Author name cluster

Richard M. Murray

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

45 papers

2 author rows

IROS Conference 2025 Conference Paper

Quadrotor Morpho-Transition: Learning vs Model-Based Control Strategies

Ioannis Mandralis
Richard M. Murray
Morteza Gharib

Quadrotor Morpho-Transition, or the act of transitioning from air to ground through mid-air transformation, involves complex aerodynamic interactions and a need to operate near actuator saturation, complicating controller design. In recent work, morpho-transition has been studied from a model-based control perspective, but these approaches remain limited due to unmodeled dynamics and the requirement for planning through contacts. Here, we train an end-to-end Reinforcement Learning (RL) controller to learn a morpho-transition policy and demonstrate successful transfer to hardware. We find that the RL control policy achieves agile landing, but only transfers to hardware if motor dynamics and observation delays are taken into account. On the other hand, a baseline MPC controller transfers out-of-the-box without knowledge of the actuator dynamics and delays, at the cost of reduced recovery from disturbances in the event of unknown actuator failures. Our work opens the way for more robust control of agile in-flight quadrotor maneuvers that require mid-air transformation. Video; Code.

IROS Conference 2023 Conference Paper

Evaluation Metrics of Object Detection for Quantitative System-Level Analysis of Safety-Critical Autonomous Systems

Apurva Badithela
Tichakorn Wongpiromsarn
Richard M. Murray

This paper proposes two metrics for evaluating learned object detection models: the proposition-labeled and distance-parametrized confusion matrices. These metrics are leveraged to quantitatively analyze the system with respect to its system-level formal specifications via probabilistic model checking. In particular, we derive transition probabilities from these confusion matrices to compute the probability that the closed-loop system satisfies its system-level specifications expressed in temporal logic. Instead of using object class labels, the proposition-labeled confusion matrix uses atomic propositions relevant to the high-level control strategy. Furthermore, unlike the traditional confusion matrix, the proposed distance-parametrized confusion matrix accounts for variations in detection performance with respect to the distance between the ego and the object. Empirically, these evaluation metrics, chosen by considering system-level specifications and control module design, result in less conservative system-level evaluations than those from traditional confusion matrices. We demonstrate this framework on a car-pedestrian example by computing the satisfaction probabilities for safety requirements formalized in Linear Temporal Logic.

ICRA Conference 2023 Conference Paper

Synthesizing Reactive Test Environments for Autonomous Systems: Testing Reach-Avoid Specifications with Multi-Commodity Flows

Apurva Badithela
Josefine B. Graebener
Wyatt Ubellacker
Eric Mazumdar
Aaron D. Ames
Richard M. Murray

We study automated test generation for testing discrete decision-making modules in autonomous systems. Linear temporal logic is used to encode the system specification - requirements of the system under test - and the test specification, which is unknown to the system and describes the desired test behavior. The reactive test synthesis problem is to find constraints on system actions such that in a test execution, both the system and test specifications are satisfied. To do this, we use the specifications and their corresponding Büchi automata to construct the specification product automaton. Then, a virtual product graph representing all possible test executions of the system is constructed from the transition system and the specification product automaton. The main result of this paper is framing the test synthesis problem as a multi-commodity network flow optimization. This optimization is used to derive reactive constraints on system actions, which constitute the test environment. The resulting test environment ensures that the system meets the test specification while also satisfying the system specification. We illustrate this framework in simulation using grid world examples and demonstrate it on hardware with the Unitree A1 quadruped, where we test dynamic locomotion behaviors reactively.

AAAI Conference 2021 Conference Paper

Constrained Risk-Averse Markov Decision Processes

Mohamadreza Ahmadi
Ugo Rosolia
Michel D. Ingham
Richard M. Murray
Aaron D. Ames

We consider the problem of designing policies for Markov decision processes (MDPs) with dynamic coherent risk objectives and constraints. We begin by formulating the problem in a Lagrangian framework. Under the assumption that the risk objectives and constraints can be represented by a Markov risk transition mapping, we propose an optimization-based method to synthesize Markovian policies that lower-bound the constrained risk-averse problem. We demonstrate that the formulated optimization problems are in the form of difference convex programs (DCPs) and can be solved by the disciplined convex-concave programming (DCCP) framework. We show that these results generalize linear programs for constrained MDPs with total discounted expected costs and constraints. Finally, we illustrate the effectiveness of the proposed method with numerical experiments on a rover navigation problem involving conditional-value-at-risk (CVaR) and entropic-value-at-risk (EVaR) coherent risk measures.

ICRA Conference 2021 Conference Paper

Limits of Probabilistic Safety Guarantees when Considering Human Uncertainty

Richard Cheng
Richard M. Murray
Joel W. Burdick

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 ≥ 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 −8, and (2) current learning-based methods are illequipped 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 ≤ 10 −8. These two issues result in unreliable confidence bounds, which can have dangerous implications if deployed on safety-critical systems.

AAAI Conference 2019 Conference Paper

End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Tasks

Richard Cheng
Gábor Orosz
Richard M. Murray
Joel W. Burdick

Reinforcement Learning (RL) algorithms have found limited success beyond simulated applications, and one main reason is the absence of safety guarantees during the learning process. Real world systems would realistically fail or break before an optimal controller can be learned. To address this issue, we propose a controller architecture that combines (1) a model-free RL-based controller with (2) model-based controllers utilizing control barrier functions (CBFs) and (3) online learning of the unknown system dynamics, in order to ensure safety during learning. Our general framework leverages the success of RL algorithms to learn high-performance controllers, while the CBF-based controllers both guarantee safety and guide the learning process by constraining the set of explorable polices. We utilize Gaussian Processes (GPs) to model the system dynamics and its uncertainties. Our novel controller synthesis algorithm, RL-CBF, guarantees safety with high probability during the learning process, regardless of the RL algorithm used, and demonstrates greater policy exploration efficiency. We test our algorithm on (1) control of an inverted pendulum and (2) autonomous carfollowing with wireless vehicle-to-vehicle communication, and show that our algorithm attains much greater sample efficiency in learning than other state-of-the-art algorithms and maintains safety during the entire learning process.

AAAI Conference 2019 Conference Paper

Inverse Abstraction of Neural Networks Using Symbolic Interpolation

Sumanth Dathathri
Sicun Gao
Richard M. Murray

Neural networks in real-world applications have to satisfy critical properties such as safety and reliability. The analysis of such properties typically requires extracting information through computing pre-images of the network transformations, but it is well-known that explicit computation of pre-images is intractable. We introduce new methods for computing compact symbolic abstractions of pre-images by computing their overapproximations and underapproximations through all layers. The abstraction of pre-images enables formal analysis and knowledge extraction without affecting standard learning algorithms. We use inverse abstractions to automatically extract simple control laws and compact representations for pre-images corresponding to unsafe outputs. We illustrate that the extracted abstractions are interpretable and can be used for analyzing complex properties.

IJCAI Conference 2017 Conference Paper

Learning-Based Abstractions for Nonlinear Constraint Solving

Sumanth Dathathri
Nikos Arechiga
Sicun Gao
Richard M. Murray

We propose a new abstraction refinement procedure based on machine learning to improve the performance of nonlinear constraint solving algorithms on large-scale problems. The proposed approach decomposes the original set of constraints into smaller subsets, and uses learning algorithms to propose sequences of abstractions that take the form of conjunctions of classifiers. The core procedure is a refinement loop that keeps improving the learned results based on counterexamples that are obtained from partial constraints that are easy to solve. Experiments show that the proposed techniques significantly improve the performance of state-of-the-art constraint solvers on many challenging benchmarks. The mechanism is capable of producing intermediate symbolic abstractions that are also important for many applications and for understanding the internal structures of hard constraint solving problems.

IROS Conference 2017 Conference Paper

Synthesis of correct-by-construction behavior trees

Michele Colledanchise
Richard M. Murray
Petter Ögren

In this paper we study the problem of synthesizing correct-by-construction Behavior Trees (BTs) controlling agents in adversarial environments. The proposed approach combines the modularity and reactivity of BTs with the formal guarantees of Linear Temporal Logic (LTL) methods. Given a set of admissible environment specifications, an agent model in form of a Finite Transition System and the desired task in form of an LTL formula, we synthesize a BT in polynomial time, that is guaranteed to correctly execute the desired task. To illustrate the approach, we present three examples of increasing complexity.

IROS Conference 2015 Conference Paper

Online horizon selection in receding horizon temporal logic planning

Vasumathi Raman
Mattias Fält
Tichakorn Wongpiromsarn
Richard M. Murray

Temporal logics have proven effective for correct-by-construction synthesis of controllers for a wide range of robotic applications. Receding horizon frameworks mitigate the computational intractability of reactive synthesis for temporal logic, but have thus far been limited by pursuing a single sequence of short horizon problems to the goal. We propose a receding horizon algorithm for reactive synthesis that automatically determines a path to the currently pursued goal at runtime, responding as needed to nondeterministic environment behavior. This is achieved by allowing each short horizon to have multiple local goals, and determining which local goal to pursue based on the current global goal, the currently perceived environment and a pre-computed invariant dependent on the global goal. We demonstrate the utility of this additional flexibility in grant-response tasks, using a search-and-rescue example. Moreover, we show that these goal-dependent invariants mitigate the conservativeness of the receding horizon approach.

IROS Conference 2014 Conference Paper

A compositional approach to stochastic optimal control with co-safe temporal logic specifications

Matanya B. Horowitz
Eric M. Wolff
Richard M. Murray

We introduce an algorithm for the optimal control of stochastic nonlinear systems subject to temporal logic constraints on their behavior. We compute directly on the state space of the system, avoiding the expensive pre-computation of a discrete abstraction. An automaton that corresponds to the temporal logic specification guides the computation of a control policy that maximizes the probability that the system satisfies the specification. This reduces controller synthesis to solving a sequence of stochastic constrained reachability problems. Each individual reachability problem is solved via the Hamilton-Jacobi-Bellman (HJB) partial differential equation of stochastic optimal control theory. To increase the efficiency of our approach, we exploit a class of systems where the HJB equation is linear due to structural assumptions on the noise. The linearity of the partial differential equation allows us to pre-compute control policy primitives and then compose them, at essentially zero cost, to conservatively satisfy a complex temporal logic specification.

ICRA Conference 2014 Conference Paper

Optimization-based trajectory generation with linear temporal logic specifications

Eric M. Wolff
Ufuk Topcu
Richard M. Murray

We present a mathematical programming-based method for optimal control of discrete-time dynamical systems subject to temporal logic task specifications. We use linear temporal logic (LTL) to specify a wide range of properties and tasks, such as safety, progress, response, surveillance, repeated assembly, and environmental monitoring. Our method directly encodes an LTL formula as mixed-integer linear constraints on the continuous system variables, avoiding the computationally expensive processes of creating a finite abstraction of the system and a Büchi automaton for the specification. In numerical experiments, we solve temporal logic motion planning tasks for high-dimensional (10+ continuous state) dynamical systems.

IROS Conference 2013 Conference Paper

Automaton-guided controller synthesis for nonlinear systems with temporal logic

Eric M. Wolff
Ufuk Topcu
Richard M. Murray

We develop a method for the control of discrete-time nonlinear systems subject to temporal logic specifications. Our approach uses a coarse abstraction of the system and an automaton representing the temporal logic specification to guide the search for a feasible trajectory. This decomposes the search for a feasible trajectory into a series of constrained reachability problems. Thus, one can create controllers for any system for which techniques exist to compute (approximate) solutions to constrained reachability problems. Representative techniques include sampling-based methods for motion planning, reachable set computations for linear systems, and graph search for finite discrete systems. Our approach avoids the expensive computation of a discrete abstraction, and its implementation is amenable to parallel computing. We demonstrate our approach with numerical experiments on temporal logic motion planning problems with high-dimensional (10+ states) continuous systems.

ICRA Conference 2013 Conference Paper

Efficient reactive controller synthesis for a fragment of linear temporal logic

Eric M. Wolff
Ufuk Topcu
Richard M. Murray

Motivated by robotic motion planning, we develop a framework for control policy synthesis for both non-deterministic transition systems and Markov decision processes that are subject to temporal logic task specifications. We introduce a fragment of linear temporal logic that can be used to specify common motion planning tasks such as safe navigation, response to the environment, persistent coverage, and surveillance. This fragment is computationally efficient; the complexity of control policy synthesis is a doubly-exponential improvement over standard linear temporal logic for both non-deterministic transition systems and Markov decision processes. This improvement is possible because we compute directly on the original system, as opposed to the automata-based approach commonly used. We give simulation results for representative motion planning tasks and compare to generalized reactivity(1).

ICRA Conference 2013 Conference Paper

Just-in-time synthesis for reactive motion planning with temporal logic

Scott C. Livingston
Richard M. Murray

The cost of the great expressivity of motion planning subject to temporal logic formulae is intractability. Recent advances in sampling-based methods seem to be only applicable to “low-level” control. The problem of realizing “high-level” controllers that satisfy a temporal logic specification does not readily admit approximations, unless the notion of correctness is relaxed as might be achieved with probabilistic variants of temporal logics. In this paper, we argue that not all possible environment (uncontrolled) behaviors need to be explicitly planned for, but rather short-time strategies can be generated online while maintaining global correctness. We achieve this by separating feasibility from controller synthesis, using metrics from the underlying continuous state space to ensure short-time strategies chained together provide globally correct behavior.

ICRA Conference 2013 Conference Paper

Motion planning in observations space with learned diffeomorphism models

Andrea Censi
Adam Nilsson
Richard M. Murray

We consider the problem of planning motions in observations space, based on learned models of the dynamics that associate to each action a diffeomorphism of the observations domain. For an arbitrary set of diffeomorphisms, this problem must be formulated as a generic search problem. We adapt established algorithms of the graph search family. In this scenario, node expansion is very costly, as each node in the graph is associated to an uncertain diffeomorphism and corresponding predicted observations. We describe several improvements that ameliorate performance: the introduction of better image similarities to use as heuristics; a method to reduce the number of expanded nodes by preliminarily identifying redundant plans; and a method to pre-compute composite actions that make the search efficient in all directions.

ICRA Conference 2013 Conference Paper

Patching task-level robot controllers based on a local μ-calculus formula

Scott C. Livingston
Pavithra Prabhakar
Alex B. Jose
Richard M. Murray

We present a method for mending strategies for GR(1) specifications. Given the addition or removal of edges from the game graph describing a problem (essentially transition rules in a GR(1) specification), we apply a μ-calculus formula to a neighborhood of states to obtain a “local strategy” that navigates around the invalidated parts of an original synthesized strategy. Our method may thus avoid global resynthesis while recovering correctness with respect to the new specification. We illustrate the results both in simulation and on physical hardware for a planar robot surveillance task.

ICRA Conference 2013 Conference Paper

Robot navigation in dense human crowds: the case for cooperation

Peter Trautman
Jeremy Ma
Richard M. Murray
Andreas Krause 0001

We consider mobile robot navigation in dense human crowds. In particular, we explore two questions. Can we design a navigation algorithm that encourages humans to cooperate with a robot? Would such cooperation improve navigation performance? We address the first question by developing a probabilistic predictive model of cooperative collision avoidance and goal-oriented behavior by extending the interacting Gaussian processes approach to include multiple goals and stochastic movement duration. We answer the second question with an extensive quantitative study of robot navigation in dense human crowds (488 runs completed), specifically testing how cooperation models effect navigation performance. We find that the “multiple goal” interacting Gaussian processes algorithm performs comparably with human teleoperators in crowd densities near 1 person/m 2, while a state of the art noncooperative planner exhibits unsafe behavior more than 3 times as often as this multiple goal extension, and more than twice as often as the basic interacting Gaussian processes. Furthermore, a reactive planner based on the widely used “dynamic window” approach fails for crowd densities above 0. 55 people/m 2. Based on these experimental results, and previous theoretical observations, we conclude that a cooperation model is important for safe and efficient robot navigation in dense human crowds.

ICRA Conference 2012 Conference Paper

Backtracking temporal logic synthesis for uncertain environments

Scott C. Livingston
Richard M. Murray
Joel W. Burdick

This paper considers the problem of synthesizing correct-by-construction robotic controllers in environments with uncertain but fixed structure. “Environment” has two notions in this work: a map or “world” in which some controlled agent must operate and navigate (i. e. , evolve in a configuration space with obstacles); and an adversarial player that selects continuous and discrete variables to try to make the agent fail (as in a game). Both the robot and the environment are subjected to behavioral specifications expressed as an assume-guarantee linear temporal logic (LTL) formula. We then consider how to efficiently modify the synthesized controller when the robot encounters unexpected changes in its environment. The crucial insight is that a portion of this problem takes place in a metric space, which provides a notion of nearness. Thus if a nominal plan fails, we need not resynthesize it entirely, but instead can “patch” it locally. We present an algorithm for doing this, prove soundness (correctness of output), and demonstrate it on an example gridworld.

ICRA Conference 2012 Conference Paper

Fault detection and isolation from uninterpreted data in robotic sensorimotor cascades

Andrea Censi
Magnus Hakansson
Richard M. Murray

One of the challenges in designing the next generation of robots operating in non-engineered environments is that there seems to be an infinite amount of causes that make the sensor data unreliable or actuators ineffective. In this paper, we discuss what faults are possible to detect using zero modeling effort: we start from uninterpreted streams of observations and commands, and without a prior knowledge of a model of the world. We show that in sensorimotor cascades it is possible to define static faults independently of a nominal model. We define an information-theoretic usefulness of a sensor reading and we show that it captures several kind of sensorimotor faults frequently encountered in practice. We particularize these ideas to models proposed in previous work as suitable candidates for describing generic sensorimotor cascades. We show several examples with camera and range-finder data, and we discuss a possible way to integrate these techniques in an existing robot software architecture.

ICRA Conference 2012 Conference Paper

Learning diffeomorphism models of robotic sensorimotor cascades

Andrea Censi
Richard M. Murray

The problem of bootstrapping consists in designing agents that can learn from scratch the model of their sensorimotor cascade (the series of robot actuators, the external world, and the robot sensors) and use it to achieve useful tasks. In principle, we would want to design agents that can work for any robot dynamics and any robot sensor(s). One of the difficulties of this problem is the fact that the observations are very high dimensional, the dynamics is nonlinear, and there is a wide range of “representation nuisances” to which we would want the agent to be robust. In this paper, we model the dynamics of sensorimotor cascades using diffeomorphisms of the sensel space. We show that this model captures the dynamics of camera and range-finder data, that it can be used for long-term predictions, and that it can capture nonlinear phenomena such as a limited field of view. Moreover, by analyzing the learned diffeomorphisms it is possible to recover the “linear structure” of the dynamics independently of the commands representation.

ICRA Conference 2012 Conference Paper

Towards formal synthesis of reactive controllers for dexterous robotic manipulation

Sandeep Chinchali
Scott C. Livingston
Ufuk Topcu
Joel W. Burdick
Richard M. Murray

In robotic finger gaiting, fingers continuously manipulate an object until joint limitations or mechanical limitations periodically force a switch of grasp. Current approaches to gait planning and control are slow, lack formal guarantees on correctness, and are generally not reactive to changes in object geometry. To address these issues, we apply advances in formal methods to model a gait subject to external perturbations as a two-player game between a finger controller and its adversarial environment. High-level specifications are expressed in linear temporal logic (LTL) and low-level control primitives are designed for continuous kinematics. Simulations of planar manipulation with our synthesized correct-by-construction gait controller demonstrate the benefits of this approach.

ICRA Conference 2011 Conference Paper

Bootstrapping bilinear models of robotic sensorimotor cascades

Andrea Censi
Richard M. Murray

We consider the bootstrapping problem, which consists in learning a model of the agent's sensors and actuators starting from zero prior information, and we take the problem of servoing as a cross-modal task to validate the learned models. We study the class of sensors with bilinear dynamics, for which the derivative of the observations is a bilinear form of the control commands and the observations themselves. This class of models is simple, yet general enough to represent the main phenomena of three representative sensors (field sampler, camera, and range-finder), apparently very different from one another. It also allows a bootstrapping algorithm based on Hebbian learning, and a simple bioplausible control strategy. The convergence properties of learning and control are demonstrated with extensive simulations and by analytical arguments.

IROS Conference 2011 Conference Paper

Bootstrapping sensorimotor cascades: A group-theoretic perspective

Andrea Censi
Richard M. Murray

The bootstrapping problem consists in designing agents that learn a model of themselves and the world, and utilize it to achieve useful tasks. It is different from other learning problems as the agent starts with uninterpreted observations and commands, and with minimal prior information about the world. in this paper, we give a mathematical formalization of this aspect of the problem. We argue that the vague constrain of having “no prior information” can be recast as a precise algebraic condition on the agent: that its behavior is invariant to particular classes of nuisances on the world, which we show can be well represented by actions of groups (diffeomorphisms, permutations, linear transformations) on observations and commans. We then introduce the class of bilinear gradient dynamics sensors (BGDS) as a candidate for learning generic robotic sensorimotor cascades. We show how framing the problem as rejection of group nuisances allows a compact and modular analysis of typical preprocessing stages, such as learning the topology of the sensors. We demonstrate learning and using such models on real-word range-finder and camera date from publicly available datasets.

IROS Conference 2011 Conference Paper

Containment indicator function construction via numerical conformal mapping

Shuo Han 0011
Richard M. Murray

In optimal-control-based motion planning, it is often desired to obtain a proper (preferably smooth) function, referred to as the containment indicator function in this paper, that describes the shape of the free space. The paper studies the use of numerical conformal mapping for constructing the containment indicator function for an arbitrary two-dimensional geometry. The idea of using conformal mapping is to transform the original shape of interest into a simpler target shape (e. g. disk, rectangle), which can then be characterized by elementary functions. Computational methods for finding the desired conformal maps are also studied. The procedure can be formulated as a convex optimization problem and computed efficiently.

IROS Conference 2010 Conference Paper

A bio-plausible design for visual pose stabilization

Shuo Han 0011
Andrea Censi
Andrew D. Straw
Richard M. Murray

We consider the problem of purely visual pose stabilization (also known as servoing) of a second-order rigid-body system with six degrees of freedom: how to choose forces and torques, based on the current view and a memorized goal image, to steer the pose towards a desired one. Emphasis has been given to the bio-plausibility of the computation, in the sense that the control laws could be in principle implemented on the neural substrate of simple insects. We show that stabilizing laws can be realized by bilinear/quadratic operations on the visual input. This particular computational structure has several numerically favorable characteristics (sparse, local, and parallel), and thus permits an efficient engineering implementation. We show results of the control law tested on an indoor helicopter platform.

ICRA Conference 2009 Conference Paper

A real-time helicopter testbed for insect-inspired visual flight control

Shuo Han 0011
Andrew D. Straw
Michael H. Dickinson
Richard M. Murray

The paper describes an indoor helicopter testbed that allows implementing and testing of bio-inspired control algorithms developed from scientific studies on insects. The helicopter receives and is controlled by simulated sensory inputs (e. g. visual stimuli) generated in a virtual 3D environment, where the connection between the physical world and the virtual world is provided by a video camera tracking system. The virtual environment is specified by a 3D computer model and is relatively simple to modify compared to realistic scenes. This enables rapid examinations of whether a certain control law is robust under various environments, an important feature of insect behavior. As a first attempt, flight stabilization and yaw rate control near hover are demonstrated, utilizing biologically realistic visual stimuli as in the fruit fly Drosophila melanogaster.

IROS Conference 2007 Conference Paper

Safety verification of a fault tolerant reconfigurable autonomous goal-based robotic control system

Julia M. B. Braman
Richard M. Murray
David A. Wagner 0002

Fault tolerance and safety verification of control systems are essential for the success of autonomous robotic systems. A control architecture called mission data system (MDS), developed at the Jet Propulsion Laboratory, takes a goal-based control approach. In this paper, a method for converting goal network control programs into linear hybrid systems is developed. The linear hybrid system can then be verified for safety in the presence of failures using existing symbolic model checkers. An example task is simulated in MDS and successfully verified using HyTech, a symbolic model checking software for linear hybrid systems.

ICRA Conference 2006 Conference Paper

A Decentralized Motion Coordination Strategy for Dynamic Target Tracking

Timothy H. Chung
Joel W. Burdick
Richard M. Murray

This paper presents a decentralized motion planning algorithm for the distributed sensing of a noisy dynamical process by multiple cooperating mobile sensor agents. This problem is motivated by localization and tracking tasks of dynamic targets. Our gradient-descent method is based on a cost function that measures the overall quality of sensing. We also investigate the role of imperfect communication between sensor agents in this framework, and examine the trade-offs in performance between sensing and communication. Simulations illustrate the basic characteristics of the algorithms

ICRA Conference 2006 Conference Paper

Model-based Estimation of Off-highway Road Geometry using Single-axis LADAR and Inertial Sensing

Lars B. Cremean
Richard M. Murray

This paper applies some previously studied extended Kalman filter techniques for planar road geometry estimation to the domain of autonomous navigation of off-highway vehicles. In this work, a clothoid model of the road geometry is constructed and estimated recursively based on road features extracted from single-axis LADAR range measurements. We present a method for feature extraction of the road centerline in the image plane, and describe its application to recursive estimation of the road geometry. We analyze the performance of our method against simulated motion of varied road geometries and against closed-loop detection, tracking and following of desert roads. Our method accommodates full 6 DOF motion of the vehicle as it navigates, constructs consistent estimates of the road geometry with respect to a fixed global reference frame, and requires an estimate of the sensor pose for each range measurement

ICRA Conference 2005 Conference Paper

An Experimental Platform for Motion Estimation and Maneuver Characterization in High Speed Off-Road Driving

Haomiao Huang
Lyle Chamberlain
Richard M. Murray

This paper describes a low-cost experimental platform for investigating control and dynamics of a vehicle performing high speed sliding turns in an off-road environment. The hardware design and field performance of the vehicle are discussed. State and control input data were recorded during a series of human-controlled off-road driving maneuvers. Analysis performed on the data demonstrates the ability to detect slippage and measure sideslip angle. Preliminary classification of human control inputs using pattern recognition techniques shows the ability to match steering inputs with vehicle trajectories that can be used to develop motion primitives for vehicle control. These tools and techniques will be used for the development of high speed autonomous off-road driving.

ICRA Conference 2004 Conference Paper

Identification of Decision Rules in a Human-controlled System: Vehicles at a Traffic Intersection

Claire Walton
Domitilla Del Vecchio
Richard M. Murray

The rules that govern decision making in systems controlled by humans are often simple to describe. However, deriving these rules from the actions of a group can be very difficult, making human behavior hard to predict. We develop an algorithm to determine the rules implemented by drivers at a traffic intersection by observing the trajectories of their cars. We apply such algorithm to a traffic intersection scenario reproduced in the Caltech multi-vehicle lab, with human subjects remotely driving kinematic robots. The results obtained on these data suggest that this kind of human behavior is to some extent predictable on our data set, and different subjects implement similar rules.

ICRA Conference 2004 Conference Paper

Scheduling for Distributed Sensor Networks with Single Sensor Measurement per Time Step

Timothy H. Chung
Vijay Gupta 0001
Babak Hassibi
Joel W. Burdick
Richard M. Murray

We examine the problem of distributed estimation when only one sensor can take a measurement per time step. We solve for the optimal recursive estimation algorithm when the sensor switching schedule is given. We then consider the effect of noise in communication channels. We also investigate the problem of determining an optimal sensor switching strategy. We see that this problem involves searching a tree in general and propose two strategies for pruning the tree to minimize the computation. The first is a sliding window strategy motivated by the Viterbi algorithm, and the second one uses thresholding. The performance of the algorithms is illustrated using numerical examples.

ICRA Conference 2003 Conference Paper

Cooperative task planning of multi-robot systems with temporal constraints

Feng-Li Lian
Richard M. Murray

This paper discusses a design methodology of cooperative trajectory generation for multi-robot systems. The trajectory of achieving cooperative tasks, i. e. , with temporal constraints, is constructed by a nonlinear trajectory generation (NTG) algorithm. Three scenarios of multi-robot tasking are proposed at the cooperative task planning framework. The NTG algorithm is, then, used to generate real-time trajectory for desired robot activities. Given robot dynamics and constraints, the NTG algorithm first finds trajectory curves in a lower dimensional space and parameterizes the curves by a set of B-spline representations. The coefficients of the B-splines are further solved by sequential quadratic programming to satisfy the optimization objectives and constraints. The NTG algorithm has been implemented to generate real-time trajectories for a group of cooperative robots in the presence of spatial and temporal constraints. Finally, an illustrated example of cooperative task planning with temporal constraints is presented.

ICRA Conference 2003 Conference Paper

Vehicle motion planning using stream functions

Stephen Waydo
Richard M. Murray

Borrowing a concept from hydrodynamic analysis, this paper presents stream functions which satisfy Laplace's equation as a local-minima free method for producing potential-field based navigation functions in two dimensions. These functions generate smoother paths (i. e. more suited to aircraft-like vehicles) than previous methods. A method is developed for constructing analytic stream functions to produce arbitrary vehicle behaviors while avoiding obstacles, and an exact solution for the case of a single uniformly moving obstacle is presented. The effects of introducing multiple obstacles are discussed and current work in this direction is detailed. Experimental results generated on the Cornell RoboFlag testbed are presented and discussed.

ICRA Conference 2001 Conference Paper

Nonlinear Control Methods for Planar Carangiform Robot Fish Locomotion

Kristi A. Morgansen
Vincent Duindam
Richard Mason
Joel W. Burdick
Richard M. Murray

Considers the design of motion control algorithms for robot fish. We present modeling, control design, and experimental trajectory tracking results for an experimental planar robotic fish system that is propelled using carangiform-like locomotion. Our model for the fish's propulsion is based on quasi-steady fluid flow. Using this model, we propose gaits for forward and turning trajectories and analyze system response under such control strategies. Our models and predictions are verified by experiment.

ICRA Conference 1997 Conference Paper

An experimental comparison of tradeoffs in using compliant manipulators for robotic grasping tasks

Sudipto Sur
Richard M. Murray

Controllers developed for control of flexible-link robots in hybrid force-position control tasks by a new singular perturbation analysis of flexible manipulators are implemented on an experimental two-robot grasping setup. Various performance criteria are set up and experimental results are discussed within that setting to show tradeoffs in using flexible link robots for grasping. We conclude that large flexibility can be controlled without too much additional effort, has performance comparable to rigid robots and possesses enhancing properties which make it attractive for use in certain types of applications.

ICRA Conference 1995 Conference Paper

The Mechanisms of Undulatory Locomotion: The Mixed Kinematic and Dynamic Case

Jim Ostrowski 0001
Joel W. Burdick
Andrew D. Lewis
Richard M. Murray

This paper studies the mechanics of undulatory locomotion. This type of locomotion is generated by a coupling of internal shape changes to external non-holonomic constraints. Employing methods from geometric mechanics, the authors use the dynamic symmetries and kinematic constraints to develop a specialized form of the dynamic equations which govern undulatory systems. These equations are written in terms of physically meaningful and intuitively appealing variables that show the role of internal shape changes in driving locomotion.

ICRA Conference 1994 Conference Paper

Nonholonomic Mechanics and Locomotion: The Snakeboard Example

Jim Ostrowski 0001
Andrew D. Lewis
Richard M. Murray
Joel W. Burdick

Analysis and simulations are performed for a simplified model of a commercially available variant of the skateboard, known as the Snakeboard. Although the model exhibits basic gait patterns seen in a large number of locomotion problems, the analysis tools currently available do not apply to this problem. The difficulty lies primarily in the way in which the nonholonomic constraints enter into the system. As a first step towards understanding systems represented by their model the authors present the equations of motion and perform some controllability analysis for the snakeboard. The authors also perform numerical simulations of possible gait patterns which are characteristic of snakeboard locomotion. >

ICRA Conference 1992 Conference Paper

An experimental study of hierarchical control laws for grasping and manipulation using a two-fingered planar hand

Karin Hollerbach
Richard M. Murray
S. Shankar Sastry

Compares the performance of hierarchical and single-level controllers in a grasping context, and concludes that for rapid, planar grasping motions of heavy objects the performance of a hierarchical control structure is superior to that of the two single-level controllers tested. Although the theory discussed applies to grasping problems of arbitrary complexity, the focus is on planar, two-fingered grasping for the sake of clarity and to simplify implementation and experimental testing of the proposed control algorithms. The control algorithms have been implemented on a multifingered hand. >

ICRA Conference 1992 Conference Paper

Fingerlike biomechanical robots

D. Curtis Deno
Richard M. Murray
Kristofer S. J. Pister
S. Shankar Sastry

The authors present a technique to analyze the forces and dynamics of a class of mechanical systems, called fingerlike systems, which may be viewed as an extension of simple robots to include networks for force/displacement generation and transmission. Fingerlike mechanical system can be described using a graph-theoretic approach to force and displacement generation and transmission. Branches consist of actuators, cables, springs, and other building blocks. Upon specification of the connectivity graph and branch behaviors, a symbolic mathematics program can generate the affine maps from actuator control variables to mechanical system torques and forces. This process systematizes and simplifies the determination of biological and robotic mechanical dynamics. >

ICRA Conference 1992 Conference Paper

Stabilization of trajectories for systems with nonholonomic constraints

Gregory Walsh
Dawn M. Tilbury
S. Shankar Sastry
Richard M. Murray
Jean-Paul Laumond

A technique for stabilizing nonholonomic systems to trajectories is presented. It is well known that such systems cannot be stabilized to a point using smooth static-state feedback. The authors suggest the use of control laws for stabilizing a system about a trajectory, instead of a point. Given a nonlinear system and a desired nominal feasible trajectory, an explicit control law which will locally exponentially stabilize the system to the desired trajectory is given. The theory is applied to several examples, including a car-like robot. >

ICRA Conference 1992 Conference Paper

Steering car-like systems with trailers using sinusoids

Dawn M. Tilbury
Jean-Paul Laumond
Richard M. Murray
S. Shankar Sastry
Gregory Walsh

Methods for steering car-like robots with trailers are investigated. A connection is demonstrated between Murray and Sastry's (1990, 1991) work of steering with integrally related sinusoids and Sussmann and Liu's (1991) recent work on asymptotic behavior of systems with high-frequency sinusoids as inputs. The merits of coordinate transformations, relative to the convergence properties, are discussed. Simulation results for a car-like robot with two trailers are presented. >

ICRA Conference 1990 Conference Paper

Control primitives for robot systems

D. Curtis Deno
Richard M. Murray
Kristofer S. J. Pister
S. Shankar Sastry

A methodology is developed for describing of hierarchical control of robot systems in a manner which is faithful to the underlying mechanics, structured enough to be used as an interpreted language, and sufficiently flexible to encompass a wide variety of systems. A consistent set of primitive operations which form the core of a robot system description and control language is presented. This language, motivated by the hierarchical organization of neuromuscular systems, is capable of describing a large class of robot systems under a variety of single-level and distributed control schemes. >

ICRA Conference 1989 Conference Paper

Control experiments in planar manipulation and grasping

Richard M. Murray
S. Shankar Sastry

Many algorithms have been proposed in the literature for control of multifingered robot hands. The authors compare the performance of several of these algorithms, as well as some extensions of more conventional manipulator control laws, in the case of planar grasping. Based on experiments performed on Styx, the most effective control laws are found to be the simple joint control law and the generalized computed torque law. The computed torque control law is shown to be an attractive alternative for position control of multifingered hands. >