This paper presents a fast and accurate model of a deformable linear object (DLO) – e.g., a rope, wire, or cable – integrated into an established robot physics simulator, MuJoCo. Most accurate DLO models with low computational times exist in standalone numerical simulators, which are unable or require tedious work to handle external objects. Based on an existing state-of-the-art DLO model – Discrete Elastic Rods (DER) – our implementation provides an improvement in accuracy over MuJoCo’s own native cable model. To minimize computational load, our model utilizes force-lever analysis to adapt the Cartesian stiffness forces of the DER into its generalized coordinates. As a key contribution, we introduce a novel parameter identification pipeline designed for both simplicity and accuracy, which we utilize to determine the bending and twisting stiffness of three distinct DLOs. We then evaluate the performance of each model by simulating the DLOs and comparing them to their real-world counterparts and against theoretically proven validation tests.

This work proposes a solution for the problem of training physics-informed networks under partial integro-differential equations. These equations require an infinite or a large number of neural evaluations to construct a single residual for training. As a result, accurate evaluation may be impractical, and we show that naive approximations at replacing these integrals with unbiased estimates lead to biased loss functions and solutions. To overcome this bias, we investigate three types of potential solutions: the deterministic sampling approaches, the double-sampling trick, and the delayed target method. We consider three classes of PDEs for benchmarking; one defining Poisson problems with singular charges and weak solutions of up to 10 dimensions, another involving weak solutions on electro-magnetic fields and a Maxwell equation, and a third one defining a Smoluchowski coagulation problem. Our numerical results confirm the existence of the aforementioned bias in practice and also show that our proposed delayed target approach can lead to accurate solutions with comparable quality to ones estimated with a large sample size integral. Our implementation is open-source and available at https://github.com/ehsansaleh/btspinn.

This paper addresses the problem of choosing a sparse subset of measurements for quick calibration parameter estimation. A standard solution to this is selecting a measurement only if its utility—the difference between posterior (with the measurement) and prior information (without the measurement)—exceeds some threshold. Theoretically, utility, a function of the parameter estimate, should be evaluated at the estimate obtained with all measurements selected so far, hence necessitating a recalibration with each new measurement. However, we hypothesize that utility is insensitive to changes in the parameter estimate for many systems of interest, suggesting that evaluating utility at some initial parameter guess would yield equivalent results in practice. We provide evidence supporting this hypothesis for extrinsic calibration of multiple inertial measurement units (IMUs), showing the reduction in calibration time by two orders of magnitude by forgoing recalibration for each measurement.

In this article, we present a multi-robot task and motion planning method that, when applied to the rearrangement of objects by manipulators, results in solution times up to three orders of magnitude faster than the existing methods and successfully plans for problems with up to 20 objects, more than three times as many objects as comparable methods. We achieve this improvement by decomposing the planning space to consider manipulators alone, objects, and manipulators holding objects. We represent this decomposition with a hypergraph where vertices are decomposed elements of the planning spaces and hyperarcs are transitions between elements. The existing methods use graph-based representations where vertices are full composite spaces and edges are transitions between these. Using the hypergraph reduces the representation size of the planning space for multimanipulator object rearrangement, the number of hypergraph vertices scales linearly with the number of either robots or objects, while the number of hyperarcs scales quadratically with the number of robots and linearly with the number of objects. In contrast, the number of vertices and edges in graph-based representations scales exponentially in the number of robots and objects. We show that similar gains can be achieved for other multi-robot task and motion planning problems.

In this paper, we present a policy gradient method that avoids exploratory noise injection and performs policy search over the deterministic landscape, with the goal of improving learning with long horizons and non-local rewards. By avoiding noise injection all sources of estimation variance can be eliminated in systems with deterministic dynamics (up to the initial state distribution). Since deterministic policy regularization is impossible using traditional non-metric measures such as the KL divergence, we derive a Wasserstein-based quadratic model for our purposes. We state conditions on the system model under which it is possible to establish a monotonic policy improvement guarantee, propose a surrogate function for policy gradient estimation, and show that it is possible to compute exact advantage estimates if both the state transition model and the policy are deterministic. Finally, we describe two novel robotic control environments---one with non-local rewards in the frequency domain and the other with a long horizon (8000 time-steps)---for which our policy gradient method (TDPO) significantly outperforms existing methods (PPO, TRPO, DDPG, and TD3). Our implementation with all the experimental settings and a video of the physical hardware test is available at https://github.com/ehsansaleh/tdpo .

This full research paper explores students' attitudes toward second-chance testing and how second-chance testing influences students' behavior. Second-chance testing refers to giving students the opportunity to take a second instance of each exam for some sort of grade replacement. Previous work has demonstrated that second-chance testing can lead to improved student outcomes in courses, but how to best structure second-chance testing to maximize its benefits remains an open question. We complement previous work by interviewing a diverse group of 23 students that have taken courses that use second-chance testing. From the interviews, we sought to gain insight into students' views and use of second-chance testing. We found that second-chance testing was almost universally viewed positively by the students and was frequently cited as helping to reduce test takers' anxiety and boost their confidence. Overall, we find that the majority of students prepare for second-chance exams in desirable ways, but we also note ways in which second-chance testing can potentially lead to undesirable behaviors including procrastination, overreliance on memorization, and attempts to game the system. We identified emergent themes pertaining to various facets of second-chance test-taking, including: 1) concerns about the time commitment required for second-chance exams; 2) a belief that second-chance exams promoted fairness; and 3) how second-chance testing incentivized learning. This paper will provide instructors and other stakeholders with detailed insights into students' behavior regarding second-chance testing, enabling instructors to develop better policies and avoid unintended consequences.

Tracking 6-D poses of objects from videos provides rich information to a robot in performing different tasks such as manipulation and navigation. In this article, we formulate the 6-D object pose tracking problem in the Rao–Blackwellized particle filtering framework, where the 3-D rotation and the 3-D translation of an object are decoupled. This factorization allows our approach, called PoseRBPF, to efficiently estimate the 3-D translation of an object along with the full distribution over the 3-D rotation. This is achieved by discretizing the rotation space in a fine-grained manner and training an autoencoder network to construct a codebook of feature embeddings for the discretized rotations. As a result, PoseRBPF can track objects with arbitrary symmetries while still maintaining adequate posterior distributions. Our approach achieves state-of-the-art results on two 6-D pose estimation benchmarks. We open-source our implementation athttps://github.com/NVlabs/PoseRBPF.

We explore how course policies affect students' studying and learning when a second-chance exam is offered. High-stakes, one-off exams remain a de facto standard for assessing student knowledge in STEM, despite compelling evidence that other assessment paradigms such as mastery learning can improve student learning. Unfortunately, mastery learning can be costly to implement. We explore the use of optional second-chance testing to sustainably reap the benefits of mastery-based learning at scale. Prior work has shown that course policies affect students' studying and learning but have not compared these effects within the same course context. We conducted a quasi-experimental study in a single course to compare the effect of two grading policies for second-chance exams and the effect of increasing the size of the range of dates for students taking asynchronous exams. The first grading policy, called 90-cap, allowed students to optionally take a second-chance exam that would fully replace their score on a first-chance exam except the second-chance exam would be capped at 90% credit. The second grading policy, called 90-10, combined students' first- and second-chance exam scores as a weighted average (90% max score + 10% min score). The 90-10 policy significantly increased the likelihood that marginally competent students would take the second-chance exam. Further, our data suggests that students learned more under the 90-10 policy, providing improved student learning outcomes at no cost to the instructor. Most students took exams on the last day an exam was available, regardless of how many days the exam was available.

To teach robots skills, it is crucial to obtain data with supervision. Since annotating real world data is time-consuming and expensive, enabling robots to learn in a self- supervised way is important. In this work, we introduce a robot system for self-supervised 6D object pose estimation. Starting from modules trained in simulation, our system is able to label real world images with accurate 6D object poses for self-supervised learning. In addition, the robot interacts with objects in the environment to change the object configuration by grasping or pushing objects. In this way, our system is able to continuously collect data and improve its pose estimation modules. We show that the self-supervised learning improves object segmentation and 6D pose estimation performance, and consequently enables the system to grasp objects more reliably. A video showing the experiments can be found at https://youtu.be/W1Y0Mmh1Gd8.

In this paper, we study a computerized exam system that allows students to attempt the same question multiple times. This system permits students either to receive feedback on their submitted answer immediately or to defer the feedback and grade questions in bulk. An analysis of student behavior in three courses across two semesters found similar student behaviors across courses and student groups. We found that only a small minority of students used the deferred feedback option. A clustering analysis that considered both when students chose to receive feedback and either to immediately retry incorrect problems or to attempt other unfinished problems identified four main student strategies. These strategies were correlated to statistically significant differences in exam scores, but it was not clear if some strategies improved outcomes or if stronger students tended to prefer certain strategies.

For the past five years we have been operating a Computer-Based Testing Facility (CBTF) as the primary means of summative assessment in large-enrollment STEM-oriented classes. In each of the last three semesters, it has proctored over 50,000 exams for over 6,000 unique students in 25–30 classes. Our CBTF has simultaneously improved the quality of assessment, allowed the testing of computational skills, and reduced the recurring burden of performing assessment in a broad collection of STEM-oriented classes, but it does require an up-front investment to develop the digital exam content. We have found our CBTF to be secure, cost-effective, and well liked by our faculty, who choose to use it semester after semester. We believe that there are many institutions that would similarly benefit from having a Computer-Based Testing Facility.

We present FEATS (Feature Extraction and Tracking Simulator), that synthesizes feature tracks using a camera trajectory and scene geometry (e.g. CAD, multi-view stereo). We introduce 2D feature and matching noise models that can be controlled using a few parameters. We also provide a new dataset of images and ground truth camera pose. We process this data (and a synthetic version) with several current SfM algorithms and show that the synthetic tracks are representative of the real tracks. We then show two practical uses of FEATS: (1) we generate hundreds of trajectories with varying noise and show that COLMAP is more robust to noise than OpenSfM and VisualSfM; and (2) we calculate 3D point error and show that accurate camera pose estimates do not guarantee accurate 3D maps.

This Innovative Practice Full Paper describes lessons learned from and operational details of a full-scale Computer-Based Testing Facility (CBTF) over a period of almost 4 years. The CBTF has grown into a key resource for enabling the graceful scaling of many of the largest classes in our College of Engineering. In Fall 2017, the CBTF served 21 courses from seven different departments and over 6,000 unique students. Over 52,000 exams were delivered, including 3,500 final exams.This paper discusses five main aspects of our CBTF. First, we present the basic operation of the CBTF. Second, we discuss the precautions we take to maintain a secure exam environment. Third, we discuss how we support students that require testing accommodations like extra time and/or a distraction-reduced environment. Fourth, we discuss how we organize our policies to handle exceptional circumstances with minimal intervention by faculty. Finally, we discuss the cost of operating the CBTF and how it compares to traditional exams and online services.

This paper focuses on tracking failure avoidance during vision-based navigation to a desired goal in unknown environments. While using feature-based Visual Simultaneous Localization and Mapping (VSLAM), continuous identification and association of map points are required during motion. Thus, we discuss a motion planning framework that takes into account sensory constraints for a reliable navigation. We use information available in the SLAM and propose a data-driven approach to predict the number of map points associated in a given pose. Then, a distance-optimal path planner utilizes the model to constrain paths such that the number of associated map points in each pose is above a threshold. We also include an online mapping of the environment for collision avoidance. Overall, we propose an iterative motion planning framework that enables real-time replanning after the acquisition of more information. Experiments in two environments demonstrate the performance of the proposed framework.

In this paper, we confirm the hypothesis that the magnetic field inside a building can vary significantly as a function of height. We collected data with twenty magnetometers spaced evenly from knee height to head height and mounted to a ground robot, which we drove through two different buildings on the campus of the University of Illinois at Urbana-Champaign. We applied Gaussian process regression to build a map of the magnetic field at each height. We compared these maps and saw pairwise differences of more than 1 μT in up to 20% of each test environment, a threshold that we argue would prevent meeting the requirements of common indoor positioning applications. These results call into question the planar assumption that is commonly made when deriving methods of indoor positioning that are based on the use of magnetic fields.

Current fiducial marker detection algorithms rely on marker IDs for false positive rejection. Time is wasted on potential detections that will eventually be rejected as false positives. We introduce ChromaTag, a fiducial marker and detection algorithm designed to use opponent colors to limit and quickly reject initial false detections and grayscale for precise localization. Through experiments, we show that ChromaTag is significantly faster than current fiducial markers while achieving similar or better detection accuracy. We also show how tag size and viewing direction effect detection accuracy. Our contribution is significant because fiducial markers are often used in real-time applications (e.g. marker assisted robot navigation) where heavy computation is required by other parts of the system.

Repeated mechanical failure due to accidental impact is one of the main reasons why people with upper-limb amputations abandon commercially-available prosthetic hands. To address this problem, we present the design and evaluation of a compliant four-bar linkage mechanism that makes the fingers of a prosthetic hand more impact resistant. Our design replaces both the rigid input and coupler links with a monolithic compliant bone, and replaces the follower link with three layers of pre-stressed spring steel. This design behaves like a conventional four-bar linkage but adds lateral compliance and eliminates a pin joint, which is a main site of failure on impact. Results from free-end and fixed-end impact tests show that, compared to those made with a conventional four-bar linkage, fingers made with our design absorb up to 11% more energy on impact with no mechanical failure. We also show the integration of these fingers in a prosthetic hand that is low-cost, light-weight, and easy to assemble, and that has grasping performance comparable to commercially-available hands.

In this paper, we present a publicly available dataset for the evaluation of indoor positioning algorithms that use magnetic anomalies. Our dataset contains IMU and magnetometer measurements along with ground truth position measurements that have centimeter-level accuracy. To produce this dataset, we collected over 13 hours of data (51 kilometers of total distance traveled) from three different buildings, with sensors both handheld and mounted on a wheeled robot, in environments with and without changes in the placement of objects that affect magnetometer measurements ("live loads”). We conclude the paper with a discussion of why these characteristics of our dataset are important when evaluating positioning algorithms.

In this paper, we show that the free configuration space of a Kirchhoff elastic rod is path-connected. By free configuration space, we mean the set of all equilibrium configurations of the rod that are stable (i.e. locally minimize elastic potential energy) and do not experience self-intersections. We also provide semi-analytical expressions for paths in the free configuration space that connect any two stable equilibrium configurations that do not contain self-intersections. These results are applied to the problem of manipulation planning for deformable objects.

We consider the manipulation planning problem of an extensible elastic rod in collision-free or contact space. We assume the rod can be handled by grippers either at both or at only one of its extremities and during the manipulation, the grasped end may change. We show that the use of both quasi-static and dynamic models can be coupled efficiently with sampling-based methods. By sampling directly on the submanifold of static equilibrium and contact-free configurations, we can take advantage of the dynamic model to improve the exploration in the state space. We show the necessity of considering contacts for this type of problems with several simulation experiments on various scenarios.

This paper presents the Tact hand-an anthropomorphic, open-source, myoelectric prosthetic hand that was designed for use by people with transradial amputations in developing countries. This hand matches or exceeds the performance of other state-of-the-art myoelectric prosthetic hands, but costs two orders of magnitude less ($250) and is easy to manufacture with a 3D printer and off-the-shelf parts. We describe our design process, evaluate the Tact hand with both qualitative and quantitative measures of performance, and show examples of using this hand to grasp household objects.

We present a passive mechanism for quadrotor vehicles and other hover-capable aerial robots based on the cam-follower. This mechanism has two mating parts, one attached to the quadrotor and the other attached to a payload. These two parts are joined by a toggle switch-push to connect, push to disconnect-that is easy to activate with the quadrotor by varying thrust. We discuss the design parameters and provide an inertial model for our mechanism. With hardware experiments, we demonstrate the use of this passive mechanism to autonomously place a wireless camera in several different locations on the underside of a steel beam. Our mechanism is open source and can be easily fabricated with a 3D printer.

Inverse optimal control is the problem of computing a cost function with respect to which observed trajectories of a given dynamic system are optimal. In this paper, we present a new formulation of this problem for the case where the dynamic system is differentially flat. We show that a solution is easy to obtain in this case, in fact reducing to finite-dimensional linear least-squares minimization. We also show how to make this solution robust to model perturbation, sampled data, and measurement noise, as well as provide a recursive implementation for online learning. Finally, we apply our new formulation of inverse optimal control to model human locomotion during stair ascent. Given sparse observations of human walkers, our model predicts joint angle trajectories for novel stair heights that compare well to motion capture data (R2= 0.97, RMSE = 1.95 degrees). These exemplar trajectories are the basis for an automated method of tuning controller parameters for lower-limb prosthetic devices that extends to locomotion modes other than level ground walking.

In this paper, we address the problem of estimating the shape of a planar elastic rod (e.g., a thin flexible strip of metal) using images of the rod. This is done by treating configurations of the elastic rod as solutions of a geometric optimal control problem. The necessary conditions for optimality provide coordinates over which to perform inference, and the sufficient conditions provide the gradient of the shape of the rod with respect to these coordinates. This optimal control formulation allows for configurations of the rod to be represented as points in a finite-dimensional space without having to discretize the shape of the rod. We consider the estimation problem with and without fiducial markers attached to the rod. Results from both simulations and hardware experiments demonstrate the ability of our approach to track the shape of a deforming elastic rod.

We consider the problem of manipulating a planar elastic rod using robotic grippers which grasp the rod at multiple points. Building upon previous work that considers a rod held only at its ends, we show that manipulating a rod held by n + 1 grippers is equivalent to planning a path on a smooth 3n-dimensional manifold. Using multiple grippers can be advantageous when manipulating around obstacles. We establish upper and lower bounds on the number of grippers needed for an equilibrium shape of the rod to pass between obstacles in a desired way. Finally, we consider manipulation planning when both ends of the rod are held fixed, and only the grippers located along the interior of the rod can move.

In this paper, we suggest a new way to plan coverage paths for a mobile robot whose position and velocity are subject to bounded error. Most prior approaches assume a probabilistic model of uncertainty and maximize the expected value of covered area. We assume a worst-case model of uncertainty and-for a particular choice of coverage path-are still able to guarantee complete coverage. We begin by considering the special case in which the region to be covered is a single point. The machinery we develop to express and solve this problem immediately extends to guarantee coverage of a small subset in the workspace. Finally, we use this subset as a sort of virtual coverage implement, achieving complete coverage of the entire workspace by tiling copies of the subset along boustrophedon paths.

Impedance control is a common framework for control of lower-limb prosthetic devices. This approach requires choosing many impedance controller parameters. In this paper, we show how to learn these parameters for lower-limb prostheses by observation of unimpaired human walkers. We validate our approach in simulation of a transfemoral amputee, and we demonstrate the performance of the learned parameters in a preliminary experiment with a lower-limb prosthetic device.

In this paper, we study quasi-static manipulation of a planar kinematic chain with a fixed base in which each joint is a linearly elastic torsional spring. The shape of this chain when in static equilibrium can be represented as the solution to a discrete-time optimal control problem, with boundary conditions that vary with the position and orientation of the last link. We prove that the set of all solutions to this problem is a smooth three-manifold that can be parameterized by a single chart. Empirical results in simulation show that straight-line paths in this chart are uniformly more likely to be feasible (as a function of distance) than straight-line paths in the space of boundary conditions. These results, which are consistent with an analysis of visibility properties, suggest that the chart we derive is a better choice of space in which to apply a sampling-based algorithm for manipulation planning. We describe such an algorithm and show that it is easy to implement.

In this paper, we develop an approach to inverse optimal control for a class of hybrid dynamical system with impacts. As it is usually posed, the problem of inverse optimal control is to find a cost function that is consistent with an observed sequence of decisions, under the assumption that these decisions are optimal. We assume instead that observed decisions are only approximately optimal and find a cost function that minimizes the extent to which these decisions violate first-order necessary conditions for optimality. For the hybrid dynamical system that we consider with a cost function that is a linear combination of known basis functions, this minimization is a convex program. In fact, it reduces to a simple least-squares computation that - unlike most other forms of inverse optimal control - can be solved very efficiently. We apply our approach to a dynamic bipedal climbing robot in simulation, showing that we can recover cost functions from observed trajectories that are consistent with two different modes of locomotion.

In this paper, we consider the problem of an autonomous robot searching for a target object whose position is characterized by a prior probability distribution over the workspace (the object prior). We consider the case of a continuous search domain, and a robot equipped with a single binary sensor whose ability to recognize the target object varies probabilistically as a function of the distance from the robot to the target (the sensor model). We show that when the object prior and sensor model are taken from the exponential family of distributions, the searcher's posterior probability map for the object location belongs to a finitely parameterizable class of functions, admitting an exact representation of the searcher's evolving belief. Unfortunately, the cost of the representation grows exponentially with the number of stages in the search. For this reason, we develop an approximation scheme that exploits regularized particle filtering methods. We present simulation studies for several scenarios to demonstrate the effectiveness of our approach using a simple, greedy search strategy.

A common algorithm for deployment of a mobile sensor network in a bounded domain moves each sensor toward the centroid of its Voronoi cell. This algorithm is optimal for a particular cost function that is expressed as a sum over Voronoi cells, where the placement of a sensor in its own cell has no effect on cost in other cells. We provide a probabilistic interpretation of this “partitioned” cost function in the context of a target detection task, where each sensor has a chance of seeing the target that decreases monotonically with distance and where the goal is to minimize the total probability of missed detection. We show that the partitioned cost function is exactly the probability of missed detection given that a sensor can only see a target in its own Voronoi cell. We derive the probability of missed detection in the general case - where each sensor might see the target anywhere - and show that optimal sensor placement changes. Finally, we derive the probability of missed detection given the possibility of sensor failure, producing a robust measure of cost with respect to which optimal sensor placement is different yet again. Our results are illustrated by several examples in simulation.

In this paper, we study quasi-static manipulation of a planar kinematic chain with a fixed base in which each joint is a linearly-elastic torsional spring. The shape of this chain when in static equilibrium can be represented as the solution to a discrete-time optimal control problem, with boundary conditions that vary with the position and orientation of the last link. We prove that the set of all solutions to this problem is a smooth manifold that can be parameterized by a single chart. For manipulation planning, we show several advantages of working in this chart instead of in the space of boundary conditions, particularly in the context of a sampling-based planning algorithm. Examples are provided in simulation.

In this paper, we address the problem determining the connectivity of a robot's free configuration space. Our method iteratively builds a constructive proof that two configurations lie in disjoint components of the free configuration space. Our algorithm first generates samples that correspond to configurations for which the robot is in collision with an obstacle. These samples are then weighted by their generalized penetration distance, and used to construct alpha shapes. The alpha shape defines a collection of simplices that are fully contained within the configuration space obstacle region. These simplices can be used to quickly solve connectivity queries, which in turn can be used to define termination conditions for sampling-based planners. Such planners, while typically either resolution complete or probabilistically complete, are not able to determine when a path does not exist, and therefore would otherwise rely on heuristics to determine when the search for a free path should be abandoned. An implementation of the algorithm is provided for the case of a 3D Euclidean configuration space, and a proof of correctness is provided.

Inverse optimal control is the problem of computing a cost function that would have resulted in an observed sequence of decisions. The standard formulation of this problem assumes that decisions are optimal and tries to minimize the difference between what was observed and what would have been observed given a candidate cost function. We assume instead that decisions are only approximately optimal and try to minimize the extent to which observed decisions violate first-order necessary conditions for optimality. For a discrete-time optimal control system with a cost function that is a linear combination of known basis functions, this formulation leads to an efficient method of solution as an unconstrained least-squares problem. We apply this approach to both simulated and experimental data to obtain a simple model of human walking trajectories. This model might subsequently be used either for control of a humanoid robot or for predicting human motion when moving a robot through crowded areas.

This paper presents an interface that allows a human user to specify a desired path for a mobile robot in a planar workspace with noisy binary inputs that are obtained at low bit-rates through an electroencephalograph (EEG). We represent desired paths as geodesics with respect to a cost function that is defined so that each path-homotopy class contains exactly one (local) geodesic. We apply max-margin structured learning to recover a cost function that is consistent with observations of human walking paths. We derive an optimal feedback communication protocol to select a local geodesic-equivalently, a path-homotopy class-using a sequence of noisy bits. We validate our approach with experiments that quantify both how well our learned cost function characterizes human walking data and how well human subjects perform with the resulting interface in navigating a simulated robot with EEG.

In this paper we revisit the classical plate-ball system and prove this system remains controllable under model perturbation that scales the ball radius by an unknown but bounded constant. We present an algorithm for approximate steering and validate the algorithm with hardware experiments. To perform these experiments, we introduce a new version of the plate-ball system based on magnetic actuation. This system is easy to implement and, with our steering algorithm, enables simultaneous manipulation of multiple balls with different radii.

In this paper, we derive a globally asymptotically stabilizing feedback control policy for a collection of differential-drive robots under the constraint that every robot receives exactly the same control inputs. We begin by assuming that each robot has a slightly different wheel size, which scales its forward speed and turning rate by a constant that can be found by offline or online calibration. The resulting feedback policy is easy to implement, is robust to standard models of noise, and scales to an arbitrary number (even a continuous ensemble) of robots. We validate this policy with hardware experiments, which additionally reveal that our feedback policy still works when the wheel sizes are unknown and even when the wheel sizes are all approximately identical. These results have possible future application to control of micro- and nano-scale robotic systems, which are often subject to similar constraints.

In this paper, we introduce and experimentally validate a sampling-based planning algorithm for quasi-static manipulation of a planar elastic rod. Our algorithm is an immediate consequence of deriving a global coordinate chart of finite dimension that suffices to describe all possible configurations of the rod that can be placed in static equilibrium by fixing the position and orientation of each end. Hardware experiments confirm this derivation in the case where the “rod” is a thin, flexible strip of metal that has a fixed base and that is held at the other end by an industrial robot. We show an example in which a path of the robot that was planned by our algorithm causes the metal strip to move between given start and goal configurations while remaining in quasi-static equilibrium.

This paper presents a control strategy based on model learning for a self-assembled robotic “swimmer”. The swimmer forms when a liquid suspension of ferro-magnetic micro-particles and a non-magnetic bead are exposed to an alternating magnetic field that is oriented perpendicular to the liquid surface. It can be steered by modulating the frequency of the alternating field. We model the swimmer as a unicycle and learn a mapping from frequency to forward speed and turning rate using locally-weighted projection regression. We apply iterative linear quadratic regulation with a receding horizon to track motion primitives that could be used for path following. Hardware experiments validate our approach.

This paper considers the problem of steering a nonholonomic unicycle despite model perturbation that scales both the forward speed and the turning rate by an unknown but bounded constant. We model the unicycle as an ensemble control system, show that this system is ensemble controllable, and derive an approximate steering algorithm that brings the unicycle to within an arbitrarily small neighborhood of any given Cartesian position. We apply our work to a differential-drive robot with unknown but bounded wheel radius and validate our approach with hardware experiments.

In this paper, we solve the minimum-time optimal control problem for a group of robots that can move at different speeds but that must all move in the same direction. We are motivated to solve this problem because constraints of this sort are common in micro-scale and nano-scale robotic systems. By application of the minimum principle, we obtain necessary conditions for optimality and use them to guess a candidate control policy. By showing that the corresponding value function is a viscosity solution to the Hamilton-Jacobi-Bellman equation, we verify that our guess is optimal. The complexity of finding this policy for arbitrary initial conditions is only quasilinear in the number of robots, and in fact is dominated by the computation of a planar convex hull. We extend this result to consider obstacle avoidance by explicit parameterization of all possible optimal control policies, and show examples in simulation.

In this paper, we present a hierarchical framework that enables motion planning for asymptotically stable 3-D bipedal walking in the same way that planning is already possible for zero moment point walking. This framework is based on the construction of asymptotically stable gait primitives for a class of hybrid dynamical systems with impacts. Each primitive corresponds to an asymptotically stable hybrid limit cycle that admits rules a priori for sequential composition with other primitives, reducing a high-dimensional feedback motion planning problem into a low-dimensional discrete tree search. As a constructive example, we develop this planning framework for the 3-D compass-gait biped, where each primitive corresponds to walking along an arc of constant curvature for a fixed number of steps. We apply a discrete search algorithm to plan a sequence of these primitives, taking the 3-D biped stably from start to goal in workspaces with obstacles. We finally show how this framework generalizes to more complex models by planning walking paths for an underactuated five-link biped.

The space of all possible paths through a finite dimensional configuration space is infinite-dimensional. Nevertheless, paths taken by "real" robotic systems often cluster on a finite-dimensional manifold that is embedded in this infinite dimensional space and that is governed by a principle of optimality. We take advantage of this property to enable a human user to efficiently specify a desired path for a robot moving through a planar workspace with polygonal obstacles using a sequence of noisy binary inputs, as might be derived from a brain-machine interface. First, we show that the space of all such paths having length that is bounded and locally minimal is homeomorphic to the unit disk. Second, we note that any path mapped to the interior of this disk is a subset of some other path mapped to its boundary. Third, we provide an optimal communication protocol by which the user can, with vanishing error probability, select a point on this boundary. Finally, we validate our approach in preliminary experiments with human subjects.

In this paper, we consider the problem of inverse reinforcement learning for a particular class of continuous-time stochastic systems with continuous state and action spaces, under the assumption that both the cost function and the optimal control policy are parametric with known basis functions. Our goal is to produce a cost function for which a given policy, observed in experiment, is optimal. We proceed by enforcing a constraint on the relationship between input noise and input cost that produces a maximum entropy distribution over the space of all sample paths. We apply maximum likelihood estimation to approximate the parameters of this distribution (hence, of the cost function) given a finite set of sample paths. We iteratively improve our approximation by adding to this set the sample path that would be optimal given our current estimate of the cost function. Preliminary results in simulation provide empirical evidence that our algorithm converges.

The classical problem of robot coverage is to plan a path that brings a point on the robot within a fixed distance of every point in the free space. In the presence of significant uncertainty in sensing and actuation, it may no longer be possible to guarantee that the robot covers all of the free space all the time, and so it becomes unclear what problem we are trying to solve. We will restore clarity by adopting a ¿probably approximately correct¿ measure of performance that captures the probability 1-¿ of covering a fraction 1-¿ of the free space. The problem of coverage for a robot with uncertainty is then to plan a feedback policy that achieves a given value of ¿ and ¿. Just as solutions to the classical problem are judged by the resulting path length, solutions to our problem are judged by the required execution time. We will show the practical utility of our performance measure by applying it to several examples in simulation.

This article presents a new approach to designing brain–computer interfaces (BCIs) that explicitly accounts for both the uncertainty of neural signals and the important role of sensory feedback. This approach views a BCI as the means by which users communicate intent to an external device and models intent as a string in an ordered symbolic language. This abstraction allows the problem of designing a BCI to be reformulated as the problem of designing a reliable communication protocol using tools from feedback information theory. Here, this protocol is given by a posterior matching scheme. This scheme is not only provably optimal but also easily understood and implemented by a human user. Experimental validation is provided by an interface for text entry and an interface for tracing smooth planar curves, where input is taken in each case from an electroencephalograph during left- and right-hand motor imagery.

Probabilistic language models are critical to applications in natural language processing that include speech recognition, optical character recognition, and interfaces for text entry. In this paper, we present a systematic way to learn a similar type of probabilistic language model for hand drawings from a database of existing artwork by representing each stroke as a sequence of symbols. First, we propose a language in which the symbols are circular arcs with length fixed by a scale parameter and with curvature chosen from a fixed low-cardinality set. Then, we apply an algorithm based on dynamic programming to represent each stroke of the drawing as a sequence of symbols from our alphabet. Finally, we learn the probabilistic language model by constructing a Markov model. We compute the entropy of our language in a test set as measured by the expected number of bits required for each symbol. Our language model might be applied in future work to create a drawing interface for noisy and low-bandwidth input devices, for example an electroencephalograph (EEG) that admits one binary command per second. The results indicate that by leveraging our language model, the performance of such an interface would be enhanced by about 20 percent.

This paper presents an interface that allows a human pilot to remotely teleoperate an unmanned aircraft flying at a fixed altitude with input only from an electroen-cephalograph (EEG), which is used in this case to distinguish between left- and right-hand motor imagery in the brain. The approach is to construct an ordered symbolic language for smooth planar curves and to use these curves as desired paths for the aircraft. The underlying problem is then to design a communication protocol by which the pilot can, with vanishing error probability, specify a string in this language using a sequence of bits sent through a binary symmetric channel in the presence of noiseless feedback. Such a protocol is provided by the combination of arithmetic coding as a method of lossless data compression with posterior matching as a capacity-achieving channel code. Preliminary hardware experiments demonstrate the feasibility of this approach.

This paper applies geometric reduction-based control to derive a set of asymptotically stable dynamic walking gaits for a 3-D bipedal robot, each corresponding to walking along a nominal arc of constant curvature for a fixed number of steps. We show that any such set of asymptotically stable gait primitives may be composed in arbitrary order without causing the robot to fall, so any walking path that is a sequence of these gaits may be followed by the robot. This result enables motion planning for bipedal dynamic walkers, which are fast and energetically efficient, in a similar manner to what is already possible for biped locomotion based on Zero Moment Point (ZMP) equilibrium constraints.

In this paper we derive the control policy that minimizes the total expected time for a point mass with bounded acceleration, starting from the origin at rest, to find and return to an unknown target that is distributed uniformly on the unit interval. We apply our result to proof-of-concept hardware experiments with a planar robot arm searching for a metal object using an inductive proximity sensor. In particular, we show that our approach easily extends to optimal search along arbitrary curves, such as raster-scan patterns that might be useful in other applications like robot search-and-rescue.

The paper in question [G. Arechavaleta, J. P. Laumond, H. Hicheur, and A. Berthoz, “An optimality principle governing human walking,” IEEE Trans. Robot., vol. 24, no. 1, pp. 5-14, Feb. 2008] suggested that human-walking paths minimize variation in curvature and hence can be approximated by the solution to an optimal control problem. This conclusion was reached by analysis of experimental data based on the maximum principle. We correct two errors in this analysis and consider their consequences.

This paper presents a mechanism and a control strategy that enables automated non-contact manipulation of spherical objects in three dimensions using air flow, and demonstrates several tasks that can be performed with such a system. The mechanism is a 2-DOF gimbaled air jet with a variable flow rate. The control strategy is feedback linearization based on a classical fluid dynamics model with state estimates from stereo vision data. The tasks include palletizing, sorting, and ballistics. All results are verified with hardware experiments.

We propose a complementary approach to the design of neural prosthetic interfaces that goes beyond the standard approach of estimating desired control signals from neural activity. We exploit the fact that the for a user's intended application, the dynamics of the prosthetic in fact impact subsequent desired control inputs. We illustrate that changing the dynamic response of a prosthetic device can make specific tasks significantly easier to accomplish. Our approach relies upon principles from stochastic control and feedback information theory, and we illustrate its effectiveness both theoretically and experimentally - in terms of spelling words from a menu of characters using binary surface electromyography classification.

Consider a legged robot at fixed foot placements. Where can the robot move its center of mass (CM) while remaining in static equilibrium? If the terrain is flat, the CM must lie above the convex hull of the robot's feet. If the terrain is not flat, this often-used approximation can be arbitrarily bad. Instead, the CM must lie above the projection of a nonlinear convex set that is defined by the properties of each foot placement. This paper presents an algorithm to compute the shape of this projection and gives a tight bound on the algorithm's running time. It also presents a method of amortizing the cost of this computation when it is only necessary to test static equilibrium at particular CM positions--that is, when it is only necessary to test the membership of points in the projection of a convex set rather than find its shape.

This paper considers the problem of stabilizing a unicycle-type mobile robot using a time-invariant, discontinuous control law. In order to simplify the control design, most previous approaches neglect second-order system dynamics (compensating for them later using techniques such as partial feedback linearization). This paper shows that an approach based on invariant manifold theory can be extended to account for these dynamics. The performance of the resulting control law is demonstrated in simulation.

A legged robot walking on uneven terrain can avoid falling only by applying contact forces with its feet on the ground that compensate for gravity without causing slip. To plan safe motions, it is necessary to test this constraint at every posture explored at each set of foot placements. Since a huge number of postures may be explored, this test must be as fast as possible. Existing approaches either search explicitly for contact forces at each posture, or precompute the support polygon and check that the robot's center of mass lies above it. This paper presents a new algorithm that is faster than either existing approach. This algorithm is an incremental method of projection, that computes only enough of the support polygon to decide whether static equilibrium is possible at each posture. It takes advantage of information gained testing previous postures in order to test subsequent postures more quickly

This paper presents a method of generating natural-looking motion primitives for humanoid robots. An optimization-based approach is used to generate these primitives, but the objective function is tailored to each one and complexity is reduced by identifying relevant degrees of freedom. Several examples are shown in simulation: for an arm movement to reach an object, it is better to minimize the acceleration of key parts of the robot over its entire trajectory; for a single step on flat ground, it is better to minimize the torque and instantaneous angular momentum at every posture. The primitives are precomputed off-line, but might be used by on-line planner either to provide a fixed set of maneuvers or to bias a probabilistic, sample-based search for motions

Probabilistic sampling-based motion planners are unable to detect when no feasible path exists. A common heuristic is to declare a query infeasible if a path is not found in a fixed amount of time. In applications where many queries must be processed – for instance, robotic manipulation, multi-limbed locomotion, and contact motion – a critical question arises: what should this time limit be? This paper presents a machine-learning approach to deal with this question. In an off-line learning phase, a classifier is trained to quickly predict the feasibility of a query. Then, an improved multi-step motion planning algorithm uses this classifier to avoid wasting time on infeasible queries. This approach has been successfully demonstrated in simulation on a four-limbed, free-climbing robot.

This paper presents a general framework for planning the quasi-static motion of a three-limbed climbing robot in vertical natural terrain. The problem is to generate a sequence of continuous one-step motions between consecutive holds that will allow the robot to reach a particular goal hold. A detailed algorithm is presented to compute a one-step motion considering the equilibrium constraint only. The overall framework combines this local planner with a heuristic search technique to generate a complete plan. An online implementation of the algorithm is demonstrated in simulation.