This paper explores the challenge of optimal routing for a mobile robot navigating a dynamic and shared human environment. The primary goal is to minimize the risk of performance degradation during motion, such as delays in completing tasks due to the need for safe or acceptable human robot encounters. The problem is formulated as a graph whose edge costs become progressively known only as the robot moves through the environment. We model this problem as a Markov Decision Process (MDP), enabling an offline evaluation of the expected cost of alternative routes based on statistical information about human spatial distributions and possible observations at each intersection. This compact state representation scales linearly with the number of intersections in the map. Since the memoryless property of the MDP may induce loops during online execution, we compute an offline policy and introduce an online policy adaptation mechanism to prevent cyclic behaviors. Exten sive simulations across environments of different complexity, and using data collected from real-world experiments, demonstrate that our approach outperforms reactive and advanced state-of the-art planners in terms of either performance or scalability.

Robotic automation provides a great contribution to increase efficiency and precision of several tasks. However, most of the solutions used rely on the perfect knowledge of the system’s model. While this requirement could be easily fulfilled in industrial setup, this cannot be assumed as true in more general scenarios, like daily living environment. To this aim, in this study, we present a novel theoretical framework for optimal motion planning in unknown nonlinear dynamical systems using neural abstraction. The proposed approach establishes an ε-approximate simulation relation, leveraging deep neural networks to create an abstracted representation of the system with quantified approximation errors. The state space is partitioned into polyhedral regions using neural networks with ReLU activation functions, resulting in piecewise linear dynamical models. A hybrid control scheme combining Tube Model Predictive Control and Sliding Mode Control is incorporated into this framework to generate optimal trajectories and control signals while ensuring stability in the presence of unknown external disturbances and model inaccuracies. Its effectiveness is demonstrated through a case study on object manipulation using a Franka arm equipped with a Pisa/IIT SoftHand gripper in a ROS/Gazebo simulation environment.

In this work, we propose a framework for the distributed implementation of Quadratic Programs-based controllers, building upon and rectifying a significant limitation in a previously presented approach. The proposed framework is primarily motivated by the distributed implementation of Control Barrier Functions (CBFs), whose primary objective is to make minimal adjustments to a nominal controller while ensuring constraint satisfaction. By improving over some limitations in the current state-of-the-art, we are able to apply distributed CBFs to the problem of global connectivity maintenance in presence of communication and sensing constraints. Specifically, we consider the problem of preserving connectivity for a group of quadrotors with onboard sensors under distance and field of view constraints. Leveraging distributed control barrier functions, our approach maintains global graph connectivity while optimizing the performance of the desired task. Numerical simulations validate its effectiveness.

Energy consumption is an important issue in robotics. This article deals with the problem of reducing the energy consumption of compliant electro-mechanical systems while performing periodic tasks. After deriving performance indices to quantify the energy consumption of a mechanical system, we propose a method to determine both the optimal compliant actuation parameters, and link trajectories to minimize energy consumption. We show how this problem can be cast in a simpler one where the optimization regards only parameters that define the shape of periodic trajectories to be subsequently determined by using numerical optimization tools. Indeed, in our framework, the optimal stiffness and spring preload can be analytically obtained as a function of the desired link trajectories. We then provide simulations and experimental validations of the obtained results on a two-link compliant manipulator platform which performs a repetitive pick-and-place task. Our experiments show that the use of compliant actuators instead of rigid ones and the optimization of their compliant parameters give rise to an energy saving up to 62% with respect to rigid actuation. Moreover, the simultaneous optimization of the compliant parameters and link trajectories provide an additional energy saving up to 20%.

Wearable sensing has emerged as a promising solution for enabling unobtrusive and ergonomic measurements of the human motion. However, the reconstruction performance of these devices strongly depends on the quality and the number of sensors, which are typically limited by wearability and economic constraints. A promising approach to minimize the number of sensors is to exploit dimensionality reduction approaches that fusepriorinformation with insufficient sensing signals, through minimum variance estimation. These methods were successfully used for static hand pose reconstruction, but their translation to motion reconstruction has not been attempted yet. In this work, we propose the usage of functional principal component analysis to decompose multimodal, time-varying motion profiles in terms of linear combinations of basis functions. Functional decomposition enables the estimation of thea prioricovariance matrix, and hence the fusion of scarce and noisy measured data witha prioriinformation. We also consider the problem of identifying which elemental variables to measure as the most informative for a given class of tasks. We applied our method to two different datasets of upper limb motion D1 (joint trajectories) and D2 (joint trajectories + EMG data) considering an optimal set of measures (four joints for D1 out of seven, three joints, and eight EMGs for D2 out of seven and twelve, respectively). We found that our approach enables the reconstruction of upper limb motion with a median error of$0.013 \pm 0.006$rad for D1 (relative median error 0.9%), and$0.038 \pm 0.023$rad and$0.003 \pm 0.002$mV for D2 (relative median error 2.9% and 5.1%, respectively).

This paper proposes an online optimal perception-aware strategy meant to maximize the information collected along the trajectory via the available measurements while simultaneously minimizing the negative effects of actuation/process noise. Indeed, in several robotic applications, the actuation/process noise is far from negligible and its negative effects are particularly relevant especially with intermittent measurements (e.g. collected by a vision system with limited Field-Of-View). New metrics are proposed as combinations of the Constructability Gramian, for measuring the amount of information collected via the available sensors, and the Reachability Gramian, for measuring the degrading effects of actuation/process noise. Control inputs that optimize those cost functions are provided. To show the effectiveness of our method, we consider one case study involving a unicycle-like vehicle, subject to Gaussian measurement noise and Gaussian or Brownian actuation noise, that estimates its state using intermittent distances from known environmental markers.

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This article proposes an online optimal active perception strategy for differentially flat systems meant to maximize the information collected via the available measurements along the planned trajectory. The goal is to generate online a trajectory that minimizes the maximum state estimation uncertainty provided by the employed observer. To quantify the richness of the acquired information about the current state, the smallest eigenvalue of the constructibility Gramian is adopted as a metric. In this article, we use B-splines for parametrizing the trajectory of the flat outputs and we exploit a constrained gradient descent strategy for optimizing online the location of the B-spline control points in order to actively maximize the information gathered over the whole planning horizon. To show the effectiveness of our method in maximizing the estimation accuracy, we consider two case studies involving a unicycle and a quadrotor that need to estimate their poses while measuring two distances w.r.t. two fixed landmarks. Concurrent estimation of calibration/environment parameters is also considered for illustrating how the proposed method copes with instances of active self-calibration and map building.

The goal of this paper is to increase the estimation performance of an Extended Kalman Filter for a nonlinear differentially flat system by planning trajectories able to maximize the amount of information gathered by onboard sensors in presence of both process and measurement noises. In a previous work, we presented an online gradient descent method for planning optimal trajectories along which the smallest eigenvalue of the Observability Gramian (OG) is maximized. As the smallest eigenvalue of the OG is inversely proportional to the maximum estimation uncertainty, its maximization reduces the maximum estimation uncertainty of any estimation algorithm employed during motion. However, the OG does not consider the process noise that, instead, in several applications is far from being negligible. For this reason, this paper proposes a novel solution able to cope with non-negligible process noise: this is achieved by minimizing the largest eigenvalue of the a posteriori covariance matrix obtained by solving the Continuous Riccati Equation as a measure of the total available information. This minimization is expected to maximize the information gathered by the outputs while, at the same time, limiting as much as possible the negative effects of the process noise. We apply our method to a unicycle robot. The comparison between the novel method and the one of our previous work (which did not consider process noise) shows significant improvements in the obtained estimation accuracy.

This paper deals with the problem of active sensing control for nonlinear differentially flat systems. The objective is to improve the estimation accuracy of an observer by determining the inputs of the system that maximise the amount of information gathered by the outputs over a time horizon. In particular, we use the Observability Gramian (OG) to quantify the richness of the acquired information. First, we define a trajectory for the flat outputs of the system by using B-Spline curves. Then, we exploit an online gradient descent strategy to move the control points of the B-Spline in order to actively maximise the smallest eigenvalue of the OG over the whole planning horizon. While the system travels along its planned (optimized) trajectory, an Extended Kalman Filter (EKF) is used to estimate the system state. In order to keep memory of the past acquired sensory data for online re-planning, the OG is also computed on the past estimated state trajectories. This is then used for an online replanning of the optimal trajectory during the robot motion which is continuously refined by exploiting the state estimation obtained by the EKF. In order to show the effectiveness of our method we consider a simple but significant case of a planar robot with a single range measurement. The simulation results show that, along the optimal path, the EKF converges faster and provides a more accurate estimate than along other possible (non-optimal) paths.

This paper presents a geometric approach to the problem of designing visual feedback control laws to steer a nonholonomic vehicle, equipped with a fixed monocular camera, through a gate. The originality of our approach is to introduce and exploit the natural geometry induced by the presence of a gate in the environment, e.g. bundle of hyperbolae, ellipses and circles, providing stabilizing feedback control laws that steer the vehicle through the middle of the gate. Moreover, using visual servoing we prove that this geometry can be measured directly in the camera image plane. As a consequence, we provide an image-based control scheme, avoiding the use of a state observer. Simulations in a realistic scenario and experiments are provided to show the effectiveness of our feedback control laws.

In this paper, we study the minimum length paths covered by the center of a unicycle equipped with a limited field-of-view (FOV) camera, which must keep a given landmark in sight. Previous works on this subject have provided the optimal synthesis for the cases in which the FOV is only limited in the horizontal directions (i.e., left and right bounds) or in the vertical directions (i.e., upper and lower bounds). In this paper, we show how to merge previous results and hence obtain, for a realistic image plane modeled as a rectangle, a finite alphabet of extremal arcs and the overall synthesis. As shown, this objective cannot be straightforwardly achieved from previous results but needs further analysis and developments. Moreover, there are initial configurations such that there exists no optimal path. Nonetheless, we are always able to provide an $\varepsilon$-optimal path whose length approximates arbitrarily well any other shorter path. As final results, we provide a partition of the motion plane in regions such that the optimal or $\varepsilon$ -optimal path from each point in that region is univocally determined.

This paper presents a geometric approach to the problem of steering a robot subject to nonholonomic constraints through a door by using only visual measurements coming from a single fixed on-board monocular camera. The door is represented by two landmarks located on its vertical supports. After exploring the geometric structure that naturally emerges from the problem statement, e.g., bundle of hyperbolae, ellipses, and circles, we exploit this planar geometry to provide stabilizing feedback control laws to drive the vehicle through the middle of the door. Using visual servoing, we prove that this geometry can be directly measured in the camera image plane. Hence, we provide an image-based control scheme, avoiding the use of a state observer. Simulations in a realistic scenario and experiments are provided to show the effectiveness of the feedback control laws.

The importance of Variable Stiffness Actuators (VSA) in safety and performance of robots has been extensively discussed in the last decade. It has also been shown recently that a VSA brings performance advantages with respect to common actuators. For instance, the solution of the optimal control problem of maximizing the speed of a VSA for impact maximization at a given position with free final time is achieved by applying a control policy that synchronizes stiffness changes with link speed and acceleration. This problem can be regarded as the formalization of the performance of a soccer player's free kick.

This paper investigates the optimal design of low-cost gloves for hand pose sensing. This problem becomes particularly relevant when limits on the production costs of sensing gloves are taken into account. These cost constraints may limit both the number and the quality of sensors used as well as the technology adopted. For this reason, an optimal distribution of sensors on the glove during the design phase is mandatory in order to obtain good hand pose reconstruction. In this paper, by exploiting the knowledge on how humans most frequently use their hands in grasping tasks, we study the problem of how and where to place sensors on the glove in order to get the maximum information about the actual hand posture, and hence minimize in average the reconstruction error. Simulations and experiments of reconstruction performance are reported to validate the proposed optimal design of sensing devices.

In this paper we consider the motion planning problem for a 3D-Dubins system consisting of a pair of Dubins vehicles moving in a 3D space while maintaining constant distance. We provide a motion planning algorithm and sufficient conditions on the initial and final configurations that guarantee the existence of admissible controls, moving a first step towards the complete controllability characterization of such type of systems. Results obtained in this paper are particularly relevant in order to solve formation control problem for multiple robots as aerial or underwater vehicles, which move in 3D spaces. Simulation results demonstrate the feasibility of the motion planning algorithm proposed in this paper.

We present a complete characterization of shortest paths to a goal position for a vehicle with unicycle kinematics and a limited range sensor, constantly keeping a given landmark in sight. Previous work on this subject studied the optimal paths in case of a frontal, symmetrically limited Field-Of-View (FOV). In this paper we provide a generalization to the case of arbitrary FOVs, including the case that the direction of motion is not an axis of symmetry for the FOV, and even that it is not contained in the FOV. The provided solution is of particular relevance to applications using side-scanning, such as e.g. in underwater sonar-based surveying and navigation.

The control of a robot's mechanical impedance is attracting increasing attention of the robotics community. Recent research in Robotics has recognized the importance of Variable Stiffness Actuators (VSA) in safety and performance of robots. An important step in using VSA for safety has been to understand the optimality principles that regulate the synchronized variation of stiffness and velocity when moving in the shortest time while limiting possible impact forces (the safe brachistochrone problem). In this paper, we follow a similar program of understanding the use of VSA in performance enhancement, looking at very dynamic tasks where impacts are maximized. To this purpose we address a new optimization problem that consists in choosing the inputs for maximizing the velocity of a link at a given final position, such as, e.g., for maximizing the effect of a hammer impact. We first study the problem with fixed stiffness, and show that, under realistic modeling assumptions, there does exist an optimal linear spring for the given inertia and motor. We then study optimal control of VSA and show that varying the spring stiffness during the execution of the hammering task improves the final performance substantially. The optimal control law is obtained analytically, thus providing insight in the optimality principles underpinning general VSA control. Finally, we show the practicality of our theoretical results with experimental tests.

This paper presents an optimal feedback control scheme to drive a vehicle equipped with a limited Field-Of-View (FOV) camera towards a desired position following the shortest path and keeping a given landmark in sight. Based on the shortest path synthesis available from previous works, feedback control laws are defined for any point on the motion plane exploiting geometric properties of the synthesis itself. Moreover, by using a slightly generalized stability analysis setting, which is that of stability on a manifold, a proof of stability is given. Reported simulations demonstrate the effectiveness of the proposed technique.

In this paper we show that for an observer moving in the plane with no other information than the measurement of relative bearing to three known landmarks, it is possible to completely reconstruct its position and velocity. In particular this applies to the case where no model of the vehicle, nor odometry or acceleration measurements are available. Furthermore, in the same hypotheses, the position of any further landmark can be reconstructed from its bearing only. These results are more general than what is currently known on nonlinear observability of the SLAM problem, which relies on known observer velocities. Our results are also more general than the 2D version of known structure-from-motion observability results, which assume unknown but constant velocities. The proposed method is used to build a nonlinear observer directly applicable to a range of problems from computer vision to autonomous visual navigation.

This paper presents a complete characterization of shortest paths to a goal position for a robot with unicycle kinematics and an on-board camera with limited field-of-view (FOV), which must keep a given feature in sight. Previous work on this subject has shown that the search for a shortest path can be limited to simple families of trajectories. In this paper, we provide a complete optimal synthesis for the problem, i.e., a language of optimal control words, and a global partition of the motion plane induced by shortest paths, such that a word in the optimal language is univocally associated with a region and completely describes the shortest path from any starting point in that region to the goal point. An efficient algorithm to determine the region in which the robot is at any time is also provided.

This paper presents a correct solution to the optimal visual feedback control for a nonholonomic vehicle with limited field-of-view. Previous work on this subject has shown that the search for a shortest path can be limited to simple families of trajectories. We preliminarily provide an extension of the alphabet of optimal control words, to cover some regions of the vehicle plane where the synthesis of turns out to be suboptimal. The main contribution of this paper is an algorithm to translate the optimal synthesis to the image plane, thus enabling a purely image-based optimal control scheme. This allows better performance and increases the robustness of the overall process, avoiding the need of slowly-converging and error-prone parameter estimation algorithms. Simulations and experiments are reported which demonstrate the effectiveness of the proposed technique.