility range of each other. Furthermore, to better comply with the hardware/software limitations of mobile robotic platforms, robots actuators are assumed to be saturated. A theoretical characterization of the main properties of the proposed swarm aggregation algorithm is provided. Simulations have been carried out to validate the theoretical results and experiments have been performed with a team of low-cost mobile robots to demonstrate the effectiveness of the proposed approach in real scenario.

We develop a localization method for a single-UAV/multi-UGV heterogeneous system of robots. Considering the natural supervisory role of the UAV and the challenging (but realistic) assumption that the UAV-to-UGV measurements do not include the identities of the UGVs, we have adopted the PHD filter as a multi-target tracking technique. However, the standard version of this filter does not take into account odometric information coming from the targets, nor does it solve the problem of estimating their identities. Hence, we design ID-PHD, a modification of the PHD filter that is able to reconstruct the identities of the targets by incorporating odometric data. The proposed localization method has been successfully validated through experiments. Some preliminary results of a localization-based control scheme for the multi-robot system are also presented.

We consider the problem of planning the motion of redundant robotic systems subject to geometric task constraints in the presence of obstacles moving along known trajectories. Building on our previous results on task-constrained motion planning, we propose a control-based motion planner that works directly in the task-constrained configuration space extended with the time dimension. The generated trajectories are collision-free and satisfy the task constraint with arbitrary accuracy. Bounds on the achievable generalized velocities may also be taken into account. The proposed approach is validated through planning experiments on a 7-dof articulated robot and an 8-dof mobile manipulator.

We present a new image-based visual servoing scheme for tracking moving targets. This is achieved with a twofold approach. First, we devise a straightforward adaptation of a previously proposed depth observer to account for the fact that the target is not stationary. Second, we estimate the disturbance on the visual feature dynamics due to the target motion, and we add a related compensation term to the visual controller. In particular, the target velocity components parallel to the image plane are reconstructed using a disturbance observer, whereas the orthogonal component is retrieved from the measurement of the Focus Of Expansion. Comparative experiments show that the proposed method can improve over classical visual servoing schemes by 50% or more.

Consider a differential-drive mobile robot equipped with an on-board exteroceptive sensor that can estimate its own motion, e.g., a range-finder. Calibration of this robot involves estimating six parameters: three for the odometry (radii and distance between the wheels) and three for the pose of the sensor with respect to the robot. After analyzing the observability of this problem, this paper describes a method for calibrating all parameters at the same time, without the need for external sensors or devices, using only the measurement of the wheel velocities and the data from the exteroceptive sensor. The method does not require the robot to move along particular trajectories. Simultaneous calibration is formulated as a maximum-likelihood problem and the solution is found in a closed form. Experimental results show that the accuracy of the proposed calibration method is very close to the attainable limit given by the Cramér-Rao bound.

We present a decentralized algorithm for estimating mutual 3-D poses in a group of mobile robots, such as a team of UAVs. Our algorithm uses bearing measurements reconstructed, e.g., by a visual sensor, and inertial measurements coming from the robot IMU. Since identification of a specific robot in a group would require visual tagging and may be cumbersome in practice, we simply assume that the bearing measurements are anonymous. The proposed localization method is a non-trivial extension of our previous algorithm for the 2-D case [1], and exhibits similar performance and robustness. An experimental validation of the algorithm has been performed using quadrotor UAVs.

We propose a swarm aggregation algorithm based on local interactions in the presence of saturations on the robot actuators. This assumption allows to better model the physical limitations of actual mobile robotic platforms. In our framework, robot-to-robot interactions are limited to the visibility neighborhood, i.e., to robots that are within the range of visibility of each other. A theoretical analysis of the convergence properties is presented for the proposed swarm aggregation algorithm. Extensive simulations have been performed to corroborate the theoretical results. In addition, experiments with a team of low-cost mobile robots have been carried out to show the effectiveness of the proposed approach.

For a quadrotor aircraft, we study the problem of planning a trajectory that connects two arbitrary states while allowing the UAV to grasp a moving target at some intermediate time. To this end, two classes of canonical grasping maneuvers are defined and characterized. A planning strategy relying on differential flatness is then proposed to concatenate one or more grasping maneuvers by means of spline-based subtrajectories, with the additional objective of minimizing the total transfer time. The proposed planning algorithm is not restricted to pure hovering-to-hovering motions and takes into account practical constraints, such as the finite duration of the grasping phase. The effectiveness of the proposed approach is shown by means of physically-based simulations.

Our aim is to afford a remote person the opportunity to participate virtually in some event by using a surrogate robot to communicate with local participants while moving about freely at the venue. Accordingly, we propose a mutual telexistence surrogate robot system, called TELESAR4, which was designed and constructed by development of the following: an immersive audiovisual system; an omnidirectionally mobile robot with a robot arm and hand; an omnidirectional stereo camera system (VORTEX); a head with a retroreflective screen for embodiment of the remote participant; and a retroreflective projection system for local participants. This paper describes the development of the TELESAR4 system, whose efficacy has been verified through demonstration experiments.

This paper formulates and investigates a novel problem called Mutual Localization with Anonymous Position Measures. This is an extension of Mutual Localization with Position Measures, with the additional assumption that the identities of the measured robots are not known. A necessary and sufficient condition for the uniqueness of the solution is presented, which requires O(n2= log n) to be verified and is based on the notion of rotational symmetry in R2. We also derive the relationship between the number of robots and the number of possible solutions, and classify the solutions in a number of equivalence classes which is linear in n. A control law is finally proposed that effectively breaks symmetric formations so as to guarantee unique solvability of the problem is also proposed; its performance is illustrated through simulations.

We consider the kinematic control problem for nonholonomic mobile manipulators (NMMs) whose base contains steering wheels. For all typical tasks, the steering velocity inputs of such systems do not appear in the differential relationship between the first-order time derivative of the task output and the available NMM inputs. As a consequence, these inputs are not used by velocity-level control laws based on simple (pseudo)inversion of the task Jacobian, leading in general to the impossibility of completing the task. We propose two control solutions to this open problem based on the framework of input-output feedback linearization. First, a static feedback law is presented that defines the unspecified steering velocities via an optimization action in the null space of the task Jacobian. A dynamic feedback law is then proposed based on the input-output differential map obtained by considering the task acceleration. In this case, the velocity of the steering wheels becomes an active input for task execution, together with the manipulator joint accelerations and the driving accelerations of the base. The feasibility and performance of the two kinematic controllers are compared in simulation for a car-like base carrying a planar manipulator.

We address the mutual localization problem for a multi-robot system, under the assumption that each robot is equipped with a sensor that provides a measure of the relative position of nearby robots without their identity. Anonymity generates a combinatorial ambiguity in the inversion of the measure equations, leading to a multiplicity of admissible relative pose hypotheses. To solve the problem, we propose a two-stage localization system based on MultiReg, an innovative algorithm that computes on-line all the possible relative pose hypotheses, whose output is processed by a data associator and a multiple EKF to isolate and refine the best estimates. The performance of the mutual localization system is analyzed through experiments, proving the effectiveness of the method and, in particular, its robustness with respect to false positives (objects that look like robots) and false negatives (robots that are not detected) of the measure process.

This paper presents a novel method for sensor-based exploration of unknown environments by a general robotic system equipped with multiple sensors. The method is based on the incremental generation of a configuration-space data structure called Sensor-based Exploration Tree (SET). The expansion of the SET is driven by information at the world level, where the perception process takes place. In particular, the frontiers of the explored region efficiently guide the search for informative view configurations. Different exploration strategies may be obtained by instantiating the general SET method with different sampling techniques. Two such strategies are presented and compared by simulations in non-trivial 2D and 3D worlds. A completeness analysis of SET is given in the paper.

We consider the problem of planning collision-free motions for general (i.e., possibly nonholonomic) redundant robots subject to task space constraints. Previous approaches to the solution are based on the idea of sampling and inverting the task constraint to build a roadmap of task-constrained configurations which are then connected by simple local paths; hence, task tracking is not enforced during the motion between samples. Here, we present a control-based randomized approach relying on a motion generation scheme that guarantees continued satisfaction of such constraint. The resulting planner allows to achieve accurate execution of the desired task without increasing the size of the roadmap. Numerical results on a fixed-base manipulator and a free-fying mobile manipulator are presented to illustrate the performance improvement obtained with the proposed technique.

We present an image-based visual servoing controller enabling nonholonomic mobile robots with a fixed pinhole camera to reach and follow a continuous path on the ground. The controller utilizes only a small set of features extracted from the image plane, without using the complete geometric representation of the path. A Lyapunov-based stability analysis is carried out. The performance of the controller is validated and compared by simulations and experiments on a car-like robot equipped with a pinhole camera.

Modeling robot motion planning with uncertainty in a Bayesian framework leads to a computationally intractable stochastic control problem. We seek hypotheses that can justify a separate implementation of control, localization and planning. In the end, we reduce the stochastic control problem to path- planning in the extended space of poses x covariances; the transitions between states are modeled through the use of the Fisher information matrix. In this framework, we consider two problems: minimizing the execution time, and minimizing the final covariance, with an upper bound on the execution time. Two correct and complete algorithms are presented. The first is the direct extension of classical graph-search algorithms in the extended space. The second one is a back-projection algorithm: uncertainty constraints are propagated backward from the goal towards the start state.

For a differential-drive mobile robot equipped with an on-board range sensor, there are six parameters to calibrate: three for the odometry (radii and distance between the wheels), and three for the pose of the sensor with respect to the robot frame. This paper describes a method for calibrating all six parameters at the same time, without the need for external sensors or devices. Moreover, it is not necessary to drive the robot along particular trajectories. The available data are the measures of the angular velocities of the wheels and the range sensor readings. The maximum-likelihood calibration solution is found in a closed form.

In the image-based visual servoing framework, image moments provide an appealing choice as visual features since they can be easily evaluated on any shape on the image plane, and do not require tracking and matching of individual geometric structures between distinct image frames (i.e., the so-called correspondence problem). However, computation of the moment interaction matrix still requires the knowledge of specific unmeasurable 3D quantities relative to the target object, quantities that are usually approximated in practical implementations. Therefore, in this paper we analyze the possibility to estimate on-line the value of such 3D quantities during the camera motion with the only assumption of a target shape with planar limb surface. The proposed estimation scheme builds upon the theory of nonlinear observers, and in particular exploits the basic formulation of the persistency of excitation Lemma. Simulation results are then presented in order to support the effectiveness of the proposed approach.

Within the standard IBVS framework for control of generic robotic systems, a suitable exploitation of redundancy w.r.t. the given visual task can significantly improve the overall task execution. Indeed, redundancy can be used to avoid occlusions, joint limits, or to realize tasks that would be ill-conditioned if addressed altogether. In this respect, we propose an experimental evaluation of the performance of two redundancy resolution schemes, namely Task Priority and Task Sequencing, when adopted to realize IBVS tasks on a mobile robot equipped with a pan-tilt camera onboard.

We present a visual servoing scheme enabling non-holonomic mobile robots with a fixed pinhole camera to reach and follow a continuous path on the ground. The controller utilizes only a small set of features extracted from the image plane, without using the complete geometric representation of the path. The scheme is position-based, and a Lyapunov-based stability analysis is carried out. The performance of our control design is experimentally validated on a car-like robot equipped with a pinhole camera.

We present a method for sensor-based exploration of unknown environments by a robotic system equipped with rangefinders. The method is based on the incremental generation of a configuration-space data structure called sensor-based exploration tree (SET). The expansion of the SET is driven by information at the world level, where the perception process takes place. In particular, the frontiers of the explored region are used to guide the search for informative view configurations. Various exploration strategies may be obtained by instantiating the general SET method with different sampling techniques. Two of these are compared by simulations in 2D and 3D worlds.

Assistive technology is an emerging area where robotic devices can be used to strengthen the residual abilities of individuals with motor disabilities or to help them achieve independence in the activities of daily living. This paper deals with a project aimed at designing a system that provides remote control of home-installed appliances, including the Sony AIBO, a commercial mobile robot. The development of the project is described by focusing on the design of the robot navigation system. Single step, semi-autonomous and autonomous operating modes have been realized to provide different levels of interaction with AIBO. Automatic collision avoidance is integrated in all cases. The performance of the navigation system is shown by experiments. Moreover, the system underwent clinical validation, in order to obtain a definitive assessment through patient feedback.

We present a cooperative exploration strategy for mobile robots. The method is based on the randomized incremental generation of a collection of data structures called sensor-based random trees, each representing a roadmap of an explored area with an associated safe region. Decentralized cooperation and coordination mechanisms are introduced so as to improve the exploration efficiency and to avoid conflicts. Simulations in various environments are presented to show the performance of the proposed technique.

In the image-based visual servoing framework, error signals are directly computed from image feature parameters, thus obtaining control schemes which do not need neither a 3-D model of the scene, nor a perfect knowledge of the camera calibration matrix. However, the current value of the depth Z for each considered feature must be known. We propose a method to estimate on-line the value of Z for point features while the camera is moving through the scene, by using tools from nonlinear observer theory. By interpreting Z as a continuous unknown state with known dynamics, we build an estimator which asymptotically recovers the actual depth value for the selected feature.

We present an image-based visual servoing strategy for driving a nonholonomic mobile robot equipped with a pinhole camera toward a desired configuration. The proposed approach, which exploits the epipolar geometry defined by the current and desired camera views, does not need any knowledge of the 3-D scene geometry. The control scheme is divided into two steps. In the first, using an approximate input-output linearizing feedback, the epipoles are zeroed so as to align the robot with the goal. Feature points are then used in the second translational step to reach the desired configuration. Asymptotic convergence to the desired configuration is proven, both in the calibrated and partially calibrated case. Simulation and experimental results show the effectiveness of the proposed control scheme

The ASPICE project aims at the development of a system which allows the neuromotor disabled persons to improve or recover their mobility (directly or by emulation) and communication within the surrounding environment. The system pivots around a software controller running on a personal computer, which offers a proper interface to communicate through input interfaces matched with the individual's residual abilities.This system links to the concept of user-centered interface promoted by human-computer interaction researchers. Each person has a "singular disability", thus the system must provide the possibility to use an adaptive interface customized to their own ability and requirements, which stem from contingent factors or simple preferences, depending on the user and his or her life stage, task, and environment.At this time, the system is under clinical validation, that will provide assessment through patients' feedback and guidelines for customized system installation.

We consider robotic systems made of a nonholonomic mobile platform carrying a manipulator (nonholonomic mobile manipulator, NMM). By combining the manipulator differential kinematics with the admissible differential motion of the platform, a simple and general kinematic model for NMMs is derived. Assuming that the robotic system is kinematically redundant for a given task, we present the extension of redundancy resolution schemes originally developed for standard manipulators, in particular the projected gradient (PG) and the reduced gradient (RG) optimization-based methods. The case of a configuration-dependent task specification is also discussed. The proposed modeling approach is illustrated with reference to representative NMMs, and the performance of the PG and RG methods for redundancy resolution is compared on a series of numerical case studies

We present an image-based visual servoing strategy for nonholonomic mobile robot equipped with a central catadioptric camera. This kind of vision sensor combines lens and mirrors to enlarge the field of view. The proposed approach, which exploits the epipolar geometry defined by the current and the desired camera views, does not need any knowledge of the 3-D scene geometry. The control scheme is divided in two steps. In the first one, the epipoles are used together with an approximate input-output linearizing feedback to align the robot with the goal. Feature points are then used in the second translation step to reach the desired configuration. Global asymptotic convergence is proven. Simulation and experimental results show the effectiveness of the proposed control scheme

We present an integrated exploration strategy for mobile robots. The method is based on the randomized incremental generation of a data structure called sensor-based random tree (SRT), which represents a roadmap of the explored area with an associated safe region. A continuous localization procedure based on natural features of the safe region is integrated in the scheme. Both the information gain and the localization potential are taken into account when evaluating candidate configurations for exploration. Simulations and experiments on the MagellanPro robot show the performance of the proposed technique

We present a frontier-based modification of the SRT (Sensor-based Random Tree) method, a previously proposed probabilistic strategy for sensor-based exploration of unknown environments by a mobile robot. The idea is to improve the efficiency of the method by biasing the randomized generation of configurations towards unexplored areas. Effective implementations of this strategy are proposed for SRT-Ball and SRT-Star, two instances of the general SRT method corresponding to different perception attitudes and sensing equipments. Comparative simulations are presented to show the benefits of the proposed technique.

We consider the problem of planning collision-free motions for a mobile manipulator whose end-effector must travel along a given path. Algorithmic solutions are devised by adapting a technique developed for fixed-base redundant robots. In particular, we exploit the natural partition of generalized coordinates between the manipulator and the mobile base, whose nonholonomy is accounted for at the planning stage. The approach is based on the randomized generation of configurations that are compatible with the end-effector path constraint. The performance of the proposed algorithms is illustrated by several planning experiments.

We present a vision-based scheme for driving a nonholonomic mobile robot to intercept a moving target. Our method relies on a two-level approach. On the lower level, the pan-tilt platform which carries the on-board camera is controlled so as to keep the target at the center of the image plane. On the higher level, the robot operates under the assumption that the camera system achieves perfect tracking. In particular, the relative position of the ball is retrieved from the pan/tilt angles through simple geometry, and used to compute a control law driving the robot to the target. Various possible choices are discussed for the high-level robot controller. The proposed visual interception method is validated through simulations as well as experiments on the mobile robot MagellanPro.

We present a framework for the stabilization of nonholonomic systems that do not possess special properties such as flatness or exact nilpotentizability. Our approach makes use of two tools: an iterative control scheme and a nilpotent approximation of the system dynamics. The latter is used to compute an approximate steering control which, repeatedly applied to the system, guarantees asymptotic stability with exponential convergence to any desired set point, under appropriate conditions. For illustration, we apply the proposed strategy to design a stabilizing controller for the plate-ball manipulation system, a canonical example of nonflat nonholonomic mechanism. The theoretical performance and robustness of the controller are confirmed by simulations, both in the nominal case and in the presence of a perturbation on the ball radius.

A new image-based visual servoing algorithm is presented for nonholonomic mobile robots. The algorithm, based on epipolar geometry, consists of three independent and sequential steps making use of both the estimated epipoles and the image features. In particular, due to the nonlinear dynamics of the camera-robot system, an input-output feedback linearizing control law is used during the second step. Simulations results are presented to validate the proposed visual servoing technique.

We present a method for sensor-based exploration of unknown environments by a mobile robot. The method is based on the randomized incremental generation of a data structure called sensor-based random tree (SRT), which represents a roadmap of the explored area with an associated safe region. Different exploration strategies may be obtained by instantiating the general method with different perception techniques. Two such techniques are discussed: the first, conservative and particularly suited to noisy sensors, results in an exploration strategy called SRT-Ball. The second perception technique is more confident, and the corresponding strategy is called SRT-Star. The two strategies are critically compared by simulations as well as by experiments on the MagellanPro robot.

Robotic manipulation by rolling contacts is an appealing method for achieving dexterity with relatively simple hardware. While there exist techniques for planning motions of rigid bodies in rolling contact under nominal conditions, an inescapable challenge is the design of robust controllers of provable performance in the presence of model perturbations. As a preliminary step in this direction, we present in this paper an iterative robust planner of arbitrary accuracy for the plate-ball manipulation system subject to perturbations on the sphere radius. The basic tool is an exact geometric planner for the nominal system, whose repeated application guarantees the desired robustness property on the basis of the iterative steering paradigm. Simulation results under perturbed conditions show the effectiveness of the method.

An experimental study is presented on vision-based feedback control methods for the nonholonomic wheeled mobile robot SuperMARIO. The robot posture is measured via a camera fixed on the ceiling of an indoor environment. To this end, a simple localization algorithm has been developed. Performance on trajectory following and parking tasks is compared under different controllers and using either odometric or visual feedback. The improvement with the latter is obtained at the expense of a limited increase in sampling time.

We describe the design and implementation of a biped locomotion strategy for the robot Sony ERS-210 (AIBO). Being designed for quadruped gaits, this robot has several limitations which make biped locomotion a challenging task, such as passive feet, a high barycenter in the erect posture, and relatively weak actuators. We have therefore chosen to fully exploit the double support phase, in which the robot has both feet on the ground, in order to achieve the correct take-off conditions for performing the single support phase. During the latter, the mechanism motion is essentially uncontrolled but can be predicted and planned using a simple equivalent mechanical system. Both simulation and experimental results show the positive outcome of our study.

We consider the problem of planning collision-free motions for a redundant robot whose end-effector must travel along a given path. Although collision avoidance is one of the main reasons for introducing kinematic redundancy in manipulators, the planning methods so far proposed for this particular problem are neither efficient nor complete. In this paper, we introduce some algorithms that may be considered as an extension of probabilistic planning techniques to the problem at hand. All the algorithms are based on the same simple mechanism for generating random samples of the configuration space that are compatible with the end-effector path constraint. Experimental results illustrate the performance of the planners.

Considers the localization problem for a unicycle robot equipped with range finders and moving in environments with nonsmooth geometry, i.e., whose obstacle-free region, has a piecewise-linear boundary. Using the multi-hypothesis density filter, a multi-modal estimator based on the Bayesian framework, an innovative localization system is devised and implemented on the ATRV-Jr robot. Experiments illustrate the superior performance of the new filter with respect to the classical extended Kalman filter.

We consider the stabilization problem for an underactuated prismatic-rotational (PR) robot with the second joint passive and moving on the horizontal plane. After a controllability analysis, a nilpotent approximation of the system is derived and used for designing an open-loop polynomial command that reduces the state error in finite time. Under suitable hypotheses, the iterative application of this command, computed as a function of the state at the end of each iteration, leads to exponential convergence to the desired equilibrium configuration. Simulation results are reported, also in the presence of unmodeled viscous friction.

We consider the plate-ball system as a typical example of manipulation by rolling contacts. While there exist techniques for planning motions of this nonholonomic mechanism in nominal conditions, our objective in this paper is the robust execution of maneuvers in the presence of model perturbations. To this end, we adopt an iterative steering paradigm based on the use of a nilpotent approximation of the system. Simulation results are reported to confirm the robustness achieved with the proposed feedback controller.

We present a new method for motion planning and feedback control of three-link planar robot arms with a passive rotational third joint. These underactuated mechanical systems are shown to be fully linearizable and input-output decouplable by means of a a nonlinear dynamic feedback, provided a physical singularity is avoided. The linearizing output is the position of the so-called center of percussion of the third link. Based on this result, one can plan smooth motions joining in finite time any initial and desired final state of the robot. Moreover, it is easy to design an exponentially stabilizing feedback along the planned trajectory. Simulation results are reported for a 3R robot.

Existing methods for nonholonomic feedback stabilization can only be applied to exactly nilpotentizable or flat systems. In this paper, a car towing two off-hooked trailers is considered as a canonical example of robot that does not fall into the above class. We show that exponential convergence to arbitrary configurations can be obtained by means of an iterative steering technique based on a nonhomogeneous nilpotent approximation of the system. Simulation results illustrate the performance of the method.

Presents a method for planning motions of three-link planar robots with a passive rotational third joint in the presence of gravity. These underactuated mechanisms can be fully linearized and input-output decoupled by means of a nonlinear dynamic state feedback, provided that a physical singularity is avoided. The linearizing output is the position of the center of percussion of the third link. Based on this, one can plan motions joining any initial and desired final state in finite time; in particular, transfers between inverted equilibria and swing-up maneuvers are easily obtained. Simulation results are reported for a 3R robot.

Existing methods for nonholonomic motion planning can only be applied to exactly nilpotentizable or flat systems. For nonholonomic systems that do not fall into the above classes, we conjecture that globally defined nilpotent approximations will allow the synthesis of efficient steering and stabilization strategies. In the paper, a car towing two off-hooked trailers is considered as a case study. First, it is shown how to derive a nilpotent approximation that is valid in the neighborhood of both regular and singular points. Then, such approximate model is used to compute steering controls. Simulation results are reported to show the satisfactory performance of the method.

We present a new approach for the control of the Acrobot, an interesting example of underactuated mechanical system. In particular, our objective is to transfer the system state from the downward equilibrium to the inverted equilibrium position. The proposed method prescribes the execution of three phases. In the first two phases, the robot is preliminarily swung up using an open-loop input and then driven by a suitable feedback to the inverted equilibrium manifold. In the last phase, the Acrobot is steered along this manifold to the inverted equilibrium position, under the action of a robust feedback controller based on the iterative state steering technique. Simulation results are given to show the performance of the method.

A particular class of underactuated systems is obtained by considering kinematically redundant manipulators for which all joints are passive and the only available inputs are forces/torques acting on the end-effector. Under the assumption that the degree of redundancy is provided by prismatic joints located at the base, we address the problem of steering the robot between two arbitrary equilibrium configurations. By performing a preliminary partial feedback linearization, the dynamic equations take a convenient triangular form, which is further simplified under additional hypotheses. We give sufficient conditions for controllability of this kind of mechanisms. With a PPR robot as a case study, an algorithm is proposed for computing end-effector commands that produce the desired reconfiguration in finite time. Simulation results and a discussion on possible generalizations are given.

An algorithmic solution method is presented for the problem of autonomous robot motion in completely unknown environments. Our approach is based on the alternate execution of two fundamental processes: map building and navigation. In the former, range measures are collected through the robot exteroceptive sensors and processed in order to build a local representation of the surrounding area. This representation is then integrated in the global map so far reconstructed by filtering out insufficient or conflicting information. In the navigation phase, an A*-based planner generates a local path from the current robot position to the goal. Such a path is safe inside the explored area and provides a direction for further exploration. The robot follows the path up to the boundary of the explored area, terminating its motion if unexpected obstacles are encountered. The most peculiar aspects of our method are the use of fuzzy logic for the efficient building and modification of the environment map, and the iterative application of A*, a complete planning algorithm which takes full advantage of local information. Experimental results for a NOMAD 200 mobile robot show the real-time performance of the proposed method, both in static and moderately dynamic environments.

We outline a general approach for the stabilization of robots with passive joints, an interesting example of mechanical systems that may not be controllable in the first approximation. The proposed method is based on a recently introduced iterative steering paradigm, which prescribes the repeated application of a contracting open-loop control law. In order to complete efficiently such a law, the dynamic equations of the robot are put in a suitable form, via partial feedback linearization and approximate nilpotentization. The design procedure is illustrated for a 2R robot moving in the horizontal plane with a single actuator at the base. Experimental results are presented for a laboratory prototype.

We analyze the behavior of redundant robots when the joint motion is generated by inverting task velocity commands through a kinematic control scheme. Depending on the chosen inversion scheme, the robot motion is subject to differential constraints that may or may not be integrable. Accordingly, we give a classification in terms of holonomic, partially nonholonomic, and completely nonholonomic behavior, pointing out also the relationship with the so-called cyclicity property. This general classification is illustrated by means of several examples. When the kinematic control scheme is nonholonomic, the whole configuration space of the robot is accessible by a proper choice of the task input commands. Under this assumption, we address the joint reconfiguration problem, namely the design of end-effector velocity commands that drive the robot to a desired joint configuration. To solve this problem, it is possible to borrow existing methods for motion planning of nonholonomic mechanical systems, such as the sinusoidal steering technique for chained-form systems.

We present a local approach for planning the motion of a car-like robot navigating among obstacles, suitable for sensor-based implementation. The nonholonomic nature of the robot kinematics is explicitly taken into account. The strategy is to modify the output of a generic local holonomic planner, so as to provide commands that realize the desired motion in a least-squares sense. A feedback action tends to align the vehicle with the local force field. In order to avoid the motion stops away from the desired goal, various force fields are considered and compared by simulation.

The authors analyze the dynamic mobility of a kinematically redundant robot driven by forces/torques imposed on the end-effector, an interesting example of underactuated system. Under suitable assumptions, the system can be put via feedback in two special forms, namely the second-order triangular and Caplygin forms. Nonlinear controllability tools are used to derive conditions under which the robot can be steered between two given configurations using end-effector commands. With a PPR robot as a case study, a steering algorithm is proposed that achieves reconfiguration in finite time.

We present an iterative learning controller for nonholonomic systems in chained form. The learning algorithm relies on the fact that chained-form systems are linear under piecewise-constant inputs. The proposed control scheme requires the execution of a small number of experiments in order to drive the system to the desired state in finite time, with nice convergence and robustness properties with respect to modeling inaccuracies as well as disturbances. As a case study, a car-like wheeled mobile robot is considered. Both simulation and experimental results are reported in order to show the performance of the proposed method.

The problem of sensor-based robot motion planning in unknown environments is addressed. The proposed solution approach prescribes the repeated sequence of two fundamental processes: perception and navigation. In the former, the robot collects data from its sensors, builds local maps and integrates them with the global maps so far reconstructed, using fuzzy logic operators. During the navigation process, a planner based on the A* algorithm proposes a path from the current position to the goal. The robot moves along this path until one of two termination conditions is verified namely (i) an unexpected obstructing obstacle is detected, or (ii) the robot is leaving the area in which reliable information has been gathered. Experimental results are presented for a Nomad 200 mobile robot.

We present a simple approach for planning the motion of nonholonomic robots among obstacles. Existing methods lead to open-loop solutions which are either obtained in two stages, approximating a previously built holonomic path, or computationally intensive, being based on configuration space discretization. Our nonholonomic planner employs a direct projection strategy to modify online the output of a holonomic incremental planner, and generates velocity control inputs that realize the desired motion in a least-squares sense. As a result, a feedback scheme is obtained which can use only local sensor information. The proposed approach is applied to unicycle kinematics, with artificial potential fields or vortex fields as local holonomic planners.>

Kinematic redundancy endows a robotic manipulator with the possibility of executing self-motions, that is changing its configuration without moving the end-effector This ability may be used to assume the most convenient posture for a given task, to avoid singularities or workspace obstacles, as well as to obtain closed joint motion on cyclic end-effector paths. We investigate the self-motion stabilization problem: the objective is to design a feedback scheme which drives the robot joint variables to a reference value keeping the end-effector still. Two main approaches are presented. The first is based on the idea of projecting the error term in the null space of the Jacobian matrix. Pure proportional feedback yields simple stability in general, and asymptotic stability in special cases. More interestingly, by using time-varying feedback joint convergence to the desired configuration is achieved. The second approach exploits the concept of reduction in the space of redundant degrees of freedom to design stabilization schemes which take advantage of the mechanical structure of the manipulator. Both approaches are illustrated by application to planar robot arms.>

The authors investigate the problem of how to achieve a cyclic joint behavior in redundant robots performing cyclic tasks, motivated by the fact that most singularity-free local resolution methods produce nonrepeatable joint motions. A controllability analysis of the inverse kinematic system makes it possible to recover the well-known repeatability conditions of T. Shamir and Y. Yomdin (1988), and to further conclude that no null space velocity can be specified if a repeatable scheme is sought, unless it is chosen as a linear term in the end-effector velocity. The problem of achieving asymptotic cyclicity for a given inversion strategy has been solved via suitable kinematic controls, which guarantee convergence to cyclic joint trajectories along the desired end-effector path. Depending on the structure of the feedforward and feedback terms in the control law, a number of different schemes are proposed, yielding exact or asymptotic end-effector tracking. The stability proofs and the satisfactory simulation results confirm the advantage of using these simple control strategies.>

The control problem for robot manipulators having some unactuated joints is addressed. The nonholonomic nature of the constraint expressing the dynamics of the free joints is recognized in the general case, and conditions are derived to identify special cases in which such a constraint is integrable. In contrast to most examples in the literature, the free-joint dynamics is an instance of second-order nonholonomic constraint. It is shown that smooth feedback stabilization to a single equilibrium point is not possible. A feedback scheme achieving stabilization to a manifold of equilibrium positions is proposed. Its correctness is established theoretically as well as confirmed by simulation results.>