Suitable representations of dynamical systems can simplify their analysis and control. On this line of thought, this paper aims to answer the following question:Can a transformation of the generalized coordinates under which the actuators directly perform work on a subset of the configuration variables be found?Not only we show that the answer to this question isyes, but we also provide necessary and sufficient conditions. More specifically, we look for a representation of the configuration space such that the right-hand side of the dynamics in Euler-Lagrange form becomes [IO]tu, being u the system input. We identify a class of systems, calledcollocated, for which this problem is solvable. Under mild conditions on the input matrix, a simple test is presented to verify whether a system is collocated or not. By exploiting power invariance, we provide necessary and sufficient conditions that a change of coordinates decouples the input channels if and only if the dynamics is collocated. In addition, we use the collocated form to derive novel controllers for damped underactuated mechanical systems. To demonstrate the theoretical findings, we consider several Lagrangian systems with a focus on continuum soft robots.

Performing precise, repetitive motions is essential in many robotic and automation systems. Iterative learning control (ILC) allows determining the necessary control command by using a very rough system model to speed up the process. Functional iterative learning control is a novel technique that promises to solve several limitations of classic ILC. It operates by merging the input space into a large functional space, resulting in an over-determined control task in the iteration domain. In this way, it can deal with systems having more outputs than inputs and accelerate the learning process without resorting to model discretizations. However, the framework lacks so far a validation in experiments. This paper aims to provide such experimental validation in the context of robotics. To this end, we designed and built a one-link flexible arm that is actuated by a stepper motor, which makes the development of an accurate model more challenging and the validation closer to the industrial practice. We provide multiple experimental results across several conditions, proving the feasibility of the method in practice.

In physical human-robot interaction (pHRI) it is essential to reliably estimate and localize contact forces between the robot and the environment. In this paper, a complete contact detection, isolation, and reaction scheme is presented and tested on a new 6-dof industrial collaborative robot. We combine two popular methods, based on monitoring energy and generalized momentum, to detect and isolate collisions on the whole robot body in a more robust way. The experimental results show the effectiveness of our implementation on the LARA 5 cobot, that only relies on motor current and joint encoder measurements. For validation purposes, contact forces are also measured using an external GTE CoboSafe sensor. After a successful collision detection, the contact point location is isolated using a combination of the residual method based on the generalized momentum with a contact particle filter (CPF) scheme. We show for the first time a successful implementation of such combination on a real robot, without relying on joint torque sensor measurements.

Physical human-robot interaction is known to be a crucial aspect in modern lightweight robotics. Herein, the estimation of external interactions is essential for the effective and safe collaboration. In this work, an extended momentum-based disturbance observer is presented which includes the sensing redundancy related to additional force-torque measurements. The observer eliminates the need for acceleration measurements/estimates and it is able to accurately reconstruct multiple simultaneous contact locations. Moreover, it provides uncoupled, configuration-independent, and singularity-free estimates of the external forces. The performance of the approach is experimentally validated on the SARA robot, the new generation of DLR lightweight robots, involving high resolution force-torque sensors in a redundant arrangement.

We present an approach to safe physical Human-Robot Interaction (pHRI) for industrial robots, including collision detection, distinguishing accidental from intentional contacts, and achieving collaborative tasks. Typical industrial robots have a closed control architecture that accepts only velocity/position reference inputs, there are no joint torque sensors, and little or no information is available to the user on robot dynamics and on low-level joint controllers. Nonetheless, taking also advantage of the presence of a Force/Torque (F/T) sensor at the end-effector, a safe pHRI strategy based on kinematic information, on measurements from joint encoders and motor currents, and on end-effector forces/torques can be realized. An admittance control law has been implemented for collaboration in manual guidance mode, with whole-body collision detection in place both when the robot is in autonomous operation and when is simultaneously collaborating with a human. Several pHRI experiments validate the approach on a KUKA KR5 Sixx R650 robot equipped with an ATI F/T sensor.

We present an optimization framework for the design and analysis of underactuated biped walkers, characterized by passive or actuated joints with rigid or non-negligible elastic actuation/transmission elements. The framework is based on optimal control, dealing with geometric constraints and various dynamic objective functions, as well as boundary conditions, which helps in selecting optimal values both for the actuation and the transmission parameters. Solutions of the formulated problems are shown for different kinds of bipedal architectures, and comparisons drawn between traditional rigid robots and compliant ones show the energy-efficiency of compliant actuators in the context of locomotion.

We revisit the classical problem of estimating the dynamic parameters of an unknown payload rigidly held by the robot end effector. The approach relies on the analysis of the symbolic expressions of the robot dynamic coefficients (i.e., combinations of dynamic parameters) when working with and without payload, with no special assumptions on payload structure. The linearity of the associated changes in the dynamic coefficients due to the payload addition is exploited so as to estimate the gravity and inertial parameters of the payload. The procedure is illustrated in simulation on a planar 2R robot with asymmetric payload and through experiments on a 7R KUKA LWR arm with medium payloads. Accurate estimates of non-inertial payload parameters can be obtained even by running the identification scheme on few small motions in a restricted area. The results are shown to be useful for improving the sensorless collision detection capabilities of a robot arm in the presence of an a priori unknown payload.

In the framework of Human-Robot Collaboration, a robot and a human operator may need to move in close coordination within the same workspace. A contactless coordinated motion can be achieved using vision, mounting a camera either on the robot end-effector or on the human. We consider here one instance of such a visual coordination task, with the robot end-effector that should maintain a prescribed position with respect to a moving RGB-D camera while pointing at it. For the 3D localization of the moving camera, we compare three different techniques and introduce some improvements to the best solution found for our application. For the motion tracking problem, we introduce a relaxed version of the pointing part of the task. This allows to take advantage of the redundancy of the robot, distributing the control effort over the available degrees of freedom. The effectiveness of the proposed approach is shown by V-REP simulations and experiments with the 7-dof KUKA LWR manipulator.

We present further computational tools and control results in the framework of human-robot coexistence and collaboration. A GPU parallel processing algorithm is introduced for real-time monitoring of dynamic distances between a robot and generic obstacles moving in its environment, taking advantage of the handling of RGB-D data directly in the depth space of the sensor. Combined with the use of model-based residual signals, this approach allows efficient detection of contact points on the robot with simultaneous estimation of the exchanged contact forces. When the robot is kinematically redundant for the original task and undergoes a physical contact, a control scheme accommodates collaboration trying to preserve task execution, or reacts by abandoning the task if the estimated contact forces exceed some safety threshold. Experimental results are reported for a KUKA LWR.

Robot assistants and professional coworkers are becoming a commodity in domestic and industrial settings. In order to enable robots to share their workspace with humans and physically interact with them, fast and reliable handling of possible collisions on the entire robot structure is needed, along with control strategies for safe robot reaction. The primary motivation is the prevention or limitation of possible human injury due to physical contacts. In this survey paper, based on our early work on the subject, we review, extend, compare, and evaluate experimentally model-based algorithms for real-time collision detection, isolation, and identification that use only proprioceptive sensors. This covers the context-independent phases of the collision event pipeline for robots interacting with the environment, as in physical human–robot interaction or manipulation tasks. The problem is addressed for rigid robots first and then extended to the presence of joint/transmission flexibility. The basic physically motivated solution has already been applied to numerous robotic systems worldwide, ranging from manipulators and humanoids to flying robots, and even to commercial products.

We consider the problem of extracting a complete set of numerical parameters that characterize the robot dynamics, starting from the identified values of dynamic coefficients that linearly parametrize the robot dynamic equations. This information is relevant when realistic dynamic simulations have to be performed using standard packages, or when addressing the efficient numerical implementation of model-based control laws using recursive Newton-Euler algorithms. The formulated problem is highly nonlinear and is solved through the use of global optimization techniques, while imposing also physical bounds on the dynamic parameters. The identification and parameter extraction process is illustrated and experimentally validated on the link dynamics of a KUKA LWR IV+ robot.

While collision detection and contact-related injury reduction in physical human-robot interaction has been studied intensively, safety issues in physical human-robot collaboration (pHRC) with continuous coupling of human and robot(s) has received little attention so far. We develop an energy monitoring control system that observes energy flows among the different subsystems involved in pHRC, shaping them to improve human safety according to selected metrics. Port-Hamiltonian formalisms are used to model each sub-system and their interconnection. An energy-based compliance controller that enhances safety by adapting the robot behavior is proposed and validated through extensive simulations.

We address the problem of estimating an external wrench acting along the structure of a robot manipulator, together with the contact position where the external force is being applied. For this, we consider the combined use of a force/torque sensor mounted at the robot base and of a model-based virtual sensor. The virtual sensor is provided by the residual vector commonly used for collision detection and isolation in human-robot interaction. Integrating the two types of measurement tools provides an efficient way to estimate all unknown quantities, using also the recursive Newton-Euler algorithm for dynamic computations. Different operative conditions are considered, including the special cases of pointwise interaction (pure contact force), known contact location, and of a base sensor measuring only forces. We highlight also the conditions for a correct estimation to be fully virtual, i.e., without resorting to a force/torque sensor. Realistic simulations assess the estimation performance for a 7R robot in motion, subject to an unknown external force applied to an unknown location.

During human-robot collaboration tasks, we may physically touch the robot at a generic location and engage an intentional exchange of forces while realizing coordinated motion of the common contact point. In order to control the relative motion and the exchanged contact forces, the latter need to be estimated without using any local force sensing device. Building upon our recent works, we generalize the classical hybrid force/velocity control design to this situation, handling complementary quantities along the directions of a suitable contact task frame in a dynamically decoupled way. The contact force is estimated online using our residual method together with an external sensor to localize the contact point, and the time-varying contact task frame is obtained analytically from this estimate. Experimental results are presented for a KUKA LWR4 robot using a Kinect sensor.

A model predictive controller is developed for following the position of a human dancer in robot ballroom dancing. The control design uses a dynamic model of a dancer, based on a variant of the so-called 3D Linear Inverted Pendulum Mode that includes also the swing foot. This model serves as a basis for a Kalman predictor of the human motion during the single-support phase, while a simpler kinematic technique is used during the double-support phase. The output of the prediction filter enables to design a Model Predictive Control (MPC) law, by recursively solving on line and within a preview window a convex linear-quadratic optimization problem, constrained by differential kinematic bounds on robot commands. Two different control strategies, either at the velocity or at the acceleration level, are proposed and compared in simulations and in actual experiments. Accurate and reactive behaviors are obtained by the ballroom robot follower, confirming the benefit of the predictive/filtering nature of a MPC approach to handle uncertainty of human intentions and noisy signals.

During human-robot interaction tasks, a human may physically touch a robot and engage in a collaboration phase with exchange of contact forces and/or requiring coordinated motion of a common contact point. Under the premise of keeping the interaction safe, the robot controller should impose a desired motion/force behavior at the contact or explicitly regulate the contact forces. Since intentional contacts may occur anywhere along the robot structure, the ability of controlling generalized contact motion and force becomes an essential robot feature. In our recent work, we have shown how to estimate contact forces without an explicit force sensing device, relying on residual signals to detect contact and on the use of an external (depth) sensor to localize the contact point. Based on this result, we introduce two control schemes that generalize the impedance and direct force control paradigms to a generic contact location on the robot, making use of the estimated contact forces. The issue of human-robot task compatibility is pointed out in case of control of generalized contact forces. Experimental results are presented for a KUKA LWR robot using a Kinect sensor.

We consider the problem of computing the inverse dynamics of a serial robot manipulator with N elastic joints in a recursive numerical way. The solution algorithm is a generalized version of the standard Newton-Euler approach, running still with linear complexity O(N) but requiring to set up recursions that involve higher order derivatives of motion and force variables. Mimicking the case of rigid robots, we use this algorithm and a numerical factorization of the link inertia matrix (which needs to be inverted in the elastic joint case) for implementing on-line a feedback linearization control law for trajectory tracking purposes. The complete method has a complexity that grows as O(N3). The developed tools are generic, easy to use, and do not require symbolic Lagrangian modeling and customization, thus being of particular interest when the number N of elastic joints becomes large.

Our recently developed Reverse Priority (RP) redundancy resolution method is extended here to the presence of unilateral constraints. The RP method computes the solution to a stack of prioritized tasks starting from the lowest priority one, and adding iteratively the contributions of higher priority tasks. In this framework, unilateral constraints can be added efficiently, while guaranteeing also continuity of joint velocity commands. Since unilateral (hard) constraints are typically placed at the highest priority levels, their treatment within the RP method leads to the least possible modification of the solution computed so far, when analyzing the need to activate or not these constraints. The effectiveness of the approach is shown by simulations on a planar 6R robot and on a humanoid robot, as well as experiments on a KUKA LWR manipulator.

We present an efficient method for addressing online the inversion of differential task kinematics for redundant manipulators, in the presence of hard limits on joint space motion that can never be violated. The proposed Saturation in the Null Space (SNS) algorithm proceeds by successively discarding the use of joints that would exceed their motion bounds when using the minimum norm solution. When processing multiple tasks with priority, the SNS method realizes a preemptive strategy by preserving the correct order of priority in spite of the presence of saturations. In the single- and multitask case, the algorithm automatically integrates a least possible task-scaling procedure, when an original task is found to be unfeasible. The optimality properties of the SNS algorithm are analyzed by considering an associated quadratic programming problem. Its solution leads to a variant of the algorithm, which guarantees optimality even when the basic SNS algorithm does not. Numerically efficient versions of these algorithms are proposed. Their performance allows real-time control of robots executing many prioritized tasks with a large number of hard bounds. Experimental results are reported.

The capability of controlling both the position/torque and the stiffness of the joints is the main feature of the next generation of robots based on Variable Stiffness Actuators (VSA). For the purpose of accurate control, recent works have pointed out that is not possible to rely completely on analytical models of the stiffness characteristics of the transmissions/joints and that an on-line estimation of stiffness is often mandatory. Building on our previous results, we present a new method to estimate the stiffness based only on input-output signals, without any knowledge of motor parameters nor the need of joint torque sensing. In addition, a Recursive Least Squares method based on a QR decomposition (QR-RLS) is used, which is very robust to poor excitation conditions. In order to deal more efficiently with noisy signals, a combination of two filtering actions is also considered, with a causal Kinematic Kalman Filter (KKF) and a non-causal Savitzky-Golay (SG) filter. Simulation results and comparison with two other state-of-the-art stiffness estimators are presented.

The paper addresses the following problem for redundant robots. Given a second-order inverse differential scheme that realizes instantaneously a desired task acceleration and has some specified properties in terms of joint acceleration or torque, define a discrete-time joint velocity command that shares the same characteristics under suitable hypotheses. The goal is to obtain simpler implementations of possibly complex robot control laws that i) can be directly interfaced to the low-level servo loops of a robot, ii) require less task information and on-line computations, iii) are still provably good with respect to some target performance. The method is illustrated by considering the conversion into discrete-time velocity commands of control schemes for redundant robots that minimize the (possibly, weighted) norm of joint acceleration or joint torque, or that add null-space damping to overcome floating motion of the robot joints. Numerical results are presented for the kinematic control of a 7R KUKA LWR.

An approach is presented for the model identification of the so-called link dynamics used by the KUKA LWR-IV, a lightweight manipulator with elastic joints that is very popular in robotics research but for which a complete and reliable dynamic model is not yet publicly available. The control software interface of this robot provides numerical values of the link inertia matrix and the gravity vector at each configuration, together with link position and joint torque sensor data. Taking advantage of this information, a general procedure is set up for determining the structure and identifying the value of the relevant dynamic coefficients used by the manufacturer in the evaluation of these robot model terms. We call this a reverse engineering approach, because our main goal is to match the numerical data provided by the software interface, using a suitable symbolic model of the robot dynamics and the inertial and gravity coefficients that are being estimated. Only configuration-dependent terms are involved in this process, and thus static experiments are sufficient for this task. The main issues of dynamic model identification for robots with elastic joints are discussed in general, highlighting the pros and cons of the approach taken for this class of KUKA lightweight manipulators. The main identification results, including training and validation tests, are reported together with additional dynamic validation experiments that use the complete identified model and joint torque sensor data.

A novel method to handle multiple robotic tasks with priorities is presented. The occurrence of singularities, both of the kinematic and algorithmic type, may affect the correct hierarchy in task execution. Existing methods deal with singularities either by using damped least squares solutions or by relaxing the enforcement of secondary tasks. Damped pseudo-inversion mitigates undesired effects near singularities, at the cost of non-negligible task errors and deformation even of the highest priority task. When secondary tasks are not enforced, hierarchy is preserved but these tasks are not executed accurately even when this would be possible. In our approach, joint motion contributions are added following the reverse order of task priorities and working with suitable projection operators. Higher priority tasks are processed at the end, avoiding possible deformations caused by singularities occurring in lower priority tasks. The proposed Reverse Priority (RP) method allows executing at best all tasks while still preserving the desired hierarchy. The effectiveness of the RP method is shown through numerical simulations and with experiments on a 7-dof KUKA LWR.

Physical human-robot collaboration is characterized by a suitable exchange of contact forces between human and robot, which can occur in general at any point along the robot structure. If the contact location and the exchanged forces were known in real time, a safe and controlled collaboration could be established. We present a novel approach that allows localizing the contact between a robot and human parts with a depth camera, while determining in parallel the joint torques generated by the physical interaction using the so-called residual method. The combination of such exteroceptive sensing and model-based techniques is sufficient, under suitable conditions, for a reliable estimation of the actual exchanged force at the contact, realizing thus a virtual force sensor. Multiple contacts can be handled as well. We validate quantitatively the proposed estimation method with a number of static experiments on a KUKA LWR. An illustration of the use of estimated contact forces in the realization of collaborative behaviors is given, reporting preliminary experiments on a generalized admittance control scheme at the contact point.

For robots that are redundant with respect to a given task, we present an optimal differential kinematic inversion method in the presence of hard bounds on joint range, joint velocity, and joint acceleration. These hard bounds specify the robot motion capabilities that cannot be exceeded at any time. On the other hand, scaling of the desired task trajectory is allowed whenever the robot capabilities are insufficient to execute the original task. For a problem formulated in this way, we have recently presented the Saturation in the Null Space (SNS) algorithm that produces an efficient solution, based on Jacobian pseudoinversion and recovery in the null space of the saturation effects of a reduced number of joint velocity commands. To investigate the optimality properties of the SNS algorithm, we recast the problem as a constrained quadratic programming (QP) problem, in which the joint velocity norm as well as the task scaling are to be minimized. Its solution leads to a variant of the original algorithm, the Optimal Saturation in the Null Space (Opt-SNS). The Opt-SNS guarantees an optimal solution also when the basic SNS fails to do so and improves the numerical performance over the state-of-the-art QP solver. The possible existence of discontinuous solutions for the formulated problem is avoided by the introduction of a task scaling margin. The extension to the multi-task case is also presented. Simulation results for the 7R lightweight KUKA LWR IV robot illustrate the properties and computational efficiency of the new algorithm.

In physical Human-Robot Interaction, the basic problem of fast detection and safe robot reaction to unexpected collisions has been addressed successfully on advanced research robots that are torque controlled, possibly equipped with joint torque sensors, and for which an accurate dynamic model is available. In this paper, an end-user approach to collision detection and reaction is presented for an industrial manipulator having a closed control architecture and no additional sensors. The proposed detection and reaction schemes have minimal requirements: only the outer joint velocity reference to the robot manufacturer's controller is used, together with the available measurements of motor currents and joint positions. No a priori information on the robot dynamic model and existing low-level joint controllers is strictly needed. A suitable on-line processing of the motor currents allows to distinguish between accidental collisions and intended human-robot contacts, so as to switch the robot to a collaboration mode when needed. Two examples of reaction schemes for collaboration are presented, with the user pushing/pulling the robot at any point of its structure (e.g., for manual guidance) or with a compliant-like robot behavior in response to forces applied by the human. The actual performance of the methods is illustrated through experiments on a KUKA KR5 manipulator.

A kinematically redundant robot with limited motion capabilities, expressed by inequality constraints of the box type on joint variables and commands, needs to perform a set of tasks, expressed by linear equality constraints on robot commands, possibly organized with priorities. Robot motion capabilities cannot be exceeded at any time, and the resulting constraints are to be considered as hard bounds. Instead, robot tasks can be relaxed by velocity scaling if no feasible solution exists. To address this redundancy resolution problem, we developed a method in which joint space commands are successively saturated and their effect compensated in the null space of a suitable task Jacobian (SNS, Saturation in the Null Space). Computationally efficient versions of the basic and optimal SNS algorithms are proposed here, based on a task augmentation reformulation, a QR factorization of the main matrices involved, and a so-called warm start procedure. The obtained performance allows to control in real time robots with high-dimensional configuration spaces executing a large number of prioritized tasks, and with an associated high number of hard bounds that saturate during motion.

The video illustrates on-going activities at DIAG Sapienza on physical Human-Robot Collaboration (pHRC), based on a control framework imposing robot behaviors that are consistent with safety and coexistence requirements.

In this paper a real-time collision avoidance approach is presented for safe human-robot coexistence. The main contribution is a fast method to evaluate distances between the robot and possibly moving obstacles (including humans), based on the concept of depth space. The distances are used to generate repulsive vectors that are used to control the robot while executing a generic motion task. The repulsive vectors can also take advantage of an estimation of the obstacle velocity. In order to preserve the execution of a Cartesian task with a redundant manipulator, a simple collision avoidance algorithm has been implemented where different reaction behaviors are set up for the end-effector and for other control points along the robot structure. The complete collision avoidance framework, from perception of the environment to joint-level robot control, is presented for a 7-dof KUKA Light-Weight-Robot IV using the Microsoft Kinect sensor. Experimental results are reported for dynamic environments with obstacles and a human.

We present a novel efficient method addressing the inverse differential kinematics problem for redundant manipulators in the presence of different hard bounds (joint range, velocity, and acceleration limits) on the joint space motion. The proposed SNS (Saturation in the Null Space) iterative algorithm proceeds by successively discarding the use of joints that would exceed their motion bounds when using the minimum norm solution and reintroducing them at a saturated level by means of a projection in a suitable null space. The method is first defined at the velocity level and then moved to the acceleration level, so as to avoid joint velocity discontinuities due to the switching of saturated joints. Moreover, the algorithm includes an optimal task scaling in case the desired task trajectory is unfeasible under the given joint bounds. We also propose the integration of obstacle avoidance in the Cartesian space by properly modifying on line the joint bounds. Simulation and experimental results reported for the 7-dof lightweight KUKA LWR IV robot illustrate the properties and computational efficiency of the method.

We present an efficient method for motion control of redundant robots performing multiple prioritized tasks in the presence of hard bounds on joint range, velocity, and acceleration/ torque. This is an extension of our recently proposed SNS (Saturation in the Null Space) algorithm developed for single tasks. The method is defined at the level of acceleration commands and proceeds by successively discarding one at a time the commands that would exceed their bounds for a task of given priority, and reintroducing them at their saturated levels by projection in the null space of a suitable Jacobian associated to the already considered tasks. When processing all tasks in their priority order, a correct preemptive strategy is realized in this way, i.e., a task of higher priority uses in the best way the feasible robot capabilities it needs, while lower priority tasks are accommodated with the residual capability and do not interfere with the execution of higher priority tasks. The algorithm automatically integrates a multi-task least possible scaling strategy, when some ordered set of original tasks is found to be unfeasible. Simulation and experimental results on a 7-dof lightweight KUKA LWR IV robot illustrate the good performance of the method.

We propose a novel approach for estimating the nonlinear stiffness of robot joints with flexible transmissions. Based on the definition of dynamic residual signals, we derive stiffness estimation methods that use only position and velocity measurements on the motor side and needs only the knowledge of the dynamic parameters of the motors. In particular, no extra force/torque sensing is needed. Two different strategies are considered, a model-based stiffness estimator and a black-box stiffness estimator. Both strategies consist of two stages. The first stage of the model-based estimator generates a residual signal that is a first-order filtered version of the flexibility torque of the transmission, while in the second stage a least squares fitting method is used to estimate the model parameters of the stiffness. The black-box estimator uses in the first stage a second-order residual that is directly a filtered version of the stiffness multi plied by the deformation rate of the transmission. In the second stage, a simple regressor provides the transmission stiffness in a singularity-robust way. Numerical results reported for the cases of constant, nonlinear, or variable stiffness transmissions demonstrate the effectiveness of the approach and the relative merits of the two estimation strategies.

We present a new control approach to regulation tasks for robots with elastic joints in the presence of gravity. The control law combines a term that cancels the gravity effects on the robot link dynamics with a PD-type error feedback on the motor variables. The first control component follows from the feedback equivalence principle when imposing to the link variables the same dynamic behavior as if gravity were absent. The PD component can then be designed in a rather straightforward way. Global asymptotic stability is shown via Lyapunov analysis, without the need of strictly positive lower bounds neither on the proportional control gain nor on the structural joint stiffness. The control approach is also extended to the case of robot joints with nonlinear stiffness.

Affine-invariant feature matching plays an important role in many robot vision applications, such as robot visual navigation, object detection, visual tracking and visual SLAM, etc. In the early stages, invariant keypoints are used to detect the affine transformation. But the accuracy is very low. In recent years, some people introduce SIFT method into robot vision field, which greatly enhances the accuracy. But it is too time-consuming to meet the requirements of real-time robot vision applications. In this paper, we propose a novel learning-based feature matching approach to address the problem. First, it uses a fast algorithm to extract keypoints. Then, our method identifies keypoints that belong to different objects or background by color and texture representation. The keypoints are clustered into corresponding groups. At last, a two-stage multilayer ferns classifier is trained to recognize the local patches and get the estimate of viewpoint. We test our approach on public datasets and apply it in a visual SLAM application. The result demonstrates that our method can provide robust and powerful matching ability. Even on some difficult matching cases, it also performs remarkably well. Further more, because there is no need to compute descriptors for the image, our method is very fast at run-time.

A general concept for the gaze control of a redundant humanoid robot head is presented. It is based on an adaptive Kalman filter that predicts the next state of the moving target, processing the position information provided by a head-mounted stereo camera. The trajectory tracking control at the task level combines a proportional feedback and a feedforward term. The gains of both control actions are adapted in order to provide optimal dynamic response for unknown arbitrary target trajectories. Inverse differential kinematics is evaluated so that human-like joint motions are achieved. To exploit kinematic redundancy, a weighted pseudoinverse is realized that takes into account different optimization criteria. Additional self-motions of the head are also considered. Experimental results on the head of the humanoid robot ARMAR-III are presented.

Despite many recent developments in virtual reality, an effective locomotion interface which allows for normal walking through large virtual environments was until recently still lacking. Here, we describe the new CyberWalk omnidirectional treadmill system, which makes it possible for users to walk endlessly in any direction, while never leaving the confines of the limited walking surface. The treadmill system improves on previous designs, both in its mechanical features and in the control system employed to keep users close to the center of the treadmill. As a result, users are able to start walking, vary their walking speed and direction, and stop walking as they would on a normal, stationary surface. The treadmill system was validated in two experiments, in which both the walking behavior and the performance in a basic spatial updating task were compared to that during normal overground walking. The results suggest that walking on the CyberWalk treadmill is very close to normal walking, especially after some initial familiarization. Moreover, we did not find a detrimental effect of treadmill walking in the spatial updating task. The CyberWalk system constitutes a significant step forward to bringing the real world into the laboratory or workplace.

Depth and presence sensors are used to prevent collisions in environments where human/robot coexistence is relevant. To address the problem of occluded areas, we extend in this paper a recently introduced efficient approach for preventing collisions using a single depth sensor to multiple depth and/or presence sensors. Their integration is systematically handled by resorting to the concept of image planes, where computations can be suitable carried out on 2D data without reconstructing obstacles in 3D. To maximize the on-line collision detection performance by multiple sensor integration, an off-line optimal sensor placement problem is formulated in a probabilistic framework, using a cell decomposition and characterizing the probability of cells being in the shadow of obstacles or unobserved. This approach allows to fit the optimal numerical solution to the most probable operating conditions of a human and a robot sharing the same working area. Three examples of optimal sensor placement are presented.

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.

For us humans, walking is our most natural way of moving through the world. One of the major challenges in present research on navigation in virtual reality is to enable users to physically walk through virtual environments. Although treadmills, in principle, allow users to walk for extended periods of time through large virtual environments, existing setups largely fail to produce a truly immersive sense of navigation. Partially, this is because of inadequate control of treadmill speed as a function of walking behavior. Here, we present a new control algorithm that allows users to walk naturally on a treadmill, including starting to walk from standstill, stopping, and varying walking speed. The treadmill speed control consists of a feedback loop based on the measured user position relative to a given reference position, plus a feed-forward term based on online estimation of the user's walking velocity. The purpose of this design is to make the treadmill compensate fully for any persistent walker motion, while keeping the accelerations exerted on the user as low as possible. We evaluated the performance of the algorithm by conducting a behavioral experiment in which we varied its most important parameters. Participants walked at normal walking speed and then, on an auditory cue, abruptly stopped. After being brought back to the center of the treadmill by the control algorithm, they rated how smoothly the treadmill had changed its velocity in response to the change in walking speed. Ratings, in general, were quite high, indicating good control performance. Moreover, ratings clearly depended on the control algorithm parameters that were varied. Ratings were especially affected by the way the treadmill reversed its direction of motion. In conclusion, controlling treadmill speed in such a way that changes in treadmill speed are unobtrusive and do not disturb VR immersiveness is feasible on a normal treadmill with a straightforward control algorithm.

We present a modified recursive Newton-Euler method for computing some dynamic expressions that arise in two problems of fault detection and control of serial robot manipulators, and which cannot be evaluated numerically using the standard method. The two motivating problems are: i) the computation of the residual vector that allows accurate detection of actuator faults or unexpected collisions using only robot proprioceptive measurements, and ii) the evaluation of a passivity-based trajectory tracking control law. The modified Newton-Euler algorithm generates factorization matrices of the Coriolis and centrifugal terms that satisfy the skew-symmetric property. The computational advantages with respect to numerical evaluation of symbolically obtained dynamic expressions is illustrated on a 7R DLR lightweight manipulator.

Variable stiffness actuation (VSA) devices are being used to jointly address the issues of safety and performance in physical human-robot interaction. With reference to the VSA-II prototype, we present a feedback linearization approach that allows the simultaneous decoupling and accurate tracking of motion and stiffness reference profiles. The operative condition that avoids control singularities is characterized. Moreover, a momentum-based collision detection scheme is introduced, which does not require joint torque sensing nor information on the time-varying stiffness of the device. Based on the residual signal, a collision reaction strategy is presented that takes advantage of the proposed nonlinear control to rapidly let the arm bounce away after detecting the impact, while limiting contact forces through a sudden reduction of the stiffness. Simulations results are reported to illustrate the performance and robustness of the overall approach. Extensions to the multidof case of robot manipulators equipped with VSA-II devices are also considered.

The CyberWalk is a large size 2D omni-directional platform that allows unconstrained locomotion possibilities to a walking user for VR exploration. In this paper we present the motion control design for the platform, which has been developed within the homonymous European research project. The objective is to compensate the intentional motion of the user, so as to keep her/him always close to the platform center while limiting the perceptual effects due to actuation commands. The controller acts at the acceleration level, using suitable observers to estimate the unmeasurable intentional walker's velocity and acceleration. A moving reference position is used to limit the accelerations felt by the user in critical transients, e.g., when the walker suddenly stops motion. Experimental results are reported that show the benefit of designing separate control gains in the two orthogonal directions (lateral and sagittal) of a frame attached to the walker.

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.

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.

Physical human-robot interaction requires the development of safe and dependable robots. This involves the mechanical design of lightweight and compliant manipulators and the definition of motion control laws that allow to combine compliant behavior in reaction to possible collisions, while preserving accuracy and performance of rigid robots in free space. In this framework, great attention has been given to robots manipulators with relevant elasticity at the joints/transmissions. While the modeling and control of robots with elastic joints of finite but constant stiffness is a well- established topic, few results are available for the case of robot structures with variable joint stiffness -mostly limited to the 1-dof case. We present here a basic control study for a general class of multi-dof manipulators with variable joint stiffness, taking into account different possible modalities for changing the joint stiffness on the fly by an additional set of commands. It is shown that nonlinear control laws, based either on static or dynamic state feedback, are able to exactly linearize the closed- loop equations and allow to simultaneously impose a desired behavior to the robot motion and to the joint stiffness in an decoupled way. Illustrative simulations results are presented.

In the framework of physical Human-Robot Interaction (pHRI), methodologies and experimental tests are presented for the problem of detecting and reacting to collisions between a robot manipulator and a human being. Using a lightweight robot that was especially designed for interactive and cooperative tasks, we show how reactive control strategies can significantly contribute to ensuring safety to the human during physical interaction. Several collision tests were carried out, illustrating the feasibility and effectiveness of the proposed approach. While a subjective “safety” feeling is experienced by users when being able to naturally stop the robot in autonomous motion, a quantitative analysis of different reaction strategies was lacking. In order to compare these strategies on an objective basis, a mechanical verification platform has been built. The proposed collision detection and reactions methods prove to work very reliably and are effective in reducing contact forces far below any level which is dangerous to humans. Evaluations of impacts between robot and human arm or chest up to a maximum robot velocity of 2.7 m/s are presented.

We present a method that allows automatic reaction of a robot to physical collisions, while preserving as much as possible the execution of a Cartesian task for which the robot is kinematically redundant. The work is motivated by human-robot interaction scenarios, where ensuring safety is of primary concern whereas preserving task performance is an appealing secondary goal. Unexpected collisions may occur anywhere along the manipulator structure. Their fast detection is realized using our previous momentum-based method, which does not require any external sensing. The reaction torque applied to the joints reduces the effective robot inertia seen at the contact and lets the robot safely move away from the collision area. If we wish, however, to continue the execution of a Cartesian trajectory, robot redundancy can be exploited by projecting the reaction torque into the null space of a dynamic task matrix so as not to affect the original end-effector motion. This leads to the use of the so-called dynamically consistent approach to redundancy resolution, which is further elaborated in the paper. A partial task relaxation strategy can also be devised, with the objective of keeping contact forces below a user-defined safety threshold. Simulation results are reported for the 7R KUKA/DLR lightweight robot arm.

In this paper we introduce a friction observer for robots with joint torque sensing (in particular for the DLR medical robot) in order to increase the positioning accuracy and the performance of torque control. The observer output corresponds to the low-pass filtered friction torque. It is used for friction compensation in conjunction with a MIMO controller designed for flexible joint arms. A passivity analysis is done for this friction compensation, allowing a Lyapunov based convergence analysis in the context of the nonlinear robot dynamics. For the complete controlled system, global asymptotic stability can be shown. Experimental results validate the practical efficiency of the approach.

2008 brings important changes in the operation of the IEEE Transactions on Robotics (T-RO). T-RO has a new paper handling system, an additional fifth Editor, and an Editor-in-Chief Elect.

The CyberCarpet is an actuated platform that allows unconstrained locomotion of a walking user for VR exploration. The platform has two actuating devices (linear and angular) and the motion control problem is dual to that of nonholonomic wheeled mobile robots. The main control objective is to keep the walker close to the platform center. We first recall global kinematic control schemes developed at the velocity level, i.e., with the linear and angular velocities of the platform as input commands. Then, we use backstepping techniques and the theory of cascaded systems to move the design to control laws at the acceleration level. Acceleration control is more suitable to take into account the limitations imposed to the platform motion by the actuation system and/or the physiological bounds on the human walker. In particular, the availability of platform accelerations allows the analytical computation of the apparent accelerations felt by the user.

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.

Robots that use cycloidal gears, belts, or long shafts for transmitting motion from the motors to the driven rigid links display visco-elastic phenomena that can be assumed to be concentrated at the joints. For the design of advanced, possibly nonlinear, trajectory tracking control laws that are able to fully counteract the vibrations due to joint elasticity, full state feedback is needed. However, no robot with elastic joints has sensors available for its whole state, i.e., for measuring positions and velocities of both motors and links. Several nonlinear observers have been proposed in the past, assuming different reduced sets of measurements. We introduce here a new observer which uses only motor position sensing, together with accelerometers suitably mounted on the links of the robot arm. Its main advantage is that the error dynamics on the estimated state is independent from the dynamic parameters of the robot links, and can be tuned with standard decentralized linear techniques (locally to each joint). We present an experimental validation of this observer for the three base joints of a KUKA KR15/2 industrial robot and illustrate the control use of the obtained results.

Exploration of virtual worlds with unconstrained locomotion possibilities for the user is the main objective of the European research project CyberWalk. This should be achieved through the use of an actuated platform (the CyberCarpet) that compensates for the walker's locomotion in such a way to keep her/him close to the platform center. This paper presents the control problem for the platform motion, including objectives and constraints, overall control architecture, and kinematic modeling. Since the platform has only two actuating devices (linear and angular), the control problem is similar to that of output regulation for nonholonomic wheeled mobile robots in the presence of an unpredictable disturbance due to walker's locomotion. Based on the kinematic model, a velocity control design achieving input-output decoupling and linearization is proposed and its performance is verified by simulations

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

A robot manipulator sharing its workspace with humans should be able to quickly detect collisions and safely react for limiting injuries due to physical contacts. In the absence of external sensing, relative motions between robot and human are not predictable and unexpected collisions may occur at any location along the robot arm. Based on physical quantities such as total energy and generalized momentum of the robot manipulator, we present an efficient collision detection method that uses only proprioceptive robot sensors and provides also directional information for a safe robot reaction after collision. The approach is first developed for rigid robot arms and then extended to the case of robots with elastic joints, proposing different reaction strategies. Experimental results on collisions with the DLR-III lightweight manipulator are reported

Feedback linearization is a viable nonlinear control technique for solving trajectory tracking problems in robots with (and without) elastic joints. However, the additional presence of dissipative effects due to joint viscosity destroys full state feedback linearizability. For robots with visco-elastic joints, the use of a static state feedback can achieve at most input-output linearization and decoupling, since an internal nonlinear dynamics is left in the closed-loop system. Although the stability properties of this unobservable dynamics still guarantee perfect output tracking in nominal conditions, control design based on static feedback becomes ill-conditioned as joint viscosity decreases. Instead, resorting to a nonlinear dynamic state feedback leads to the same closed-loop properties, but with a regularized control effort for any level of joint viscosity and elasticity. Static and dynamic nonlinear feedback control designs are presented for a reduced and a complete dynamic model of visco-elastic joint robots. A numerical comparison on a simple case study illustrates the benefits of the dynamic input-output linearization approach.

We consider the problem of real-time detection of collisions between a robot manipulator and obstacles of unknown geometry and location in the environment without the use of extra sensors. The idea is to handle a collision at a generic point along the robot as a fault of its actuating system. A previously developed dynamic FDI (fault detection and isolation) technique is used, which does not require acceleration or force measurements. The actual robot link that has collided can also be identified. Once contact has been detected, it is possible to switch to a suitably defined hybrid force/motion controller that enables to keep the contact, while sliding on the obstacle, and to regulate the interaction force. Simulation results are shown for a two-link planar robot.

We present a scheme for identifying the time profile of actuator faults that may affect a robot manipulator. Starting from our previous method for fault detection and isolation (FDI) based on generalized momenta, fault identification is additionally obtained through the H/sub /spl infin//-design of a state observer for uncertain systems. For each separate fault channel, the identifier consists of a linear filter driven by the corresponding residual signal. Under the weak assumption of bounded time derivative for the otherwise unknown fault input to be identified, the fault estimation error is shown to be ultimately uniformly bounded, with ultimate bound that can be set arbitrarily small. The information on the type and severity of the fault may then be used for reconfiguring the control strategy. Experimental results on a 2R planar manipulator are presented.

An adaptive scheme is presented for actuator fault detection and isolation (FDI) in robotic systems, based on the use of generalized momenta and of a suitable overparametrization of the uncertain robot dynamics. This allows to obtain an accurate and reliable detection and isolation of possibly concurrent faults also during the parameter adaptation phase. Experimental results are reported for a planar robot under gravity, considering partial, total, or bias-type failures of the motor torques.

In this paper a PD control with on-line gravity compensation is proposed for robot manipulators with elastic joints. The work extends the existing PD control with constant gravity compensation, where only the gravity torque needed at the desired configuration is used throughout motion. The control law requires measuring only position and velocity on the motor side of the elastic joints, and the on-line compensation scheme estimates the actual gravity torque using a biased measure of the motor position. It is proved via a Lyapunov argument that the control law globally stabilizes the desired robot configuration. Experimental results on an 8-d.o.f. robot manipulator with elastic joints show that this control scheme improves the transient behavior with respect to a PD controller with constant gravity compensation. In addition, it can be usefully applied in combination with a point-to-point interpolating trajectory leading to a reduction of final steady-state errors due to static friction and/or uncertainty in the gravity compensation.

We present a method based on the use of generalized momenta for detecting and isolating actuator faults in robot manipulators. The FDI scheme does not need acceleration estimates or simulation of the nominal robot dynamics and covers a general class of input faults. Numerical results for a 2R robot undergoing also concurrent actuator faults are reported. This method is extended to robots with joint elasticity and to the inclusion of actuator dynamics.

The classical dynamic scaling property of robot trajectories is analyzed in the case of presence of elastic transmissions. We present a technique for recovering the fastest motion under torque constraints, when uniform time scaling is used along a given path. The scaling algorithm is based on the solution of a complete quartic polynomial equation, which reduces to a biquadratic one in the absence of viscous friction. Consequences on the organization of inverse dynamics computation are pointed out. Numerical results are reported for a planar 2R arm, illustrating the differences that arise with respect to the fully rigid case.

We consider the controllability problem, i.e., the existence of a suitable control input that achieves a desired reconfiguration, for underactuated mechanical systems. Since there is no general analytic tool for investigating this natural controllability property in nonlinear systems, one possibility is to study small-time local controllability (STLC), a property which is sufficient for stating controllability. The available STLC conditions require the computation of Lie brackets on the classical state-space form of the dynamic model equations. In this paper, we provide a simple sufficient condition for testing STLC in underactuated mechanical systems with n degrees of freedom and n - 1 control inputs, directly based on the terms of the system inertia matrix. As an application, we analyze the STLC of planar robots with n rotational joints, one of which is passive.

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 consider the trajectory planning problem for the class of XYnR~ planar underactuated robots, having the first two (rotational or prismatic) joints actuated and the last n rotational joints passive. Under the assumption that each passive link is attached at the center of percussion of the previous passive link, the dynamic model assumes a simplified form and we show how to recursively design a dynamic feedback that completely linearizes the system equations. This result allows to plan smooth rest-to-rest motions using polynomial interpolation. As an example, we report the numerical results obtained for trajectory planning of an RR2R~ robot.

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 present a survey of the nominal motion generation schemes and of the associated simple control solutions for robots displaying flexibility effects. Two model classes are considered: robots with elastic joints but rigid links, and robots with flexible links. Model-based feedforward laws are derived for the two basic motion tasks of state-to-state transfer in given time and exact trajectory execution. In particular, we present a new solution to the finite-time reconfiguration problem for a one-link flexible arm. Finally, we use the developed commands into a simple feedback scheme that requires only standard sensors on the motors.

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.

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.

We consider the trajectory tracking control problem for a 4-wheel differentially driven mobile robot moving on an outdoor terrain. A dynamic model is presented accounting for the effects of wheel skidding. A model-based nonlinear controller is designed, following the dynamic feedback linearization paradigm. An operational nonholonomic constraint is added at this stage, so as to obtain a predictable behavior for the instantaneous center of rotation thus preventing excessive skidding. The controller is then robustified, using conventional linear techniques, against uncertainty in the soil parameters at the ground-wheel contact. Simulation results show the good performance in tracking spline-type trajectories on a virtual terrain with varying characteristics.

For a general class of robots with elastic joints, we introduce an inversion algorithm for the synthesis of a dynamic feedback control law that gives input-output decoupling and full state linearization. Control design is performed directly on the second-order robot dynamic equations. The linearizing control law is expressed in terms of the original model components and of their time derivatives, allowing an efficient organization of computations. A tight upper bound for the dimension of the needed dynamic compensator is also obtained.

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.

We consider the inverse dynamics problem for robot arms with flexible links, i.e., the computation of the input torque that allows exact tracking of a trajectory defined for the manipulator end-effector. A stable inversion controller is derived numerically, based on the computation of bounded link deformations and, from these, of the required feedforward torque associated with the desired tip motion. For a general class of multi-link flexible manipulators, three alternative computational algorithms are presented, all defined on the second-order robot dynamic equations. Trajectory tracking is obtained by adding a (partial) state feedback, within a nonlinear regulation approach. Experimental results are reported for the FLEXARM robot.

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.

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.

We consider the theoretical aspects of the control problem for robots with rigid links which consist of some rigid joints and some non-negligible elastic joints. We start from the reduced model of robots with all elastic joints introduced by Spong, which is linearizable by static feedback (as for the rigid robot model). For the mixed rigid/elastic joints, we give the structural necessary and sufficient conditions for input-output decoupling and full state linearization via static state feedback. These turn out to be very restrictive. However, when a robot fails to satisfy these conditions, we show that a dynamic state feedback always guarantees the same result. This implies that, for the mixed rigid/elastic joint case, the role of dynamic feedback is essential. The explicit forms of the needed nonlinear controllers are provided in terms of the dynamic model elements.

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.

A general control-oriented formalism has been introduced by DeLuca and Manes (1991, 1994) to describe robot-environment interaction in the case of a single robot in contact with a possibly dynamic environment. Two possibilities were obtained in the design of hybrid motion-force control laws depending on whether motion or force is explicitly controlled along properly defined dynamic directions. An extension of this formalism for modeling and controlling cooperating robots in the manipulation of a payload is presented. Several contact arrangements and environmental constraints on the object can be considered, mixing the presence of kinematic constraints and dynamic interactions. The modeling approach leads to the characterization of complementary directions in the task space: those where only end-effector velocities are admissible, those where only reaction forces may exist, and those in which energy can be transferred between each robot and the payload. Two classes of model-based hybrid force-motion controllers are then designed similarly to the single robot case. The authors show that the classical approach of controlling payload motion and internal forces for cooperating robots is recovered as one special case. Moreover, within this framework a new control alternative naturally arises, namely the possibility of controlling both internal forces and active forces producing motion. Numerical simulation results are reported for power grasp and hard finger point contacts and with the two alternative control laws.

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.>

A control-oriented modeling approach for describing kinematics and dynamics of robots in contact with a dynamic environment is presented. In many robotic tasks the manipulator in contact cannot be simply modeled as a kinematically constrained system. Conversely, modeling of robot-environment interactions through dynamic impedance may not fit the task layout. A suitable model structure is proposed in this note that handles the more general case in which purely kinematic constraints on the robot end-effector live together with dynamic interactions. Feasible end-effector configurations are parameterized from the environment point of view, using a minimal set of coordinates. Accordingly, a description is obtained also for admissible velocities and contact forces. In particular, a force parameterization is chosen so as to separate static reaction forces from active forces responsible for energy transfer between robot and environment. The overall dynamics of the coupled robot-environment system is obtained in a single framework. The introduced modeling technique naturally leads to the design of new hybrid control laws.>

A simple controller is presented for the regulation problem of robot arms with flexible links under gravity. It consists of a joint PD feedback plus a constant feedforward. Global asymptotic stability of the reference equilibrium state is shown under a structural assumption about link elasticity and a mild condition on the proportional gain. The result holds also in the absence of internal damping of the flexible arm. A numerical case study is presented.>

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 design of a repetitive learning controller for robots with elastic joints, following a frequency-domain approach, is presented. An efficient and simple iterative learning algorithm is presented, allowing solution of the output tracking problem with limited knowledge of system dynamics and using only a linear stabilizing feedback on the motor variables. Simulation results reported for a two-link planar robot under gravity showed good motion performance in this critical case.>

An iterative scheme is proposed for learning the input torques that produce a specified repetitive end-effector trajectory for a redundant manipulator, without explicit knowledge of the robot dynamic model. The approach does not rely on a specific inverse kinematic solution. In the learning problem, the number of driving error signals (in the task space) is strictly less than the number of inputs to be determined (in the joint space). During the iterative process, control effort is transferred from a linear feedback law designed for the end-effector error to the learned feedforward term. Joint velocity damping stabilizes the closed loop system. The basic learning algorithm is designed in the frequency domain, while a digital implementation of the necessary signal filtering improves the speed and uniformity of convergence of the learning performance. Simulations are reported for a three-link planar manipulator. The inclusion of a kinematic singularity avoidance scheme is also illustrated.>

Closed-form equations of motion are presented for planar lightweight robot arms with multiple flexible links. The kinematic model is based on standard frame transformation matrices describing both rigid rotation and flexible displacement, under small deflection assumption. The Lagrangian approach is used to derive the dynamic model of the structure. Links are modeled as Euler-Bernoulli beams with proper clamped-mass boundary conditions. The assumed modes method is adopted in order to obtain a finite-dimensional model. Explicit equations of motion are detailed for two-link case assuming two modes of vibration for each link. The associated eigenvalue problem is discussed in relation with the problem of time-varying mass boundary conditions for the first link. The model is cast in a compact form that is linear with respect to a suitable set of constant parameters. Extensive simulation results that validate the theoretical derivation are included.>

Reference is made to the problem of controlling the dynamic behavior of robots with rigid links but in presence of joint elasticity. It is shown that use of the more general class of dynamic nonlinear state-feedback allows solving both the feedback linearization and the input-output decoupling problems. A constructive procedure for the decoupling and linearizing feedback is given which is based on generalization system inversion and on the properties of the so-called zero-dynamics of the system. A case study of a planar two-link robot with elastic joints is included. The role of dynamic feedback for this class of robots is discussed.>