arXiv subjects

Ian M. Mitchell

Publications and source records attributed to Ian M. Mitchell.

9 recordsLinked to original sources

arXiv2025

Comparing Parameterizations and Objective Functions for Maximizing the Volume of Zonotopic Invariant Sets

In formal safety verification, many proposed algorithms use parametric set representations and convert the computation of the relevant sets into an optimization problem; consequently, the choice of parameterization and objective function have a significant impact on the efficiency and accuracy of the resulting computation. In particular, recent papers have explored the use of zonotope set representations for various types of invariant sets. In this paper we collect two zonotope parameterizations that are numerically well-behaved and demonstrate that the volume of the corresponding zonotopes is log-concave in the parameters. We then experimentally explore the use of these two parameterizations in an algorithm for computing the maximum volume zonotope invariant under affine dynamics within a specified box constraint over a finite horizon. The true volume of the zonotopes is used as an objective function, along with two alternative heuristics that are faster to compute. We conclude that the heuristics are much faster in practice, although the relative quality of their results declines as the dimension of the problem increases; however, our conclusions are only preliminary due to so-far limited availability of compute resources.

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arXiv2022

ROS-X-Habitat: Bridging the ROS Ecosystem with Embodied AI

We introduce ROS-X-Habitat, a software interface that bridges the AI Habitat platform for embodied learning-based agents with other robotics resources via ROS. This interface not only offers standardized communication protocols between embodied agents and simulators, but also enables physically and photorealistic simulation that benefits the training and/or testing of vision-based embodied agents. With this interface, roboticists can evaluate their own Habitat RL agents in another ROS-based simulator or use Habitat Sim v2 as the test bed for their own robotic algorithms. Through in silico experiments, we demonstrate that ROS-X-Habitat has minimal impact on the navigation performance and simulation speed of a Habitat RGBD agent; that a standard set of ROS mapping, planning and navigation tools can run in Habitat Sim v2; and that a Habitat agent can run in the standard ROS simulator Gazebo.

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arXiv2021

Safe Motion Planning against Multimodal Distributions based on a Scenario Approach

We present the design of a motion planning algorithm that ensures safety for an autonomous vehicle. In particular, we consider a multimodal distribution over uncertainties; for example, the uncertain predictions of future trajectories of surrounding vehicles reflect discrete decisions, such as turning or going straight at intersections. We develop a computationally efficient, scenario-based approach that solves the motion planning problem with high confidence given a quantifiable number of samples from the multimodal distribution. Our approach is based on two preprocessing steps, which 1) separate the samples into distinct clusters and 2) compute a bounding polytope for each cluster. Then, we rewrite the motion planning problem approximately as a mixed-integer problem using the polytopes. We demonstrate via simulation on the nuScenes dataset that our approach ensures safety with high probability in the presence of multimodal uncertainties, and is computationally more efficient and less conservative than a conventional scenario approach.

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arXiv2019

Invariant, Viability and Discriminating Kernel Under-Approximation via Zonotope Scaling

Scalable safety verification of continuous state dynamic systems has been demonstrated through both reachability and viability analyses using parametric set representations; however, these two analyses are not interchangable in practice for such parametric representations. In this paper we consider viability analysis for discrete time affine dynamic systems with adversarial inputs. Given a set of state and input constraints, and treating the inputs in best-case and/or worst-case fashion, we construct invariant, viable and discriminating sets, which must therefore under-approximate the invariant, viable and discriminating kernels respectively. The sets are constructed by scaling zonotopes represented in center-generator form. The scale factors are found through efficient convex optimizations. The results are demonstrated on two toy examples and a six dimensional nonlinear longitudinal model of a quadrotor.

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arXiv2018

Learning Motion Predictors for Smart Wheelchair using Autoregressive Sparse Gaussian Process

Constructing a smart wheelchair on a commercially available powered wheelchair (PWC) platform avoids a host of seating, mechanical design and reliability issues but requires methods of predicting and controlling the motion of a device never intended for robotics. Analog joystick inputs are subject to black-box transformations which may produce intuitive and adaptable motion control for human operators, but complicate robotic control approaches; furthermore, installation of standard axle mounted odometers on a commercial PWC is difficult. In this work, we present an integrated hardware and software system for predicting the motion of a commercial PWC platform that does not require any physical or electronic modification of the chair beyond plugging into an industry standard auxiliary input port. This system uses an RGB-D camera and an Arduino interface board to capture motion data, including visual odometry and joystick signals, via ROS communication. Future motion is predicted using an autoregressive sparse Gaussian process model. We evaluate the proposed system on real-world short-term path prediction experiments. Experimental results demonstrate the system's efficacy when compared to a baseline neural network model.

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arXiv2018

Reducing Conservatism in Model-Invariant Safety-Preserving Control of Propofol Anesthesia Using Falsification

This work provides a formalized model-invariant safety system for closed-loop anesthesia that uses feedback from measured data for model falsification to reduce conservatism. The safety system maintains predicted propofol plasma concentrations, as well as the patient's blood pressure, within safety bounds despite uncertainty in patient responses to propofol. Model-invariant formal verification is used to formalize the safety system. This technique requires a multi-model description of model-uncertainty. Model-invariant verification considers all possible dynamics of an uncertain system, and the resulting safety system may be conservative for systems that do not exhibit the worst-case dynamical response. In this work, we employ model falsification to reduce conservatism of the model-invariant safety system. Members of a model set that characterizes model- uncertainty are falsified if discrepancy between predictions of those models and measured responses of the uncertain system is established, thereby reducing model uncertainty. We show that including falsification in a model-invariant safety system reduces conservatism of the safety system.

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arXiv2017

Autonomous Mobile Robot Navigation in Uneven and Unstructured Indoor Environments

Robots are increasingly operating in indoor environments designed for and shared with people. However, robots working safely and autonomously in uneven and unstructured environments still face great challenges. Many modern indoor environments are designed with wheelchair accessibility in mind. This presents an opportunity for wheeled robots to navigate through sloped areas while avoiding staircases. In this paper, we present an integrated software and hardware system for autonomous mobile robot navigation in uneven and unstructured indoor environments. This modular and reusable software framework incorporates capabilities of perception and navigation. Our robot first builds a 3D OctoMap representation for the uneven environment with the 3D mapping using wheel odometry, 2D laser and RGB-D data. Then we project multilayer 2D occupancy maps from OctoMap to generate the the traversable map based on layer differences. The safe traversable map serves as the input for efficient autonomous navigation. Furthermore, we employ a variable step size Rapidly Exploring Random Trees that could adjust the step size automatically, eliminating tuning step sizes according to environments. We conduct extensive experiments in simulation and real-world, demonstrating the efficacy and efficiency of our system.

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arXiv2013

Scalable Safety-Preserving Robust Control Synthesis for Continuous-Time Linear Systems

We present a scalable set-valued safety-preserving controller for constrained continuous-time linear time-invariant (LTI) systems subject to additive, unknown but bounded disturbance or uncertainty. The approach relies upon a conservative approximation of the discriminating kernel using robust maximal reachable sets---an extension of our earlier work on computation of the viability kernel for high-dimensional systems. Based on ellipsoidal techniques for reachability, a piecewise ellipsoidal algorithm with polynomial complexity is described that under-approximates the discriminating kernel under LTI dynamics. This precomputed piecewise ellipsoidal set is then used online to synthesize a permissive state-feedback safety-preserving controller. The controller is modeled as a hybrid automaton and can be formulated such that under certain conditions the resulting control signal is continuous across its transitions. We show the performance of the controller on a twelve-dimensional flight envelope protection problem for a quadrotor with actuation saturation and unknown wind disturbances.

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arXiv2013

Best Practices for Scientific Computing

Scientists spend an increasing amount of time building and using software. However, most scientists are never taught how to do this efficiently. As a result, many are unaware of tools and practices that would allow them to write more reliable and maintainable code with less effort. We describe a set of best practices for scientific software development that have solid foundations in research and experience, and that improve scientists' productivity and the reliability of their software.

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