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Source author record

Ram Vasudevan

Ram Vasudevan appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
RoboticsSystems and ControlComputer Visionmath.OCeess.SYeess.IVeess.SPMachine Learningmath.DS

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Published work

26 published item(s)

preprint2026arXiv

HumanSplatHMR: Closing the Loop Between Human Mesh Recovery and Gaussian Splatting Avatar

Accurately recovering human pose and appearance from video is an essential component of scene reconstruction, with applications to motion capture, motion prediction, virtual reality, and digital twinning. Despite significant interest in building realistic human avatars from video, this paper demonstrates that existing methods do not accurately recover the 3D geometry of humans. ViT-based approaches are not consistently reliable and can overfit to 2D views, while NeRF- and Gaussian Splatting-based avatars treat pose and appearance separately, limiting rendering generalization to new poses. To resolve these shortcomings, this paper proposes HumanSplatHMR, a joint optimization framework that refines 3D human poses while simultaneously learning a high-fidelity avatar for novel-view and novel-pose synthesis. Our key insight is to close the loop between geometric pose estimation and differentiable rendering. Unlike prior human avatar methods that rely on accurate human pose obtained through motion capture systems or offline refinement, which are impractical in in-the-wild scenarios, our approach uses only human mesh estimates from a state-of-the-art human pose estimator to better reflect real-world conditions. Therefore, instead of using the human pose only as a deformation prior, HumanSplatHMR backpropagates photometric, segmentation, and depth losses through a differentiable renderer to the pose parameters and global position. This coupling refines the global 3D pose over time, improving accuracy and alignment while producing better renderings from novel views. Experiments show consistent improvements over pose recovery baselines that omit image-level refinement and avatar baselines that decouple pose estimation from avatar reconstruction.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

BiPOCO: Bi-Directional Trajectory Prediction with Pose Constraints for Pedestrian Anomaly Detection

We present BiPOCO, a Bi-directional trajectory predictor with POse COnstraints, for detecting anomalous activities of pedestrians in videos. In contrast to prior work based on feature reconstruction, our work identifies pedestrian anomalous events by forecasting their future trajectories and comparing the predictions with their expectations. We introduce a set of novel compositional pose-based losses with our predictor and leverage prediction errors of each body joint for pedestrian anomaly detection. Experimental results show that our BiPOCO approach can detect pedestrian anomalous activities with a high detection rate (up to 87.0%) and incorporating pose constraints helps distinguish normal and anomalous poses in prediction. This work extends current literature of using prediction-based methods for anomaly detection and can benefit safety-critical applications such as autonomous driving and surveillance. Code is available at https://github.com/akanuasiegbu/BiPOCO.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Guaranteed Globally Optimal Planar Pose Graph and Landmark SLAM via Sparse-Bounded Sums-of-Squares Programming

Autonomous navigation requires an accurate model or map of the environment. While dramatic progress in the prior two decades has enabled large-scale SLAM, the majority of existing methods rely on non-linear optimization techniques to find the MLE of the robot trajectory and surrounding environment. These methods are prone to local minima and are thus sensitive to initialization. Several recent papers have developed optimization algorithms for the Pose-Graph SLAM problem that can certify the optimality of a computed solution. Though this does not guarantee a priori that this approach generates an optimal solution, a recent extension has shown that when the noise lies within a critical threshold that the solution to the optimization algorithm is guaranteed to be optimal. To address the limitations of existing approaches, this paper illustrates that the Pose-Graph SLAM and Landmark SLAM can be formulated as polynomial optimization programs that are SOS convex. This paper then describes how the Pose-Graph and Landmark SLAM problems can be solved to a global minimum without initialization regardless of noise level using the Sparse-BSOS hierarchy. This paper also empirically illustrates that convergence happens at the second step in this hierarchy. In addition, this paper illustrates how this Sparse-BSOS hierarchy can be implemented in the complex domain and empirically shows that convergence happens also at the second step of this complex domain hierarchy. Finally, the superior performance of the proposed approach when compared to existing SLAM methods is illustrated on graphs with several hundred nodes.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Input Influence Matrix Design for MIMO Discrete-Time Ultra-Local Model

Ultra-Local Models (ULM) have been applied to perform model-free control of nonlinear systems with unknown or partially known dynamics. Unfortunately, extending these methods to MIMO systems requires designing a dense input influence matrix which is challenging. This paper presents guidelines for designing an input influence matrix for discrete-time, control-affine MIMO systems using an ULM-based controller. This paper analyzes the case that uses ULM and a model-free control scheme: the Hölder-continuous Finite-Time Stable (FTS) control. By comparing the ULM with the actual system dynamics, the paper describes how to extract the input-dependent part from the lumped ULM dynamics and finds that the tracking and state estimation error are coupled. The stability of the ULM-FTS error dynamics is affected by the eigenvalues of the difference (defined by matrix multiplication) between the actual and designed input influence matrix. Finally, the paper shows that a wide range of input influence matrix designs can keep the ULM-FTS error dynamics (at least locally) asymptotically stable. A numerical simulation is included to verify the result. The analysis can also be extended to other ULM-based controllers.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Leveraging Trajectory Prediction for Pedestrian Video Anomaly Detection

Video anomaly detection is a core problem in vision. Correctly detecting and identifying anomalous behaviors in pedestrians from video data will enable safety-critical applications such as surveillance, activity monitoring, and human-robot interaction. In this paper, we propose to leverage trajectory localization and prediction for unsupervised pedestrian anomaly event detection. Different than previous reconstruction-based approaches, our proposed framework rely on the prediction errors of normal and abnormal pedestrian trajectories to detect anomalies spatially and temporally. We present experimental results on real-world benchmark datasets on varying timescales and show that our proposed trajectory-predictor-based anomaly detection pipeline is effective and efficient at identifying anomalous activities of pedestrians in videos. Code will be made available at https://github.com/akanuasiegbu/Leveraging-Trajectory-Prediction-for-Pedestrian-Video-Anomaly-Detection.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Lie Algebraic Cost Function Design for Control on Lie Groups

This paper presents a control framework on Lie groups by designing the control objective in its Lie algebra. Control on Lie groups is challenging due to its nonlinear nature and difficulties in system parameterization. Existing methods to design the control objective on a Lie group and then derive the gradient for controller design are non-trivial and can result in slow convergence in tracking control. We show that with a proper left-invariant metric, setting the gradient of the cost function as the tracking error in the Lie algebra leads to a quadratic Lyapunov function that enables globally exponential convergence. In the PD control case, we show that our controller can maintain an exponential convergence rate even when the initial error is approaching $π$ in SO(3). We also show the merit of this proposed framework in trajectory optimization. The proposed cost function enables the iterative Linear Quadratic Regulator (iLQR) to converge much faster than the Differential Dynamic Programming (DDP) with a well-adopted cost function when the initial trajectory is poorly initialized on SO(3).

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

These Maps Are Made For Walking: Real-Time Terrain Property Estimation for Mobile Robots

The equations of motion governing mobile robots are dependent on terrain properties such as the coefficient of friction, and contact model parameters. Estimating these properties is thus essential for robotic navigation. Ideally any map estimating terrain properties should run in real time, mitigate sensor noise, and provide probability distributions of the aforementioned properties, thus enabling risk-mitigating navigation and planning. This paper addresses these needs and proposes a Bayesian inference framework for semantic mapping which recursively estimates both the terrain surface profile and a probability distribution for terrain properties using data from a single RGB-D camera. The proposed framework is evaluated in simulation against other semantic mapping methods and is shown to outperform these state-of-the-art methods in terms of correctly estimating simulated ground-truth terrain properties when evaluated using a precision-recall curve and the Kullback-Leibler divergence test. Additionally, the proposed method is deployed on a physical legged robotic platform in both indoor and outdoor environments, and we show our method correctly predicts terrain properties in both cases. The proposed framework runs in real-time and includes a ROS interface for easy integration.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Learning Rotation-Invariant Representations of Point Clouds Using Aligned Edge Convolutional Neural Networks

Point cloud analysis is an area of increasing interest due to the development of 3D sensors that are able to rapidly measure the depth of scenes accurately. Unfortunately, applying deep learning techniques to perform point cloud analysis is non-trivial due to the inability of these methods to generalize to unseen rotations. To address this limitation, one usually has to augment the training data, which can lead to extra computation and require larger model complexity. This paper proposes a new neural network called the Aligned Edge Convolutional Neural Network (AECNN) that learns a feature representation of point clouds relative to Local Reference Frames (LRFs) to ensure invariance to rotation. In particular, features are learned locally and aligned with respect to the LRF of an automatically computed reference point. The proposed approach is evaluated on point cloud classification and part segmentation tasks. This paper illustrates that the proposed technique outperforms a variety of state of the art approaches (even those trained on augmented datasets) in terms of robustness to rotation without requiring any additional data augmentation.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Point Set Voting for Partial Point Cloud Analysis

The continual improvement of 3D sensors has driven the development of algorithms to perform point cloud analysis. In fact, techniques for point cloud classification and segmentation have in recent years achieved incredible performance driven in part by leveraging large synthetic datasets. Unfortunately these same state-of-the-art approaches perform poorly when applied to incomplete point clouds. This limitation of existing algorithms is particularly concerning since point clouds generated by 3D sensors in the real world are usually incomplete due to perspective view or occlusion by other objects. This paper proposes a general model for partial point clouds analysis wherein the latent feature encoding a complete point clouds is inferred by applying a local point set voting strategy. In particular, each local point set constructs a vote that corresponds to a distribution in the latent space, and the optimal latent feature is the one with the highest probability. This approach ensures that any subsequent point cloud analysis is robust to partial observation while simultaneously guaranteeing that the proposed model is able to output multiple possible results. This paper illustrates that this proposed method achieves state-of-the-art performance on shape classification, part segmentation and point cloud completion.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Reachability-based Trajectory Safeguard (RTS): A Safe and Fast Reinforcement Learning Safety Layer for Continuous Control

Reinforcement Learning (RL) algorithms have achieved remarkable performance in decision making and control tasks due to their ability to reason about long-term, cumulative reward using trial and error. However, during RL training, applying this trial-and-error approach to real-world robots operating in safety critical environment may lead to collisions. To address this challenge, this paper proposes a Reachability-based Trajectory Safeguard (RTS), which leverages reachability analysis to ensure safety during training and operation. Given a known (but uncertain) model of a robot, RTS precomputes a Forward Reachable Set of the robot tracking a continuum of parameterized trajectories. At runtime, the RL agent selects from this continuum in a receding-horizon way to control the robot; the FRS is used to identify if the agent's choice is safe or not, and to adjust unsafe choices. The efficacy of this method is illustrated on three nonlinear robot models, including a 12-D quadrotor drone, in simulation and in comparison with state-of-the-art safe motion planning methods.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Bridging the Gap Between Safety and Real-Time Performance in Receding-Horizon Trajectory Design for Mobile Robots

To operate with limited sensor horizons in unpredictable environments, autonomous robots use a receding-horizon strategy to plan trajectories, wherein they execute a short plan while creating the next plan. However, creating safe, dynamically-feasible trajectories in real time is challenging; and, planners must ensure persistent feasibility, meaning a new trajectory is always available before the previous one has finished executing. Existing approaches make a tradeoff between model complexity and planning speed, which can require sacrificing guarantees of safety and dynamic feasibility. This work presents the Reachability-based Trajectory Design (RTD) method for trajectory planning. RTD begins with an offline Forward Reachable Set (FRS) computation of a robot's motion when tracking parameterized trajectories; the FRS provably bounds tracking error. At runtime, the FRS is used to map obstacles to parameterized trajectories, allowing RTD to select a safe trajectory at every planning iteration. RTD prescribes an obstacle representation to ensure that obstacle constraints can be created and evaluated in real time while maintaining safety. Persistent feasibility is achieved by prescribing a minimum sensor horizon and a minimum duration for the planned trajectories. A system decomposition approach is used to improve the tractability of computing the FRS, allowing RTD to create more complex plans at runtime. RTD is compared in simulation with Rapidly-Exploring Random Trees and Nonlinear Model-Predictive Control. RTD is also demonstrated in randomly-crafted environments on two hardware platforms: a differential-drive Segway, and a car-like Rover. The proposed method is safe and persistently feasible across thousands of simulations and dozens of real-world hardware demos.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Covariance-Robust Dynamic Watermarking

Attack detection and mitigation strategies for cyberphysical systems (CPS) are an active area of research, and researchers have developed a variety of attack-detection tools such as dynamic watermarking. However, such methods often make assumptions that are difficult to guarantee, such as exact knowledge of the distribution of measurement noise. Here, we develop a new dynamic watermarking method that we call covariance-robust dynamic watermarking, which is able to handle uncertainties in the covariance of measurement noise. Specifically, we consider two cases. In the first this covariance is fixed but unknown, and in the second this covariance is slowly-varying. For our tests, we only require knowledge of a set within which the covariance lies. Furthermore, we connect this problem to that of algorithmic fairness and the nascent field of fair hypothesis testing, and we show that our tests satisfy some notions of fairness. Finally, we exhibit the efficacy of our tests on empirical examples chosen to reflect values observed in a standard simulation model of autonomous vehicles.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Detecting Deception Attacks on Autonomous Vehicles via Linear Time-Varying Dynamic Watermarking

Cyber-physical systems (CPS) such as autonomous vehicles rely on both on-board sensors and external communications to estimate their state. Unfortunately, these communications render the system vulnerable to cyber-attacks. While many attack detection methods have begun to address these concerns, they are limited to linear time-invariant (LTI) systems. Though LTI system models provide accurate approximations for CPS such as autonomous vehicles at constant speed and turning radii, they are inaccurate for more complex motions such as lane changes, turns, and changes in velocity. Since these more complex motions are more suitably described by linear time-varying (LTV) system models rather than LTI models, Dynamic Watermarking, which adds a private excitation to the input signal to validate measurements, has recently been extended to LTV systems. However, this extension does not allow for LTV systems that require several steps before the effect of a given control input can be seen in the measurement signal. Additionally, there is no consideration for the time-varying effects of auto-correlation. Furthermore, a proof of concept was only provided using simulations of a simplified model. This paper relaxes the requirement for inputs to be visible in a single step and constructs an auto-correlation normalizing factor to remove the effects of auto-correlation. In addition, Dynamic Watermarking is applied to a high-fidelity vehicle model in carsim and a 1/10 scale autonomous rover to further reinforce the proof of concept for realistic systems. In each case, the vehicle follows a predefined path with time-varying velocity and turning radii. A replay attack, which replays previously recorded measurements, is shown to be detectable using LTV Dynamic Watermarking in a quick and repeatable manner.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Emulating duration and curvature of coral snake anti-predator thrashing behaviors using a soft-robotic platform

This paper presents a soft-robotic platform for exploring the ecological relevance of non-locomotory movements via animal-robot interactions. Coral snakes (genus Micrurus) and their mimics use vigorous, non-locomotory, and arrhythmic thrashing to deter predation. There is variation across snake species in the duration and curvature of anti-predator thrashes, and it is unclear how these aspects of motion interact to contribute to snake survival. In this work, soft robots composed of fiber-reinforced elastomeric enclosures (FREEs) are developed to emulate the anti-predator behaviors of three genera of snake. Curvature and duration of motion are estimated for both live snakes and robots, providing a quantitative assessment of the robots' ability to emulate snake poses. The curvature values of the fabricated soft-robotic head, midsection, and tail segments are found to overlap with those exhibited by live snakes. Soft robot motion durations were less than or equal to those of snakes for all three genera. Additionally, combinations of segments were selected to emulate three specific snake genera with distinct anti-predatory behavior, producing curvature values that aligned well with live snake observations.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Koopman-based Control of a Soft Continuum Manipulator Under Variable Loading Conditions

Controlling soft continuum manipulator arms is difficult due to their infinite degrees of freedom, nonlinear material properties, and large deflections under loading. This paper presents a data-driven approach to identifying soft manipulator models that enables consistent control under variable loading conditions. This is achieved by incorporating loads into a linear Koopman operator model as states and estimating their values online via an observer within the control loop. Using this approach, real-time, fully autonomous control of a pneumatically actuated soft continuum manipulator is achieved. In several trajectory following experiments, this controller is shown to be more accurate and precise than controllers based on models that are unable to explicitly account for loading. The manipulator also successfully performs pick and place of objects with unknown mass, demonstrating the efficacy of this approach in executing real-world manipulation tasks.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

LiStereo: Generate Dense Depth Maps from LIDAR and Stereo Imagery

An accurate depth map of the environment is critical to the safe operation of autonomous robots and vehicles. Currently, either light detection and ranging (LIDAR) or stereo matching algorithms are used to acquire such depth information. However, a high-resolution LIDAR is expensive and produces sparse depth map at large range; stereo matching algorithms are able to generate denser depth maps but are typically less accurate than LIDAR at long range. This paper combines these approaches together to generate high-quality dense depth maps. Unlike previous approaches that are trained using ground-truth labels, the proposed model adopts a self-supervised training process. Experiments show that the proposed method is able to generate high-quality dense depth maps and performs robustly even with low-resolution inputs. This shows the potential to reduce the cost by using LIDARs with lower resolution in concert with stereo systems while maintaining high resolution.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Off The Beaten Sidewalk: Pedestrian Prediction In Shared Spaces For Autonomous Vehicles

Pedestrians and drivers interact closely in a wide range of environments. Autonomous vehicles (AVs) correspondingly face the need to predict pedestrians' future trajectories in these same environments. Traditional model-based prediction methods have been limited to making predictions in highly structured scenes with signalized intersections, marked crosswalks, or curbs. Deep learning methods have instead leveraged datasets to learn predictive features that generalize across scenes, at the cost of model interpretability. This paper aims to achieve both widely applicable and interpretable predictions by proposing a risk-based attention mechanism to learn when pedestrians yield, and a model of vehicle influence to learn how yielding affects motion. A novel probabilistic method, Off the Sidewalk Predictions (OSP), uses these to achieve accurate predictions in both shared spaces and traditional scenes. Experiments on urban datasets demonstrate that the realtime method achieves state-of-the-art performance.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

On-Demand Trajectory Predictions for Interaction Aware Highway Driving

Highway driving places significant demands on human drivers and autonomous vehicles (AVs) alike due to high speeds and the complex interactions in dense traffic. Merging onto the highway poses additional challenges by limiting the amount of time available for decision-making. Predicting others' trajectories accurately and quickly is crucial to safely executing maneuvers. Many existing prediction methods based on neural networks have focused on modeling interactions to achieve better accuracy while assuming the existence of observation windows over 3s long. This paper proposes a novel probabilistic model for trajectory prediction that performs competitively with as little as 400ms of observations. The proposed model extends a deterministic car-following model to the probabilistic setting by treating model parameters as unknown random variables and introducing regularization terms. A realtime inference procedure is derived to estimate the parameters from observations in this new model. Experiments on dense traffic in the NGSIM dataset demonstrate that the proposed method achieves state-of-the-art performance with both highly constrained and more traditional observation windows.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Pixel-Wise Motion Deblurring of Thermal Videos

Uncooled microbolometers can enable robots to see in the absence of visible illumination by imaging the "heat" radiated from the scene. Despite this ability to see in the dark, these sensors suffer from significant motion blur. This has limited their application on robotic systems. As described in this paper, this motion blur arises due to the thermal inertia of each pixel. This has meant that traditional motion deblurring techniques, which rely on identifying an appropriate spatial blur kernel to perform spatial deconvolution, are unable to reliably perform motion deblurring on thermal camera images. To address this problem, this paper formulates reversing the effect of thermal inertia at a single pixel as a Least Absolute Shrinkage and Selection Operator (LASSO) problem which we can solve rapidly using a quadratic programming solver. By leveraging sparsity and a high frame rate, this pixel-wise LASSO formulation is able to recover motion deblurred frames of thermal videos without using any spatial information. To compare its quality against state-of-the-art visible camera based deblurring methods, this paper evaluated the performance of a family of pre-trained object detectors on a set of images restored by different deblurring algorithms. All evaluated object detectors performed systematically better on images restored by the proposed algorithm rather than any other tested, state-of-the-art methods.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Safe, Optimal, Real-time Trajectory Planning with a Parallel Constrained Bernstein Algorithm

To move through the world, mobile robots typically use a receding-horizon strategy, wherein they execute an old plan while computing a new plan to incorporate new sensor information. A plan should be dynamically feasible, meaning it obeys constraints like the robot's dynamics and obstacle avoidance; it should have liveness, meaning the robot does not stop to plan so frequently that it cannot accomplish tasks; and it should be optimal, meaning that the robot tries to satisfy a user-specified cost function such as reaching a goal location as quickly as possible. Reachability-based Trajectory Design (RTD) is a planning method that can generate provably dynamically-feasible plans. However, RTD solves a nonlinear polynmial optimization program at each planning iteration, preventing optimality guarantees; furthermore, RTD can struggle with liveness because the robot must brake to a stop when the solver finds local minima or cannot find a feasible solution. This paper proposes RTD*, which certifiably finds the globally optimal plan (if such a plan exists) at each planning iteration. This method is enabled by a novel Parallelized Constrained Bernstein Algorithm (PCBA), which is a branch-and-bound method for polynomial optimization. The contributions of this paper are: the implementation of PCBA; proofs of bounds on the time and memory usage of PCBA; a comparison of PCBA to state of the art solvers; and the demonstration of PCBA/RTD* on a mobile robot. RTD* outperforms RTD in terms of optimality and liveness for real-time planning in a variety of environments with randomly-placed obstacles.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Stochastic Sampling Simulation for Pedestrian Trajectory Prediction

Urban environments pose a significant challenge for autonomous vehicles (AVs) as they must safely navigate while in close proximity to many pedestrians. It is crucial for the AV to correctly understand and predict the future trajectories of pedestrians to avoid collision and plan a safe path. Deep neural networks (DNNs) have shown promising results in accurately predicting pedestrian trajectories, relying on large amounts of annotated real-world data to learn pedestrian behavior. However, collecting and annotating these large real-world pedestrian datasets is costly in both time and labor. This paper describes a novel method using a stochastic sampling-based simulation to train DNNs for pedestrian trajectory prediction with social interaction. Our novel simulation method can generate vast amounts of automatically-annotated, realistic, and naturalistic synthetic pedestrian trajectories based on small amounts of real annotation. We then use such synthetic trajectories to train an off-the-shelf state-of-the-art deep learning approach Social GAN (Generative Adversarial Network) to perform pedestrian trajectory prediction. Our proposed architecture, trained only using synthetic trajectories, achieves better prediction results compared to those trained on human-annotated real-world data using the same network. Our work demonstrates the effectiveness and potential of using simulation as a substitution for human annotation efforts to train high-performing prediction algorithms such as the DNNs.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

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.

0 citations0 reviewsNo code linkedOpen access