arXiv subjects

Roberto Tron

Publications and source records attributed to Roberto Tron.

At least 55 records · Page 3Linked to original sources

arXiv2022

Koopman pose predictions for temporally consistent human walking estimations

We tackle the problem of tracking the human lower body as an initial step toward an automatic motion assessment system for clinical mobility evaluation, using a multimodal system that combines Inertial Measurement Unit (IMU) data, RGB images, and point cloud depth measurements. This system applies the factor graph representation to an optimization problem that provides 3-D skeleton joint estimations. In this paper, we focus on improving the temporal consistency of the estimated human trajectories to greatly extend the range of operability of the depth sensor. More specifically, we introduce a new factor graph factor based on Koopman theory that embeds the nonlinear dynamics of several lower-limb movement activities. This factor performs a two-step process: first, a custom activity recognition module based on spatial temporal graph convolutional networks recognizes the walking activity; then, a Koopman pose prediction of the subsequent skeleton is used as an a priori estimation to drive the optimization problem toward more consistent results. We tested the performance of this module on datasets composed of multiple clinical lowerlimb mobility tests, and we show that our approach reduces outliers on the skeleton form by almost 1 m, while preserving natural walking trajectories at depths up to more than 10 m.

cs.CV↗

arXiv2022

Technical Report on Optimal Linear Multiple Estimation for Landmark-Based Planning via Control Synthesis

A common way to implement navigation in mobile robots is through the use of landmarks. In this case, the main goal of the controller is to make progress toward a goal location (stability), while avoiding the boundary of the environment (safety). In our previous work, we proposed a method to synthesize global controllers for environments with a polyhedral decomposition; our solution uses a Quadratically Constrained Quadratic Program with Chance Constraints to take into account the uncertainty in landmark measurements. Building upon this work, we introduce the concept of virtual landmarks, which are defined as linear combinations of actual landmark measurements that minimize the uncertainty in the resulting control actions. Interestingly, our results show that the first minimum-variance landmark is independent of the feedback control matrix, thus decoupling the design of the landmark from the one of the controller; attempting to derive additional, statistically independent landmarks, however, requires solving non-convex problems that involve also the controller. Numerical experiments demonstrate that, by minimizing the variance of the inputs, the resulting controller will be less conservative, and the robot is able to complete navigation tasks more effectively (faster and with less jitter in the trajectory).

math.DS↗

arXiv2022

Robust Control Barrier Functions for Nonlinear Control Systems with Uncertainty: A Duality-based Approach

This paper studies the design of controllers that guarantee stability and safety of nonlinear control affine systems with parametric uncertainty in both the drift and control vector fields. To this end, we introduce novel classes of robust control barrier functions (RCBF) and robust control Lyapunov functions (RCLF) that facilitate the synthesis of safety-critical controllers in the presence of parametric uncertainty using quadratic programming. Since the initial bounds on the system uncertainty may be highly conservative, we present a data-driven approach to reducing such bounds using input-output data collected online. In particular, we leverage an integral set-membership identification algorithm that iteratively shrinks the set of possible system parameters online and guarantees stability and safety during learning. The efficacy of the developed approach is illustrated on two numerical examples.

math.OC↗

arXiv2022

Adaptive Sampling-based Motion Planning with Control Barrier Functions

Sampling-based algorithms, such as Rapidly Exploring Random Trees (RRT) and its variants, have been used extensively for motion planning. Control barrier functions (CBFs) have been recently proposed to synthesize controllers for safety-critical systems. In this paper, we combine the effectiveness of RRT-based algorithms with the safety guarantees provided by CBFs in a method called CBF-RRT$^\ast$. CBFs are used for local trajectory planning for RRT$^\ast$, avoiding explicit collision checking of the extended paths. We prove that CBF-RRT$^\ast$ preserves the probabilistic completeness of RRT$^\ast$. Furthermore, in order to improve the sampling efficiency of the algorithm, we equip the algorithm with an adaptive sampling procedure, which is based on the cross-entropy method (CEM) for importance sampling (IS). The procedure exploits the tree of samples to focus the sampling in promising regions of the configuration space. We demonstrate the efficacy of the proposed algorithms through simulation examples.

cs.RO↗

arXiv2022

Output-Feedback Path Planning with Robustness to State-Dependent Errors

We consider the problem of sample-based feedback motion planning from measurements affected by systematic errors. Our previous work presented output feedback controllers that use measurements from landmarks in the environment to navigate through a cell-decomposable environment using duality, Control Lyapunov and Barrier Functions (CLF, CBF), and Linear Programming. In this paper, we build on this previous work with a novel strategy that allows the use of measurements affected by systematic errors in perceived depth (similarly to what might be generated by vision-based sensors), as opposed to accurate displacement measurements. As a result, our new method has the advantage of providing more robust performance (with quantitative guarantees) when inaccurate sensors are used. We test the proposed algorithm in the simulation to evaluate the performance limits of our approach predicted by our theoretical derivations.

cs.RO↗

arXiv2022

Bearing-Based Formation Control with Optimal Motion Trajectory

Bearing-based distributed formation control is attractive because it can be implemented using vision-based measurements to achieve a desired formation. Gradient-descent-based controllers using bearing measurements have been shown to have many beneficial characteristics, such as global convergence, applicability to different graph topologies and workspaces of arbitrary dimension, and some flexibility in the choice of the cost. In practice, however, such controllers typically yield convoluted paths from their initial location to the final position in the formation. In this paper we propose a novel procedure to optimize gradient-descent-based bearing-based formation controllers to obtain shorter paths. Our approach is based on the parameterization of the cost function and, by extension, of the controller. We form and solve a nonlinear optimization problem with the sum of path lengths of the agent trajectories as the objective and subject to the original equilibria and global convergence conditions for formation control. Our simulation shows that the parameters can be optimized from a very small number of training samples (1 to 7) to straighten the trajectory by around 16% for a large number of random initial conditions for bearing-only formation. However, in the absence of any range information, the scale of the formation is not fixed and this optimization may lead to an undesired compression of the formation size. Including range measurements avoids this issue and leads to further trajectories straightening by 66%.

eess.SY↗

arXiv2022

Sample-Based Output-Feedback Navigation with Bearing Measurements

We consider the problem of sample-based feedback-based motion planning from bearing (direction-only) measurements. We build on our previous work that defines a cell decomposition of the environment using RRT*, and finds an output feedback controller to navigate through each cell toward a goal location using duality, Control Lyapunov and Barrier Functions (CLF, CBF), and Linear Programming. In this paper, we propose a novel strategy that uses relative bearing measurements with respect to a set of landmarks in the environment, as opposed to full relative displacements. The main advantage is then that the measurements can be obtained using a simple monocular camera. We test the proposed algorithm in the simulation, and then in an experimental environment to evaluate the performance of our approach with respect to practical issues such as mismatches in the dynamical model of the robot, and measurements acquired with a camera with a limited field of view.

cs.RO↗

arXiv2021

Robust Sample-Based Output-Feedback Path Planning

We propose a novel approach for sampling-based and control-based motion planning that combines a representation of the environment obtained via a modified version of optimal Rapidly-exploring Random Trees (RRT*), with landmark-based output-feedback controllers obtained via Control Lyapunov Functions, Control Barrier Functions, and robust Linear Programming. Our solution inherits many benefits of RRT*-like algorithms, such as the ability to implicitly handle arbitrarily complex obstacles, and asymptotic optimality. Additionally, it extends planning beyond the discrete nominal paths, as feedback controllers can correct deviations from such paths, and are robust to discrepancies between the map used for planning and the real environment. We test our algorithms first in simulations and then in experiments, testing the robustness of the approach to practical conditions, such as deformations of the environment, mismatches in the dynamical model of the robot, and measurements acquired with a camera with a limited field of view.

cs.RO↗

arXiv2021

Stable Haptic Teleoperation of UAVs via Small $L_2$ Gain and Control Barrier Functions

We present a novel haptic teleoperation approach that considers not only the safety but also the stability of a teleoperation system. Specifically, we build upon previous work on haptic shared control, which uses control barrier functions (CBFs) to generate a reference haptic feedback that informs the human operator on the internal state of the system, helping them to safely navigate the robot without taking away their control authority. Crucially, in this approach the force rendered to the user is not directly reflected in the motion of the robot (which is still directly controlled by the user); however, previous work in the area neglected to consider the feedback loop through the user, possibly resulting in unstable closed trajectories. In this paper we introduce a differential constraint on the rendered force that makes the system finite-gain $L_2$ stable; the constraint results in a Quadratically Constrained Quadratic Program (QCQP), for which we provide a closed-form solution. Our constraint is related to but less restrictive than the typical passivity constraint used in previous literature. We conducted an experimental simulation in which a human operator flies a UAV near an obstacle to evaluate the proposed method.

cs.RO↗

arXiv2021

Haptic Feedback Improves Human-Robot Agreement and User Satisfaction in Shared-Autonomy Teleoperation

Shared autonomy teleoperation can guarantee safety, but does so by reducing the human operator's control authority, which can lead to reduced levels of human-robot agreement and user satisfaction. This paper presents a novel haptic shared autonomy teleoperation paradigm that uses haptic feedback to inform the user about the inner state of a shared autonomy paradigm, while still guaranteeing safety. This differs from haptic shared control, which uses haptic feedback to inform the user's actions, but gives the human operator full control over the robot's actions. We conducted a user study in which twelve users flew a simulated UAV in a search-and-rescue task with no assistance or assistance provided by haptic shared control, shared autonomy, or haptic shared autonomy. All assistive teleoperation methods use control barrier functions to find a control command that is both safe and as close as possible to the human-generated control command. For assistive teleoperation conditions with haptic feedback, we apply a force to the user that is proportional to the difference between the human-generated control and the safe control. We find that haptic shared autonomy improves the user's task performance and satisfaction. We also find that haptic feedback in assistive teleoperation can improve the user's situational awareness. Finally, results show that adding haptic feedback to shared-autonomy teleoperation can improve human-robot agreement.

cs.RO↗

arXiv2020

Bearing-Only Navigation with Field of View Constraints

This paper addresses the problem of navigation using only relative direction measurements (i.e., relative distances are unknown) under field of view constraints. We present a novel navigation vector field for the bearing-based visual homing problem with respect to static visual landmarks in 2-D and 3-D environments. Our method employs two control fields that are tangent and normal to ellipsoids having landmarks as their foci. The tangent field steers the robot to a set of points where the average of observed bearings is parallel to the average of the desired bearings, and the normal field uses the angle between a pair of bearings as a proxy to adjust the robot's distance from landmarks and to satisfy the field of view constraints. Both fields are blended together to construct an almost globally stable control law. Our method is easy to implement, as it requires only comparisons between average bearings, and between angles of pairs of vectors. We provide simulations that demonstrate the performance of our approach for a double integrator system and unicycles.

eess.SY↗

arXiv2020

Chance Constraint Robust Control with Control Barrier Functions

In this paper, we propose a novel approach to synthesize linear feedback controllers for navigating in polygonal environments using noisy measurements and a convex cell decomposition. Our method is based on formulating chance constraints for the convergence and collision avoidance condition. In particular, the stability and safety guarantees come from chance Control Barrier Function (CBF) constraints and chance Control Lyapunov Function (CLF) constraints, respectively. We use convex over-approximations to get upper bounds of the constraints, leading to a convex robust quadratic program for finding the controller. We apply and provide simulation results for equilibrium control and path control. The result shows that the controller is robust with the noise input.

math.OC↗

arXiv2020

Robust Planning and Control For Polygonal Environments via Linear Programming

We propose a novel approach for navigating in polygonal environments by synthesizing controllers that take as input relative displacement measurements with respect to a set of landmarks. Our algorithm is based on solving a sequence of robust min-max Linear Programming problems on the elements of a cell decomposition of the environment. The optimization problems are formulated using linear Control Lyapunov Function (CLF) and Control Barrier Function (CBF) constraints, to provide stability and safety guarantees, respectively. The inner maximization problem ensures that these constraints are met by all the points in each cell, while the outer minimization problem balances the different constraints in a robust way. We show that the min-max optimization problems can be solved efficiently by transforming it into regular linear programming via the dualization of the inner maximization problem. We test our algorithm to agents with first and second-order integrator dynamics, although our approach is in principle applicable to any system with piecewise linear dynamics. Through our theoretical results and simulations, we show that the resulting controllers: are optimal (with respect to the criterion used in the formulation), are applicable to linear systems of any order, are robust to changes to the start location (since they do not rely on a single nominal path), and to significant deformations of the environment.

eess.SY↗

arXiv2020

Non-uniform Sampled Motion Planning for Continuous-time STL

This paper presents an offline motion planner for linear cyber-physical systems that satisfy a continuous-time Signal Temporal Logic (STL) specification, in which controls are applied in a Zeroth-order Hold (ZOH) manner. The motion planning problem is formulated as a Mixed-integer Program (MIP) with nonuniform control updates. We develop a novel method to obtain bounds of Control Barrier Functions (CBF) and linear predicates to render both spatial and temporal requirements. The theoretical results are validated in numerical examples.

eess.SY↗

arXiv2020

Statistical Outlier Identification in Multi-robot Visual SLAM using Expectation Maximization

This paper introduces a novel and distributed method for detecting inter-map loop closure outliers in simultaneous localization and mapping (SLAM). The proposed algorithm does not rely on a good initialization and can handle more than two maps at a time. In multi-robot SLAM applications, maps made by different agents have nonidentical spatial frames of reference which makes initialization very difficult in the presence of outliers. This paper presents a probabilistic approach for detecting incorrect orientation measurements prior to pose graph optimization by checking the geometric consistency of rotation measurements. Expectation-Maximization is used to fine-tune the model parameters. As ancillary contributions, a new approximate discrete inference procedure is presented which uses evidence on loops in a graph and is based on optimization (Alternate Direction Method of Multipliers). This method yields superior results compared to Belief Propagation and has convergence guarantees. Simulation and experimental results are presented that evaluate the performance of the outlier detection method and the inference algorithm on synthetic and real-world data.

cs.CV↗

arXiv2019

Distributed and Consistent Multi-Image Feature Matching via QuickMatch

In this work we consider the multi-image object matching problem, extend a centralized solution of the problem to a distributed solution, and present an experimental application of the centralized solution. Multi-image feature matching is a keystone of many applications, including simultaneous localization and mapping, homography, object detection, and structure from motion. We first review the QuickMatch algorithm for multi-image feature matching. We then present a scheme for distributing sets of features across computational units (agents) that largely preserves feature match quality and minimizes communication between agents (avoiding, in particular, the need of flooding all data to all agents). Finally, we show how QuickMatch performs on an object matching test with low quality images. The centralized QuickMatch algorithm is compared to other standard matching algorithms, while the Distributed QuickMatch algorithm is compared to the centralized algorithm in terms of preservation of match consistency. The presented experiment shows that QuickMatch matches features across a large number of images and features in larger numbers and more accurately than standard techniques.

cs.CV↗

arXiv2019

A Computational Theory of Robust Localization Verifiability in the Presence of Pure Outlier Measurements

The problem of localizing a set of nodes from relative pairwise measurements is at the core of many applications such as Structure from Motion (SfM), sensor networks, and Simultaneous Localization And Mapping (SLAM). In practical situations, the accuracy of the relative measurements is marred by noise and outliers; hence, we have the problem of quantifying how much we should trust the solution returned by some given localization solver. In this work, we focus on the question of whether an L1-norm robust optimization formulation can recover a solution that is identical to the ground truth, under the scenario of translation-only measurements corrupted exclusively by outliers and no noise; we call this concept verifiability. On the theoretical side, we prove that the verifiability of a problem depends only on the topology of the graph of measurements, the edge support of the outliers, and their signs, while it is independent of ground truth locations of the nodes, and of any positive scaling of the outliers. On the computational side, we present a novel approach based on the dual simplex algorithm that can check the verifiability of a problem, completely characterize the space of equivalent solutions if they exist, and identify subgraphs that are verifiable. As an application of our theory, we provide a procedure to compute a priori probability of recovering a solution congruent or equivalent to the ground truth given a measurement graph and the probabilities of each edge containing an outlier.

stat.CO↗

arXiv2019

Bearing-Only Consensus and Formation Control under Directed Topologies

We address the problems of bearing-only consensus and formation control, where each agent can only measure the relative bearings of its neighbors and relative distances are not available. We provide stability results for the Filippov solutions of two gradient-descent laws from non-smooth Lyapunov functions in the context of differential inclusion. For the consensus and formation control problems with undirected sensing topologies, we prove finite-time and asymptotic convergence of the proposed non-smooth gradient flows. For the directed consensus problem, we prove asymptotic convergence using a different non-smooth Lyapunov function given that the sensing graph has a globally reachable node. Finally, For the directed formation control problem we prove asymptotic convergence for directed cycles and directed acyclic graphs and also introduce a new notion of bearing persistence which guarantees convergence to the desired bearings.

eess.SY↗