arXiv subjects

Joel W. Burdick

Publications and source records attributed to Joel W. Burdick.

At least 55 records · Page 3Linked to original sources

arXiv2022

Learning Disturbances Online for Risk-Aware Control: Risk-Aware Flight with Less Than One Minute of Data

Recent advances in safety-critical risk-aware control are predicated on apriori knowledge of the disturbances a system might face. This paper proposes a method to efficiently learn these disturbances online, in a risk-aware context. First, we introduce the concept of a Surface-at-Risk, a risk measure for stochastic processes that extends Value-at-Risk -- a commonly utilized risk measure in the risk-aware controls community. Second, we model the norm of the state discrepancy between the model and the true system evolution as a scalar-valued stochastic process and determine an upper bound to its Surface-at-Risk via Gaussian Process Regression. Third, we provide theoretical results on the accuracy of our fitted surface subject to mild assumptions that are verifiable with respect to the data sets collected during system operation. Finally, we experimentally verify our procedure by augmenting a drone's controller and highlight performance increases achieved via our risk-aware approach after collecting less than a minute of operating data.

eess.SY↗

arXiv2022

Adaptive Conformal Prediction for Motion Planning among Dynamic Agents

This paper proposes an algorithm for motion planning among dynamic agents using adaptive conformal prediction. We consider a deterministic control system and use trajectory predictors to predict the dynamic agents' future motion, which is assumed to follow an unknown distribution. We then leverage ideas from adaptive conformal prediction to dynamically quantify prediction uncertainty from an online data stream. Particularly, we provide an online algorithm uses delayed agent observations to obtain uncertainty sets for multistep-ahead predictions with probabilistic coverage. These uncertainty sets are used within a model predictive controller to safely navigate among dynamic agents. While most existing data-driven prediction approached quantify prediction uncertainty heuristically, we quantify the true prediction uncertainty in a distribution-free, adaptive manner that even allows to capture changes in prediction quality and the agents' motion. We empirically evaluate of our algorithm on a simulation case studies where a drone avoids a flying frisbee.

cs.RO↗

arXiv2022

Distributionally Robust Model Predictive Control with Total Variation Distance

This paper studies the problem of distributionally robust model predictive control (MPC) using total variation distance ambiguity sets. For a discrete-time linear system with additive disturbances, we provide a conditional value-at-risk reformulation of the MPC optimization problem that is distributionally robust in the expected cost and chance constraints. The distributionally robust chance constraint is over-approximated as a simpler, tightened chance constraint that reduces the computational burden. Numerical experiments support our results on probabilistic guarantees and computational efficiency.

eess.SY↗

arXiv2022

Sample-Based Bounds for Coherent Risk Measures: Applications to Policy Synthesis and Verification

The dramatic increase of autonomous systems subject to variable environments has given rise to the pressing need to consider risk in both the synthesis and verification of policies for these systems. This paper aims to address a few problems regarding risk-aware verification and policy synthesis, by first developing a sample-based method to bound the risk measure evaluation of a random variable whose distribution is unknown. These bounds permit us to generate high-confidence verification statements for a large class of robotic systems. Second, we develop a sample-based method to determine solutions to non-convex optimization problems that outperform a large fraction of the decision space of possible solutions. Both sample-based approaches then permit us to rapidly synthesize risk-aware policies that are guaranteed to achieve a minimum level of system performance. To showcase our approach in simulation, we verify a cooperative multi-agent system and develop a risk-aware controller that outperforms the system's baseline controller. We also mention how our approach can be extended to account for any $g$-entropic risk measure - the subset of coherent risk measures on which we focus.

cs.AI↗

arXiv2022

Moving Obstacle Avoidance: a Data-Driven Risk-Aware Approach

This paper proposes a new structured method for a moving agent to predict the paths of dynamically moving obstacles and avoid them using a risk-aware model predictive control (MPC) scheme. Given noisy measurements of the a priori unknown obstacle trajectory, a bootstrapping technique predicts a set of obstacle trajectories. The bootstrapped predictions are incorporated in the MPC optimization using a risk-aware methodology so as to provide probabilistic guarantees on obstacle avoidance. We validate our methods using simulations of a 3-dimensional multi-rotor drone that avoids various moving obstacles, such as a thrown ball and a frisbee with air drag.

cs.RO↗

arXiv2021

Quadrotor Trajectory Tracking with Learned Dynamics: Joint Koopman-based Learning of System Models and Function Dictionaries

Nonlinear dynamical effects are crucial to the operation of many agile robotic systems. Koopman-based model learning methods can capture these nonlinear dynamical system effects in higher dimensional lifted bilinear models that are amenable to optimal control. However, standard methods that lift the system state using a fixed function dictionary before model learning result in high dimensional models that are intractable for real time control. This paper presents a novel method that jointly learns a function dictionary and lifted bilinear model purely from data by incorporating the Koopman model in a neural network architecture. Nonlinear MPC design utilizing the learned model can be performed readily. We experimentally realized this method on a multirotor drone for agile trajectory tracking at low altitudes where the aerodynamic ground effect influences the system's behavior. Experimental results demonstrate that the learning-based controller achieves similar performance as a nonlinear MPC based on a nominal dynamics model in medium altitude. However, our learning-based system can reliably track trajectories in near-ground flight regimes while the nominal controller crashes due to unmodeled dynamical effects that are captured by our method.

cs.RO↗

arXiv2021

Koopman NMPC: Koopman-based Learning and Nonlinear Model Predictive Control of Control-affine Systems

Koopman-based learning methods can potentially be practical and powerful tools for dynamical robotic systems. However, common methods to construct Koopman representations seek to learn lifted linear models that cannot capture nonlinear actuation effects inherent in many robotic systems. This paper presents a learning and control methodology that is a first step towards overcoming this limitation. Using the Koopman canonical transform, control-affine dynamics can be expressed by a lifted bilinear model. The learned model is used for nonlinear model predictive control (NMPC) design where the bilinear structure can be exploited to improve computational efficiency. The benefits for control-affine dynamics compared to existing Koopman-based methods are highlighted through an example of a simulated planar quadrotor. Prediction error is greatly reduced and closed loop performance similar to NMPC with full model knowledge is achieved.

cs.RO↗

arXiv2021

Risk-Sensitive Motion Planning using Entropic Value-at-Risk

We consider the problem of risk-sensitive motion planning in the presence of randomly moving obstacles. To this end, we adopt a model predictive control (MPC) scheme and pose the obstacle avoidance constraint in the MPC problem as a distributionally robust constraint with a KL divergence ambiguity set. This constraint is the dual representation of the Entropic Value-at-Risk (EVaR). Building upon this viewpoint, we propose an algorithm to follow waypoints and discuss its feasibility and completion in finite time. We compare the policies obtained using EVaR with those obtained using another common coherent risk measure, Conditional Value-at-Risk (CVaR), via numerical experiments for a 2D system. We also implement the waypoint following algorithm on a 3D quadcopter simulation.

eess.SY↗

arXiv2021

ROIAL: Region of Interest Active Learning for Characterizing Exoskeleton Gait Preference Landscapes

Characterizing what types of exoskeleton gaits are comfortable for users, and understanding the science of walking more generally, require recovering a user's utility landscape. Learning these landscapes is challenging, as walking trajectories are defined by numerous gait parameters, data collection from human trials is expensive, and user safety and comfort must be ensured. This work proposes the Region of Interest Active Learning (ROIAL) framework, which actively learns each user's underlying utility function over a region of interest that ensures safety and comfort. ROIAL learns from ordinal and preference feedback, which are more reliable feedback mechanisms than absolute numerical scores. The algorithm's performance is evaluated both in simulation and experimentally for three non-disabled subjects walking inside of a lower-body exoskeleton. ROIAL learns Bayesian posteriors that predict each exoskeleton user's utility landscape across four exoskeleton gait parameters. The algorithm discovers both commonalities and discrepancies across users' gait preferences and identifies the gait parameters that most influenced user feedback. These results demonstrate the feasibility of recovering gait utility landscapes from limited human trials.

cs.RO↗

arXiv2021

Risk-Averse Stochastic Shortest Path Planning

We consider the stochastic shortest path planning problem in MDPs, i.e., the problem of designing policies that ensure reaching a goal state from a given initial state with minimum accrued cost. In order to account for rare but important realizations of the system, we consider a nested dynamic coherent risk total cost functional rather than the conventional risk-neutral total expected cost. Under some assumptions, we show that optimal, stationary, Markovian policies exist and can be found via a special Bellman's equation. We propose a computational technique based on difference convex programs (DCPs) to find the associated value functions and therefore the risk-averse policies. A rover navigation MDP is used to illustrate the proposed methodology with conditional-value-at-risk (CVaR) and entropic-value-at-risk (EVaR) coherent risk measures.

eess.SY↗

arXiv2021

Limits of Probabilistic Safety Guarantees when Considering Human Uncertainty

When autonomous robots interact with humans, such as during autonomous driving, explicit safety guarantees are crucial in order to avoid potentially life-threatening accidents. Many data-driven methods have explored learning probabilistic bounds over human agents' trajectories (i.e. confidence tubes that contain trajectories with probability $δ$), which can then be used to guarantee safety with probability $1-δ$. However, almost all existing works consider $δ\geq 0.001$. The purpose of this paper is to argue that (1) in safety-critical applications, it is necessary to provide safety guarantees with $δ< 10^{-8}$, and (2) current learning-based methods are ill-equipped to compute accurate confidence bounds at such low $δ$. Using human driving data (from the highD dataset), as well as synthetically generated data, we show that current uncertainty models use inaccurate distributional assumptions to describe human behavior and/or require infeasible amounts of data to accurately learn confidence bounds for $δ\leq 10^{-8}$. These two issues result in unreliable confidence bounds, which can have dangerous implications if deployed on safety-critical systems.

cs.RO↗

arXiv2021

Learning Invariant Representation of Tasks for Robust Surgical State Estimation

Surgical state estimators in robot-assisted surgery (RAS) - especially those trained via learning techniques - rely heavily on datasets that capture surgeon actions in laboratory or real-world surgical tasks. Real-world RAS datasets are costly to acquire, are obtained from multiple surgeons who may use different surgical strategies, and are recorded under uncontrolled conditions in highly complex environments. The combination of high diversity and limited data calls for new learning methods that are robust and invariant to operating conditions and surgical techniques. We propose StiseNet, a Surgical Task Invariance State Estimation Network with an invariance induction framework that minimizes the effects of variations in surgical technique and operating environments inherent to RAS datasets. StiseNet's adversarial architecture learns to separate nuisance factors from information needed for surgical state estimation. StiseNet is shown to outperform state-of-the-art state estimation methods on three datasets (including a new real-world RAS dataset: HERNIA-20).

cs.RO↗

arXiv2020

daVinciNet: Joint Prediction of Motion and Surgical State in Robot-Assisted Surgery

This paper presents a technique to concurrently and jointly predict the future trajectories of surgical instruments and the future state(s) of surgical subtasks in robot-assisted surgeries (RAS) using multiple input sources. Such predictions are a necessary first step towards shared control and supervised autonomy of surgical subtasks. Minute-long surgical subtasks, such as suturing or ultrasound scanning, often have distinguishable tool kinematics and visual features, and can be described as a series of fine-grained states with transition schematics. We propose daVinciNet - an end-to-end dual-task model for robot motion and surgical state predictions. daVinciNet performs concurrent end-effector trajectory and surgical state predictions using features extracted from multiple data streams, including robot kinematics, endoscopic vision, and system events. We evaluate our proposed model on an extended Robotic Intra-Operative Ultrasound (RIOUS+) imaging dataset collected on a da Vinci Xi surgical system and the JHU-ISI Gesture and Skill Assessment Working Set (JIGSAWS). Our model achieves up to 93.85% short-term (0.5s) and 82.11% long-term (2s) state prediction accuracy, as well as 1.07mm short-term and 5.62mm long-term trajectory prediction error.

cs.CV↗

arXiv2020

Safe Multi-Agent Interaction through Robust Control Barrier Functions with Learned Uncertainties

Robots operating in real world settings must navigate and maintain safety while interacting with many heterogeneous agents and obstacles. Multi-Agent Control Barrier Functions (CBF) have emerged as a computationally efficient tool to guarantee safety in multi-agent environments, but they assume perfect knowledge of both the robot dynamics and other agents' dynamics. While knowledge of the robot's dynamics might be reasonably well known, the heterogeneity of agents in real-world environments means there will always be considerable uncertainty in our prediction of other agents' dynamics. This work aims to learn high-confidence bounds for these dynamic uncertainties using Matrix-Variate Gaussian Process models, and incorporates them into a robust multi-agent CBF framework. We transform the resulting min-max robust CBF into a quadratic program, which can be efficiently solved in real time. We verify via simulation results that the nominal multi-agent CBF is often violated during agent interactions, whereas our robust formulation maintains safety with a much higher probability and adapts to learned uncertainties

cs.RO↗

arXiv2020

Human Preference-Based Learning for High-dimensional Optimization of Exoskeleton Walking Gaits

Optimizing lower-body exoskeleton walking gaits for user comfort requires understanding users' preferences over a high-dimensional gait parameter space. However, existing preference-based learning methods have only explored low-dimensional domains due to computational limitations. To learn user preferences in high dimensions, this work presents LineCoSpar, a human-in-the-loop preference-based framework that enables optimization over many parameters by iteratively exploring one-dimensional subspaces. Additionally, this work identifies gait attributes that characterize broader preferences across users. In simulations and human trials, we empirically verify that LineCoSpar is a sample-efficient approach for high-dimensional preference optimization. Our analysis of the experimental data reveals a correspondence between human preferences and objective measures of dynamicity, while also highlighting differences in the utility functions underlying individual users' gait preferences. This result has implications for exoskeleton gait synthesis, an active field with applications to clinical use and patient rehabilitation.

cs.RO↗

arXiv2020

Energy-Efficient Motion Planning for Multi-Modal Hybrid Locomotion

Hybrid locomotion, which combines multiple modalities of locomotion within a single robot, enables robots to carry out complex tasks in diverse environments. This paper presents a novel method for planning multi-modal locomotion trajectories using approximate dynamic programming. We formulate this problem as a shortest-path search through a state-space graph, where the edge cost is assigned as optimal transport cost along each segment. This cost is approximated from batches of offline trajectory optimizations, which allows the complex effects of vehicle under-actuation and dynamic constraints to be approximately captured in a tractable way. Our method is illustrated on a hybrid double-integrator, an amphibious robot, and a flying-driving drone, showing the practicality of the approach.

cs.RO↗

arXiv2020

Dueling Posterior Sampling for Preference-Based Reinforcement Learning

In preference-based reinforcement learning (RL), an agent interacts with the environment while receiving preferences instead of absolute feedback. While there is increasing research activity in preference-based RL, the design of formal frameworks that admit tractable theoretical analysis remains an open challenge. Building upon ideas from preference-based bandit learning and posterior sampling in RL, we present DUELING POSTERIOR SAMPLING (DPS), which employs preference-based posterior sampling to learn both the system dynamics and the underlying utility function that governs the preference feedback. As preference feedback is provided on trajectories rather than individual state-action pairs, we develop a Bayesian approach for the credit assignment problem, translating preferences to a posterior distribution over state-action reward models. We prove an asymptotic Bayesian no-regret rate for DPS with a Bayesian linear regression credit assignment model. This is the first regret guarantee for preference-based RL to our knowledge. We also discuss possible avenues for extending the proof methodology to other credit assignment models. Finally, we evaluate the approach empirically, showing competitive performance against existing baselines.

cs.LG↗

arXiv2020

Episodic Koopman Learning of Nonlinear Robot Dynamics with Application to Fast Multirotor Landing

This paper presents a novel episodic method to learn a robot's nonlinear dynamics model and an increasingly optimal control sequence for a set of tasks. The method is based on the {\em Koopman operator} approach to nonlinear dynamical systems analysis, which models the flow of {\em observables} in a function space, rather than a flow in a state space. Practically, this method estimates a nonlinear diffeomorphism that lifts the dynamics to a higher dimensional space where they are linear. Efficient Model Predictive Control methods can then be applied to the lifted model. This approach allows for real time implementation in on-board hardware, with rigorous incorporation of both input and state constraints during learning. We demonstrate the method in a real-time implementation of fast multirotor landing, where the nonlinear ground effect is learned and used to improve landing speed and quality.

eess.SY↗