arXiv subjects

Todd Murphey

Publications and source records attributed to Todd Murphey.

At least 37 records · Page 2Linked to original sources

arXiv2021

Move Beyond Trajectories: Distribution Space Coupling for Crowd Navigation

Cooperatively avoiding collision is a critical functionality for robots navigating in dense human crowds, failure of which could lead to either overaggressive or overcautious behavior. A necessary condition for cooperative collision avoidance is to couple the prediction of the agents' trajectories with the planning of the robot's trajectory. However, it is unclear that trajectory based cooperative collision avoidance captures the correct agent attributes. In this work we migrate from trajectory based coupling to a formalism that couples agent preference distributions. In particular, we show that preference distributions (probability density functions representing agents' intentions) can capture higher order statistics of agent behaviors, such as willingness to cooperate. Thus, coupling in distribution space exploits more information about inter-agent cooperation than coupling in trajectory space. We thus introduce a general objective for coupled prediction and planning in distribution space, and propose an iterative best response optimization method based on variational analysis with guaranteed sufficient decrease. Based on this analysis, we develop a sampling-based motion planning framework called DistNav that runs in real time on a laptop CPU. We evaluate our approach on challenging scenarios from both real world datasets and simulation environments, and benchmark against a wide variety of model based and machine learning based approaches. The safety and efficiency statistics of our approach outperform all other models. Finally, we find that DistNav is competitive with human safety and efficiency performance.

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arXiv2021

Generalized Proximal Methods for Pose Graph Optimization

In this paper, we generalize proximal methods that were originally designed for convex optimization on normed vector space to non-convex pose graph optimization (PGO) on special Euclidean groups, and show that our proposed generalized proximal methods for PGO converge to first-order critical points. Furthermore, we propose methods that significantly accelerate the rates of convergence almost without loss of any theoretical guarantees. In addition, our proposed methods can be easily distributed and parallelized with no compromise of efficiency. The efficacy of this work is validated through implementation on simultaneous localization and mapping (SLAM) and distributed 3D sensor network localization, which indicate that our proposed methods are a lot faster than existing techniques to converge to sufficient accuracy for practical use.

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arXiv2021

Majorization Minimization Methods for Distributed Pose Graph Optimization with Convergence Guarantees

In this paper, we consider the problem of distributed pose graph optimization (PGO) that has extensive applications in multi-robot simultaneous localization and mapping (SLAM). We propose majorization minimization methods to distributed PGO and show that our proposed methods are guaranteed to converge to first-order critical points under mild conditions. Furthermore, since our proposed methods rely a proximal operator of distributed PGO, the convergence rate can be significantly accelerated with Nesterov's method, and more importantly, the acceleration induces no compromise of theoretical guarantees. In addition, we also present accelerated majorization minimization methods to the distributed chordal initialization that have a quadratic convergence, which can be used to compute an initial guess for distributed PGO. The efficacy of this work is validated through applications on a number of 2D and 3D SLAM datasets and comparisons with existing state-of-the-art methods, which indicates that our proposed methods have faster convergence and result in better solutions to distributed PGO.

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arXiv2021

Ergodic imitation: Learning from what to do and what not to do

With growing access to versatile robotics, it is beneficial for end users to be able to teach robots tasks without needing to code a control policy. One possibility is to teach the robot through successful task executions. However, near-optimal demonstrations of a task can be difficult to provide and even successful demonstrations can fail to capture task aspects key to robust skill replication. Here, we propose a learning from demonstration (LfD) approach that enables learning of robust task definitions without the need for near-optimal demonstrations. We present a novel algorithmic framework for learning tasks based on the ergodic metric -- a measure of information content in motion. Moreover, we make use of negative demonstrations -- demonstrations of what not to do -- and show that they can help compensate for imperfect demonstrations, reduce the number of demonstrations needed, and highlight crucial task elements improving robot performance. In a proof-of-concept example of cart-pole inversion, we show that negative demonstrations alone can be sufficient to successfully learn and recreate a skill. Through a human subject study with 24 participants, we show that consistently more information about a task can be captured from combined positive and negative (posneg) demonstrations than from the same amount of just positive demonstrations. Finally, we demonstrate our learning approach on simulated tasks of target reaching and table cleaning with a 7-DoF Franka arm. Our results point towards a future with robust, data-efficient LfD for novice users.

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arXiv2020

Formalizing and Guaranteeing* Human-Robot Interaction

Robot capabilities are maturing across domains, from self-driving cars, to bipeds and drones. As a result, robots will soon no longer be confined to safety-controlled industrial settings; instead, they will directly interact with the general public. The growing field of Human-Robot Interaction (HRI) studies various aspects of this scenario - from social norms to joint action to human-robot teams and more. Researchers in HRI have made great strides in developing models, methods, and algorithms for robots acting with and around humans, but these "computational HRI" models and algorithms generally do not come with formal guarantees and constraints on their operation. To enable human-interactive robots to move from the lab to real-world deployments, we must address this gap. This article provides an overview of verification, validation and synthesis techniques used to create demonstrably trustworthy systems, describes several HRI domains that could benefit from such techniques, and provides a roadmap for the challenges and the research needed to create formalized and guaranteed human-robot interaction.

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arXiv2020

CPL-SLAM: Efficient and Certifiably Correct Planar Graph-Based SLAM Using the Complex Number Representation

In this paper, we consider the problem of planar graph-based simultaneous localization and mapping (SLAM) that involves both poses of the autonomous agent and positions of observed landmarks. We present CPL-SLAM, an efficient and certifiably correct algorithm to solve planar graph-based SLAM using the complex number representation. We formulate and simplify planar graph-based SLAM as the maximum likelihood estimation (MLE) on the product of unit complex numbers, and relax this nonconvex quadratic complex optimization problem to convex complex semidefinite programming (SDP). Furthermore, we simplify the corresponding complex semidefinite programming to Riemannian staircase optimization (RSO) on the complex oblique manifold that can be solved with the Riemannian trust region (RTR) method. In addition, we prove that the SDP relaxation and RSO simplification are tight as long as the noise magnitude is below a certain threshold. The efficacy of this work is validated through applications of CPL-SLAM and comparisons with existing state-of-the-art methods on planar graph-based SLAM, which indicates that our proposed algorithm is capable of solving planar graph-based SLAM certifiably, and is more efficient in numerical computation and more robust to measurement noise than existing state-of-the-art methods. The C++ code for CPL-SLAM is available at https://github.com/MurpheyLab/CPL-SLAM.

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arXiv2020

Data-driven Koopman Operators for Model-based Shared Control of Human-Machine Systems

We present a data-driven shared control algorithm that can be used to improve a human operator's control of complex dynamic machines and achieve tasks that would otherwise be challenging, or impossible, for the user on their own. Our method assumes no a priori knowledge of the system dynamics. Instead, both the dynamics and information about the user's interaction are learned from observation through the use of a Koopman operator. Using the learned model, we define an optimization problem to compute the autonomous partner's control policy. Finally, we dynamically allocate control authority to each partner based on a comparison of the user input and the autonomously generated control. We refer to this idea as model-based shared control (MbSC). We evaluate the efficacy of our approach with two human subjects studies consisting of 32 total participants (16 subjects in each study). The first study imposes a linear constraint on the modeling and autonomous policy generation algorithms. The second study explores the more general, nonlinear variant. Overall, we find that model-based shared control significantly improves task and control metrics when compared to a natural learning, or user only, control paradigm. Our experiments suggest that models learned via the Koopman operator generalize across users, indicating that it is not necessary to collect data from each individual user before providing assistance with MbSC. We also demonstrate the data-efficiency of MbSC and consequently, it's usefulness in online learning paradigms. Finally, we find that the nonlinear variant has a greater impact on a user's ability to successfully achieve a defined task than the linear variant.

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arXiv2020

Ergodic Specifications for Flexible Swarm Control: From User Commands to Persistent Adaptation

This paper presents a formulation for swarm control and high-level task planning that is dynamically responsive to user commands and adaptable to environmental changes. We design an end-to-end pipeline from a tactile tablet interface for user commands to onboard control of robotic agents based on decentralized ergodic coverage. Our approach demonstrates reliable and dynamic control of a swarm collective through the use of ergodic specifications for planning and executing agent trajectories as well as responding to user and external inputs. We validate our approach in a virtual reality simulation environment and in real-world experiments at the DARPA OFFSET Urban Swarm Challenge FX3 field tests with a robotic swarm where user-based control of the swarm and mission-based tasks require a dynamic and flexible response to changing conditions and objectives in real-time.

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arXiv2020

Bayesian Particles on Cyclic Graphs

We consider the problem of designing synthetic cells to achieve a complex goal (e.g., mimicking the immune system by seeking invaders) in a complex environment (e.g., the circulatory system), where they might have to change their control policy, communicate with each other, and deal with stochasticity including false positives and negatives---all with minimal capabilities and only a few bits of memory. We simulate the immune response using cyclic, maze-like environments and use targets at unknown locations to represent invading cells. Using only a few bits of memory, the synthetic cells are programmed to perform a reinforcement learning-type algorithm with which they update their control policy based on randomized encounters with other cells. As the synthetic cells work together to find the target, their interactions as an ensemble function as a physical implementation of a Bayesian update. That is, the particles act as a particle filter. This result provides formal properties about the behavior of the synthetic cell ensemble that can be used to ensure robustness and safety. This method of simplified reinforcement learning is evaluated in simulations, and applied to an actual model of the human circulatory system.

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arXiv2019

Task-Based Hybrid Shared Control for Training Through Forceful Interaction

Despite the fact that robotic platforms can provide both consistent practice and objective assessments of users over the course of their training, there are relatively few instances where physical human robot interaction has been significantly more effective than unassisted practice or human-mediated training. This paper describes a hybrid shared control robot, which enhances task learning through kinesthetic feedback. The assistance assesses user actions using a task-specific evaluation criterion and selectively accepts or rejects them at each time instant. Through two human subject studies (total n=68), we show that this hybrid approach of switching between full transparency and full rejection of user inputs leads to increased skill acquisition and short-term retention compared to unassisted practice. Moreover, we show that the shared control paradigm exhibits features previously shown to promote successful training. It avoids user passivity by only rejecting user actions and allowing failure at the task. It improves performance during assistance, providing meaningful task-specific feedback. It is sensitive to initial skill of the user and behaves as an `assist-as-needed' control scheme---adapting its engagement in real time based on the performance and needs of the user. Unlike other successful algorithms, it does not require explicit modulation of the level of impedance or error amplification during training and it is permissive to a range of strategies because of its evaluation criterion. We demonstrate that the proposed hybrid shared control paradigm with a task-based minimal intervention criterion significantly enhances task-specific training.

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arXiv2019

Highly Parallelized Data-driven MPC for Minimal Intervention Shared Control

We present a shared control paradigm that improves a user's ability to operate complex, dynamic systems in potentially dangerous environments without a priori knowledge of the user's objective. In this paradigm, the role of the autonomous partner is to improve the general safety of the system without constraining the user's ability to achieve unspecified behaviors. Our approach relies on a data-driven, model-based representation of the joint human-machine system to evaluate, in parallel, a significant number of potential inputs that the user may wish to provide. These samples are used to (1) predict the safety of the system over a receding horizon, and (2) minimize the influence of the autonomous partner. The resulting shared control algorithm maximizes the authority allocated to the human partner to improve their sense of agency, while improving safety. We evaluate the efficacy of our shared control algorithm with a human subjects study (n=20) conducted in two simulated environments: a balance bot and a race car. During the experiment, users are free to operate each system however they would like (i.e., there is no specified task) and are only asked to try to avoid unsafe regions of the state space. Using modern computational resources (i.e., GPUs) our approach is able to consider more than 10,000 potential trajectories at each time step in a control loop running at 100Hz for the balance bot and 60Hz for the race car. The results of the study show that our shared control paradigm improves system safety without knowledge of the user's goal, while maintaining high-levels of user satisfaction and low-levels of frustration. Our code is available online at https://github.com/asbroad/mpmi_shared_control.

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arXiv2019

Operation and Imitation under Safety-Aware Shared Control

We describe a shared control methodology that can, without knowledge of the task, be used to improve a human's control of a dynamic system, be used as a training mechanism, and be used in conjunction with Imitation Learning to generate autonomous policies that recreate novel behaviors. Our algorithm introduces autonomy that assists the human partner by enforcing safety and stability constraints. The autonomous agent has no a priori knowledge of the desired task and therefore only adds control information when there is concern for the safety of the system. We evaluate the efficacy of our approach with a human subjects study consisting of 20 participants. We find that our shared control algorithm significantly improves the rate at which users are able to successfully execute novel behaviors. Experimental results suggest that the benefits of our safety-aware shared control algorithm also extend to the human partner's understanding of the system and their control skill. Finally, we demonstrate how a combination of our safety-aware shared control algorithm and Imitation Learning can be used to autonomously recreate the demonstrated behaviors.

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arXiv2019

Efficient Computation of Higher-Order Variational Integrators in Robotic Simulation and Trajectory Optimization

This paper addresses the problem of efficiently computing higher-order variational integrators in simulation and trajectory optimization of mechanical systems as those often found in robotic applications. We develop $O(n)$ algorithms to evaluate the discrete Euler-Lagrange (DEL) equations and compute the Newton direction for solving the DEL equations, which results in linear-time variational integrators of arbitrarily high order. To our knowledge, no linear-time higher-order variational or even implicit integrators have been developed before. Moreover, an $O(n^2)$ algorithm to linearize the DEL equations is presented, which is useful for trajectory optimization. These proposed algorithms eliminate the bottleneck of implementing higher-order variational integrators in simulation and trajectory optimization of complex robotic systems. The efficacy of this paper is validated through comparison with existing methods, and implementation on various robotic systems---including trajectory optimization of the Spring Flamingo robot, the LittleDog robot and the Atlas robot. The results illustrate that the same integrator can be used for simulation and trajectory optimization in robotics, preserving mechanical properties while achieving good scalability and accuracy.

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arXiv2019

Data-Driven Gait Segmentation for Walking Assistance in a Lower-Limb Assistive Device

Hybrid systems, such as bipedal walkers, are challenging to control because of discontinuities in their nonlinear dynamics. Little can be predicted about the systems' evolution without modeling the guard conditions that govern transitions between hybrid modes, so even systems with reliable state sensing can be difficult to control. We propose an algorithm that allows for determining the hybrid mode of a system in real-time using data-driven analysis. The algorithm is used with data-driven dynamics identification to enable model predictive control based entirely on data. Two examples---a simulated hopper and experimental data from a bipedal walker---are used. In the context of the first example, we are able to closely approximate the dynamics of a hybrid SLIP model and then successfully use them for control in simulation. In the second example, we demonstrate gait partitioning of human walking data, accurately differentiating between stance and swing, as well as selected subphases of swing. We identify contact events, such as heel strike and toe-off, without a contact sensor using only kinematics data from the knee and hip joints, which could be particularly useful in providing online assistance during walking. Our algorithm does not assume a predefined gait structure or gait phase transitions, lending itself to segmentation of both healthy and pathological gaits. With this flexibility, impairment-specific rehabilitation strategies or assistance could be designed.

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arXiv2018

Iterative Sequential Action Control for Stable, Model-Based Control of Nonlinear Systems

This paper presents iterative Sequential Action Control (iSAC), a receding horizon approach for control of nonlinear systems. The iSAC method has a closed-form open-loop solution, which is iteratively updated between time steps by introducing constant control values applied for short duration. Application of a contractive constraint on the cost is shown to lead to closed-loop asymptotic stability under mild assumptions. The effect of asymptotically decaying disturbances on system trajectories is also examined. To demonstrate the applicability of iSAC to a variety of systems and conditions, we employ five different systems, including a 13-dimensional quaternion-based quadrotor. Each system is tested in different scenarios, ranging from feasible and infeasible trajectory tracking, to setpoint stabilization, with or without the presence of external disturbances. Finally, limitations of this work are discussed.

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arXiv2018

Learning Models for Shared Control of Human-Machine Systems with Unknown Dynamics

We present a novel approach to shared control of human-machine systems. Our method assumes no a priori knowledge of the system dynamics. Instead, we learn both the dynamics and information about the user's interaction from observation through the use of the Koopman operator. Using the learned model, we define an optimization problem to compute the optimal policy for a given task, and compare the user input to the optimal input. We demonstrate the efficacy of our approach with a user study. We also analyze the individual nature of the learned models by comparing the effectiveness of our approach when the demonstration data comes from a user's own interactions, from the interactions of a group of users and from a domain expert. Positive results include statistically significant improvements on task metrics when comparing a user-only control paradigm with our shared control paradigm. Surprising results include findings that suggest that individualizing the model based on a user's own data does not effect the ability to learn a useful dynamic system. We explore this tension as it relates to developing human-in-the-loop systems further in the discussion.

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arXiv2018

Structured Neural Network Dynamics for Model-based Control

We present a structured neural network architecture that is inspired by linear time-varying dynamical systems. The network is designed to mimic the properties of linear dynamical systems which makes analysis and control simple. The architecture facilitates the integration of learned system models with gradient-based model predictive control algorithms, and removes the requirement of computing potentially costly derivatives online. We demonstrate the efficacy of this modeling technique in computing autonomous control policies through evaluation in a variety of standard continuous control domains.

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arXiv2018

Decentralized and Recursive Identification for Cooperative Manipulation of Unknown Rigid Body with Local Measurements

This paper proposes a fully decentralized and recursive approach to online identification of unknown kinematic and dynamic parameters for cooperative manipulation of a rigid body based on commonly used local measurements. To the best of our knowledge, this is the first paper addressing the identification problem for 3D rigid body cooperative manipulation, though the approach proposed here applies to the 2D case as well. In this work, we derive truly linear observation models for kinematic and dynamic unknowns whose state-dependent uncertainties can be exactly evaluated. Dynamic consensus in different coordinates and a filter for dual quaternion are developed with which the identification problem can be solved in a distributed way. It can be seen that in our approach all unknowns to be identified are time-invariant constants. Finally, we provide numerical simulation results to illustrate the efficacy of our approach indicating that it can be used for online identification and adaptive control of rigid body cooperative manipulation.

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