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Ram Vasudevan

Publications and source records attributed to Ram Vasudevan.

108 records · Page 6Linked to original sources

A constrained control-planning strategy for redundant manipulators

This paper presents an interconnected control-planning strategy for redundant manipulators, subject to system and environmental constraints. The method incorporates low-level control characteristics and high-level planning components into a robust strategy for manipulators acting in complex environments, subject to joint limits. This strategy is formulated using an adaptive control rule, the estimated dynamic model of the robotic system and the nullspace of the linearized constraints. A path is generated that takes into account the capabilities of the platform. The proposed method is computationally efficient, enabling its implementation on a real multi-body robotic system. Through experimental results with a 7 DOF manipulator, we demonstrate the performance of the method in real-world scenarios.

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Modeling Camera Effects to Improve Visual Learning from Synthetic Data

Recent work has focused on generating synthetic imagery to increase the size and variability of training data for learning visual tasks in urban scenes. This includes increasing the occurrence of occlusions or varying environmental and weather effects. However, few have addressed modeling variation in the sensor domain. Sensor effects can degrade real images, limiting generalizability of network performance on visual tasks trained on synthetic data and tested in real environments. This paper proposes an efficient, automatic, physically-based augmentation pipeline to vary sensor effects --chromatic aberration, blur, exposure, noise, and color cast-- for synthetic imagery. In particular, this paper illustrates that augmenting synthetic training datasets with the proposed pipeline reduces the domain gap between synthetic and real domains for the task of object detection in urban driving scenes.

cs.CV↗

PedX: Benchmark Dataset for Metric 3D Pose Estimation of Pedestrians in Complex Urban Intersections

This paper presents a novel dataset titled PedX, a large-scale multimodal collection of pedestrians at complex urban intersections. PedX consists of more than 5,000 pairs of high-resolution (12MP) stereo images and LiDAR data along with providing 2D and 3D labels of pedestrians. We also present a novel 3D model fitting algorithm for automatic 3D labeling harnessing constraints across different modalities and novel shape and temporal priors. All annotated 3D pedestrians are localized into the real-world metric space, and the generated 3D models are validated using a mocap system configured in a controlled outdoor environment to simulate pedestrians in urban intersections. We also show that the manual 2D labels can be replaced by state-of-the-art automated labeling approaches, thereby facilitating automatic generation of large scale datasets.

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Failing to Learn: Autonomously Identifying Perception Failures for Self-driving Cars

One of the major open challenges in self-driving cars is the ability to detect cars and pedestrians to safely navigate in the world. Deep learning-based object detector approaches have enabled great advances in using camera imagery to detect and classify objects. But for a safety critical application, such as autonomous driving, the error rates of the current state of the art are still too high to enable safe operation. Moreover, the characterization of object detector performance is primarily limited to testing on prerecorded datasets. Errors that occur on novel data go undetected without additional human labels. In this letter, we propose an automated method to identify mistakes made by object detectors without ground truth labels. We show that inconsistencies in the object detector output between a pair of similar images can be used as hypotheses for false negatives (e.g., missed detections) and using a novel set of features for each hypothesis, an off-the-shelf binary classifier can be used to find valid errors. In particular, we study two distinct cues - temporal and stereo inconsistencies - using data that are readily available on most autonomous vehicles. Our method can be used with any camera-based object detector and we illustrate the technique on several sets of real world data. We show that a state-of-the-art detector, tracker, and our classifier trained only on synthetic data can identify valid errors on KITTI tracking dataset with an average precision of 0.94. We also release a new tracking dataset with 104 sequences totaling 80,655 labeled pairs of stereo images along with ground truth disparity from a game engine to facilitate further research. The dataset and code are available at https://fcav.engin.umich.edu/research/failing-to-learn

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A Matrix Representation of the Multiple Vehicle Routing Problem for Pickup and Delivery

This paper develops a computationally efficient algorithm for the Multiple Vehicle Pickup and Delivery Problem (MVPDP) with the objective of minimizing the tour cost incurred while completing the task of pickup and delivery of customers. To this end, this paper constructs a novel 0-1 Integer Quadratic Programming (IQP) problem to exactly solve the MVPDP. Compared to the state-of-the-art Mixed Integer Linear Programming (MILP) formulation of the problem, the one presented here requires fewer constraints and decision variables. To ensure that this IQP formulation of the MVPDP can be solved in a computationally efficient manner, this paper devises a set of sufficient conditions to ensure convexity of this formulation when the integer variables are relaxed. In addition, this paper describes a transformation to map any non-convex IQP formulation of the MVPDP into an equivalent convex one. The superior computational efficacy of this convex IQP method when compared to the state-of-the-art MILP formulation is demonstrated through extensive simulated and real-world experiments.

math.OC↗

Robust Environmental Mapping by Mobile Sensor Networks

Constructing a spatial map of environmental parameters is a crucial step to preventing hazardous chemical leakages, forest fires, or while estimating a spatially distributed physical quantities such as terrain elevation. Although prior methods can do such mapping tasks efficiently via dispatching a group of autonomous agents, they are unable to ensure satisfactory convergence to the underlying ground truth distribution in a decentralized manner when any of the agents fail. Since the types of agents utilized to perform such mapping are typically inexpensive and prone to failure, this results in poor overall mapping performance in real-world applications, which can in certain cases endanger human safety. This paper presents a Bayesian approach for robust spatial mapping of environmental parameters by deploying a group of mobile robots capable of ad-hoc communication equipped with short-range sensors in the presence of hardware failures. Our approach first utilizes a variant of the Voronoi diagram to partition the region to be mapped into disjoint regions that are each associated with at least one robot. These robots are then deployed in a decentralized manner to maximize the likelihood that at least one robot detects every target in their associated region despite a non-zero probability of failure. A suite of simulation results is presented to demonstrate the effectiveness and robustness of the proposed method when compared to existing techniques.

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Optimal Control for Nonlinear Hybrid Systems via Convex Relaxations

This paper considers the optimal control for hybrid systems whose trajectories transition between distinct subsystems when state-dependent constraints are satisfied. Though this class of systems is useful while modeling a variety of physical systems undergoing contact, the construction of a numerical method for their optimal control has proven challenging due to the combinatorial nature of the state-dependent switching and the potential discontinuities that arise during switches. This paper constructs a convex relaxation-based approach to solve this optimal control problem. Our approach begins by formulating the problem in the space of relaxed controls, which gives rise to a linear program whose solution is proven to compute the globally optimal controller. This conceptual program is solved by constructing a sequence of semidefinite programs whose solutions are proven to converge from below to the true solution of the original optimal control problem. Finally, a method to synthesize the optimal controller is developed. Using an array of examples, the performance of the proposed method is validated on problems with known solutions and also compared to a commercial solver.

math.OC↗

Dynamic Watermarking for General LTI Systems

Detecting attacks in control systems is an important aspect of designing secure and resilient control systems. Recently, a dynamic watermarking approach was proposed for detecting malicious sensor attacks for SISO LTI systems with partial state observations and MIMO LTI systems with a full rank input matrix and full state observations; however, these previous approaches cannot be applied to general LTI systems that are MIMO and have partial state observations. This paper designs a dynamic watermarking approach for detecting malicious sensor attacks for general LTI systems, and we provide a new set of asymptotic and statistical tests. We prove these tests can detect attacks that follow a specified attack model (more general than replay attacks), and we also show that these tests simplify to existing tests when the system is SISO or has full rank input matrix and full state observations. The benefit of our approach is demonstrated with a simulation analysis of detecting sensor attacks in autonomous vehicles. Our approach can distinguish between sensor attacks and wind disturbance (through an internal model principle framework), whereas improperly designed tests cannot distinguish between sensor attacks and wind disturbance.

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Statistical Watermarking for Networked Control Systems

Watermarking can detect sensor attacks in control systems by injecting a private signal into the control, whereby attacks are identified by checking the statistics of the sensor measurements and private signal. However, past approaches assume full state measurements or a centralized controller, which is not found in networked LTI systems with subcontrollers. Since generally the entire system is neither controllable nor observable by a single subcontroller, communication of sensor measurements is required to ensure closed-loop stability. The possibility of attacking the communication channel has not been explicitly considered by previous watermarking schemes, and requires a new design. In this paper, we derive a statistical watermarking test that can detect both sensor and communication attacks. A unique (compared to the non-networked case) aspect of the implementing this test is the state-feedback controller must be designed so that the closed-loop system is controllable by each sub-controller, and we provide two approaches to design such a controller using Heymann's lemma and a multi-input generalization of Heymann's lemma. The usefulness of our approach is demonstrated with a simulation of detecting attacks in a platoon of autonomous vehicles. Our test allows each vehicle to independently detect attacks on both the communication channel between vehicles and on the sensor measurements.

math.OC↗

Technical Report for Real-Time Certified Probabilistic Pedestrian Forecasting

The success of autonomous systems will depend upon their ability to safely navigate human-centric environments. This motivates the need for a real-time, probabilistic forecasting algorithm for pedestrians, cyclists, and other agents since these predictions will form a necessary step in assessing the risk of any action. This paper presents a novel approach to probabilistic forecasting for pedestrians based on weighted sums of ordinary differential equations that are learned from historical trajectory information within a fixed scene. The resulting algorithm is embarrassingly parallel and is able to work at real-time speeds using a naive Python implementation. The quality of predicted locations of agents generated by the proposed algorithm is validated on a variety of examples and considerably higher than existing state of the art approaches over long time horizons.

cs.RO↗

Synthesizing the Optimal Luenberger-type Observer for Nonlinear Systems

Observer design typically requires the observability of the underlying system, which may be hard to verify for nonlinear systems, while guaranteeing asymptotic convergence of errors, which may be insufficient in order to satisfy performance conditions in finite time. This paper develops a method to design Luenberger-type observers for nonlinear systems which guarantee the largest possible domain of attraction for the state estimation error regardless of the initialization of the system. The observer design procedure is posed as a two step problem. In the the first step, the error dynamics are abstractly represented as a linear equation on the space of Radon measures. Thereafter, the problem of identifying the largest set of initial errors that can be driven to within the user-specified error target set in finite-time for all possible initial states, and the corresponding observer gains, is formulated as an infinite-dimensional linear program on measures. This optimization problem is solved, using Lasserre's relaxations via a sequence of semidefinite programs with vanishing conservatism. By post-processing the solution of step one, the set of gains that maximize the size of tolerable initial errors is identified in step two. To demonstrate the feasibility of the presented approach two examples are presented.

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Control Synthesis for Nonlinear Optimal Control via Convex Relaxations

This paper addresses the problem of control synthesis for nonlinear optimal control problems in the presence of state and input constraints. The presented approach relies upon transforming the given problem into an infinite-dimensional linear program over the space of measures. To generate approximations to this infinite-dimensional program, a sequence of Semi-Definite Programs (SDP)s is formulated in the instance of polynomial cost and dynamics with semi-algebraic state and bounded input constraints. A method to extract a polynomial control function from each SDP is also given. This paper proves that the controller synthesized from each of these SDPs generates a sequence of values that converge from below to the value of the optimal control of the original optimal control problem. In contrast to existing approaches, the presented method does not assume that the optimal control is continuous while still proving that the sequence of approximations is optimal. Moreover, the sequence of controllers that are synthesized using the presented approach are proven to converge to the true optimal control. The performance of the presented method is demonstrated on three examples.

math.OC↗

Driving in the Matrix: Can Virtual Worlds Replace Human-Generated Annotations for Real World Tasks?

Deep learning has rapidly transformed the state of the art algorithms used to address a variety of problems in computer vision and robotics. These breakthroughs have relied upon massive amounts of human annotated training data. This time consuming process has begun impeding the progress of these deep learning efforts. This paper describes a method to incorporate photo-realistic computer images from a simulation engine to rapidly generate annotated data that can be used for the training of machine learning algorithms. We demonstrate that a state of the art architecture, which is trained only using these synthetic annotations, performs better than the identical architecture trained on human annotated real-world data, when tested on the KITTI data set for vehicle detection. By training machine learning algorithms on a rich virtual world, real objects in real scenes can be learned and classified using synthetic data. This approach offers the possibility of accelerating deep learning's application to sensor-based classification problems like those that appear in self-driving cars. The source code and data to train and validate the networks described in this paper are made available for researchers.

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Convex Computation of the Basin of Stability to Measure the Likelihood of Falling: A Case Study on the Sit-to-Stand Task

Locomotion in the real world involves unexpected perturbations, and therefore requires strategies to maintain stability to successfully execute desired behaviours. Ensuring the safety of locomoting systems therefore necessitates a quantitative metric for stability. Due to the difficulty of determining the set of perturbations that induce failure, researchers have used a variety of features as a proxy to describe stability. This paper utilises recent advances in dynamical systems theory to develop a personalised, automated framework to compute the set of perturbations from which a system can avoid failure, which is known as the basin of stability. The approach tracks human motion to synthesise a control input that is analysed to measure the basin of stability. The utility of this analysis is verified on a Sit-to-Stand task performed by 15 individuals. The experiment illustrates that the computed basin of stability for each individual can successfully differentiate between less and more stable Sit-to-Stand strategies.

eess.SY↗

Convex Estimation of the $α$-Confidence Reachable Sets of Systems with Parametric Uncertainty

Accurately modeling and verifying the correct operation of systems interacting in dynamic environments is challenging. By leveraging parametric uncertainty within the model description, one can relax the requirement to describe exactly the interactions with the environment; however, one must still guarantee that the model, despite uncertainty, behaves acceptably. This paper presents a convex optimization method to efficiently compute the set of configurations of a polynomial dynamical system that are able to safely reach a user defined target set despite parametric uncertainty in the model. Since planning in the presence of uncertainty can lead to undesirable conservatives, this paper computes those trajectories of the uncertain nonlinear systems which are $α$-probable of reaching the desired configuration. The presented approach uses the notion of occupation measures to describe the evolution of trajectories of a nonlinear system with parametric uncertainty as a linear equation over measures whose supports coincide with the trajectories under investigation. This linear equation is approximated with vanishing conservatism using a hierarchy of semidefinite programs each of which is proven to compute an approximation to the set of initial conditions that are $α$-probable of reaching the user defined target set safely in spite of uncertainty. The efficacy of this method is illustrated on four systems with parametric uncertainty.

math.OC↗

Qualitatively accurate spectral schemes for advection and transport

The transport and continuum equations exhibit a number of conservation laws. For example, scalar multiplication is conserved by the transport equation, while positivity of probabilities is conserved by the continuum equation. Certain discretization techniques, such as particle based methods, conserve these properties, but converge slower than spectral discretization methods on smooth data. Standard spectral discretization methods, on the other hand, do not conserve the invariants of the transport equation and the continuum equation. This article constructs a novel spectral discretization technique that conserves these important invariants while simultaneously preserving spectral convergence rates. The performance of this proposed method is illustrated on several numerical experiments.

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Convex Computation of the Reachable Set for Hybrid Systems with Parametric Uncertainty

To verify the correct operation of systems, engineers need to determine the set of configurations of a dynamical model that are able to safely reach a specified configuration under a control law. Unfortunately, constructing models for systems interacting in highly dynamic environments is difficult. This paper addresses this challenge by presenting a convex optimization method to efficiently compute the set of configurations of a polynomial hybrid dynamical system that are able to safely reach a user defined target set despite parametric uncertainty in the model. This class of models describes, for example, legged robots moving over uncertain terrains. The presented approach utilizes the notion of occupation measures to describe the evolution of trajectories of a nonlinear hybrid dynamical system with parametric uncertainty as a linear equation over measures whose supports coincide with the trajectories under investigation. This linear equation with user defined support constraints is approximated with vanishing conservatism using a hierarchy of semidefinite programs that are each proven to compute an inner/outer approximation to the set of initial conditions that can reach the user defined target set safely in spite of uncertainty. The efficacy of this method is illustrated on a collection of six representative examples.

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Technical Report: Convex Optimization of Nonlinear Feedback Controllers via Occupation Measures

In this paper, we present an approach for designing feedback controllers for polynomial systems that maximize the size of the time-limited backwards reachable set (BRS). We rely on the notion of occupation measures to pose the synthesis problem as an infinite dimensional linear program (LP) and provide finite dimensional approximations of this LP in terms of semidefinite programs (SDPs). The solution to each SDP yields a polynomial control policy and an outer approximation of the largest achievable BRS. In contrast to traditional Lyapunov based approaches which are non-convex and require feasible initialization, our approach is convex and does not require any form of initialization. The resulting time-varying controllers and approximated reachable sets are well-suited for use in a trajectory library or feedback motion planning algorithm. We demonstrate the efficacy and scalability of our approach on five nonlinear systems.

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