A Learning Analytics Dashboard is a quick and efficient way for instructors to track the activities of students. In massive online learning scenarios like an international robotics competition, a dashboard is a critical tool for instructors to ensure continuous engagement of participants. Previous research on learning analytics dashboards focused on the effectiveness of dashboards and learning analytics on students along with factors affecting its success. This research discusses a dashboard developed for a massive robotics competition through which each year thousands of students are trained in engineering skills in an online Project Based Learning approach. The dashboard is developed using the dataset for the competition conducted during September 2020 to April 2021 in which more than 10,000 undergraduate students from 572 academic institutions across 7 countries participated. Team characteristics like demographics, feedback, scores, online activity, etc. are considered to cluster teams and develop models to predict the retention of participants. The Machine Learning (ML) model was able to achieve an accuracy of 80.7% and a recall value of 83.9% to identify dropping teams. Clustering provided insights on how these characteristics affected the performance of participants. These predictions along with participant engagement and feedback data was displayed on the dashboard. This visualization helps instructors identify teams requiring guidance or scaffolds to continue participation. Feedback from instructors shows the dashboard to be a promising tool for effectively managing massive online competitions.

In this paper, we present a robotic model-based reinforcement learning method that combines ideas from model identification and model predictive control. We use a feature-based representation of the dynamics that allows the dynamics model to be fitted with a simple least squares procedure, and the features are identified from a high-level specification of the robot's morphology, consisting of the number and connectivity structure of its links. Model predictive control is then used to choose the actions under an optimistic model of the dynamics, which produces an efficient and goal-directed exploration strategy. We present real time experimental results on standard benchmark problems involving the pendulum, cartpole, and double pendulum systems. Experiments indicate that our method is able to learn a range of benchmark tasks substantially faster than the previous best methods. To evaluate our approach on a realistic robotic control task, we also demonstrate real time control of a simulated 7 degree of freedom arm.

We introduce an optimization-based control approach that enables a team of robots to cooperatively track a target using onboard sensing. In this setting, the robots are required to estimate their own positions as well as concurrently track the target. Our probabilistic method generates controls that minimize the expected uncertainty of the target. Additionally, our method efficiently reasons about occlusions between robots and takes them into account for the control generation. We evaluate our approach in a number of experiments in which we simulate a team of quadrotor robots flying in three-dimensional space to track a moving target on the ground. We compare our method to other state-of-the-art approaches represented by the random sampling technique, lattice planning method, and our previous method. Our experimental results indicate that our method achieves up to 8 times smaller maximum tracking error and up to 2 times smaller average tracking error than the next best approach in the presented scenarios.

We introduce a novel haptic display designed to reproduce the sensation of both lateral and rotational slip on a user's fingertip. The device simulates three-degrees-of-freedom of slip by actuating four interleaved tactile belts on which the user's finger rests. We present the specifications for the device, the mechanical design considerations, and initial evaluation experiments. We conducted experiments on user discrimination of tangential lateral and rotational slip. Initial results from our preliminary experiments suggest the device design has potential to simulate both tangential lateral and rotational slip. Source files: https://github.com/Slip-Pad.

We consider the task of actively exploring unstructured environments to facilitate robotic grasping of occluded objects. Typically, the geometry and locations of these objects are not known a priori. We mount an RGB-D sensor on the robot gripper to maintain a 3D voxel map of the environment during exploration. The objective is to plan the motion of the sensor in order to search for feasible grasp handles that lie within occluded regions of the map. In contrast to prior work that generates exploration trajectories by sampling, we directly optimize the exploration trajectory to find grasp handles. Since it is challenging to optimize over the discrete voxel map, we encode the uncertainty of the positions of the occluded grasp handles as a mixture of Gaussians, one per occluded region. Our trajectory optimization approach encourages exploration by penalizing a measure of the uncertainty. We then plan a collision-free trajectory for the robot arm to the detected grasp handle. We evaluated our approach by actively exploring and attempting 300 grasps. Our experiments suggest that compared to the baseline method of sampling 10 trajectories, which successfully grasped 58% of the objects, our active exploration formulation with trajectory optimization successfully grasped 93% of the objects, was 1.3× faster, and had 3.2× fewer failed grasp attempts.

Grasping an object in a cluttered, unorganized environment is challenging because of unavoidable contacts and interactions between the robot and multiple immovable (static) and movable (dynamic) obstacles in the environment. Planning an approach trajectory for grasping in such situations can benefit from physics-based simulations that describe the dynamics of the interaction between the robot manipulator and the environment. In this work, we present a physics-based trajectory optimization approach for planning grasp approach trajectories. We present novel cost objectives and identify failure modes relevant to grasping in cluttered environments. Our approach uses rollouts of physics-based simulations to compute the gradient of the objective and of the dynamics. Our approach naturally generates behaviors such as choosing to push objects that are less likely to topple over, recognizing and avoiding situations which might cause a cascade of objects to fall over, and adjusting the manipulator trajectory to push objects aside in a direction orthogonal to the grasping direction. We present results in simulation for grasping in a variety of cluttered environments with varying levels of density of obstacles in the environment. Our experiments in simulation indicate that our approach outperforms a baseline approach that considers multiple straight-line trajectories modified to account for static obstacles by an aggregate success rate of 14% with varying degrees of object clutter.

Computing grasps for an object is challenging when the object geometry is not known precisely. In this paper, we explore the use of Gaussian process implicit surfaces (GPISs) to represent shape uncertainty from RGBD point cloud observations of objects. We study the use of GPIS representations to select grasps on previously unknown objects, measuring grasp quality by the probability of force closure. Our main contribution is GP-GPIS-OPT, an algorithm for computing grasps for parallel-jaw grippers on 2D GPIS object representations. Specifically, our method optimizes an approximation to the probability of force closure subject to antipodal constraints on the parallel jaws using Sequential Convex Programming (SCP). We also introduce GPIS-Blur, a method for visualizing 2D GPIS models based on blending shape samples from a GPIS. We test the algorithm on a set of 8 planar objects with transparency, translucency, and specularity. Our experiments suggest that GP-GPIS-OPT computes grasps with higher probability of force closure than a planner that does not consider shape uncertainty on our test objects and may converge to a grasp plan up to 5.7×faster than using Monte-Carlo integration, a common method for grasp planning under shape uncertainty. Furthermore, initial experiments on the Willow Garage PR2 robot suggest that grasps selected with GP-GPIS-OPT are up to 90% more successful than those planned assuming a deterministic shape. Our dataset, code, and videos of our experiments are available at http://rll.berkeley.edu/icra2015grasping/.

Automating repetitive surgical subtasks such as suturing, cutting and debridement can reduce surgeon fatigue and procedure times and facilitate supervised tele-surgery. Programming is difficult because human tissue is deformable and highly specular. Using the da Vinci Research Kit (DVRK) robotic surgical assistant, we explore a “Learning By Observation” (LBO) approach where we identify, segment, and parameterize motion sequences and sensor conditions to build a finite state machine (FSM) for each subtask. The robot then executes the FSM repeatedly to tune parameters and if necessary update the FSM structure. We evaluate the approach on two surgical subtasks: debridement of 3D Viscoelastic Tissue Phantoms (3d-DVTP), in which small target fragments are removed from a 3D viscoelastic tissue phantom; and Pattern Cutting of 2D Orthotropic Tissue Phantoms (2d-PCOTP), a step in the standard Fundamentals of Laparoscopic Surgery training suite, in which a specified circular area must be cut from a sheet of orthotropic tissue phantom. We describe the approach and physical experiments with repeatability of 96% for 50 trials of the 3d-DVTP subtask and 70% for 20 trials of the 2d-PCOTP subtask. A video is available at: http://j.mp/Robot-Surgery-Video-Oct-2014.

We present an approach for asymptotically optimal motion planning for kinodynamic systems with arbitrary nonlinear dynamics amid obstacles. Optimal sampling-based planners like RRT*, FMT*, and BIT* when applied to kinodynamic systems require solving a two-point boundary value problem (BVP) to perform exact connections between nodes in the tree. Two-point BVPs are non-trivial to solve, hence the prevalence of alternative approaches that focus on specific instances of kinodynamic systems, use approximate solutions to the two-point BVP, or use random propagation of controls. In this work, we explore the feasibility of exploiting recent advances in numerical optimal control and optimization to solve these two-point BVPs for arbitrary kinodynamic systems and how they can be integrated with existing optimal planning algorithms. We combine BIT* with a two-point BVP solver that uses sequential quadratic programming (SQP). We consider the problem of computing minimum-time trajectories. Since the duration of trajectories is not known a-priori, we include the time-step as part of the optimization to allow SQP to optimize over the duration of the trajectory while keeping the number of discrete steps fixed for every connection attempted. Our experiments indicate that using a two-point BVP solver in the inner-loop of BIT* is competitive with the state-of-the-art in sampling-based optimal planning that explicitly avoids the use of two-point BVP solvers.

Automation of repetitive tasks can improve laparoscopic surgical procedures by unloading surgeons and reducing duration, trauma, and expense. However, surgical procedures involve delicate manipulation of deformable tissues in a very dynamic environment, suggesting that automated execution of surgical tasks should be carried out under the supervision of the surgeon. We propose a teleoperated architecture that allows a surgeon to employ and supervise agents that can autonomously perform or assist with surgical tasks. The architecture is independent of the automation method. It includes a dominance factor that allows the surgeon to take control over the slave robot at any time, and an aggressiveness factor that sets the performance pace of the autonomous agent. We tested the architecture during execution of a multilateral tension-and-cut task, where a human operator and an autonomous agent are responsible for tensioning or cutting of a tissue. The architecture allowed for supervised and paced automation of the task. We found that collaboration of the human operator and autonomous agent can lead to shorter completion time compared to performance of only a human.

The Cloud infrastructure and its extensive set of Internet-accessible resources has potential to provide significant benefits to robots and automation systems. We consider robots and automation systems that rely on data or code from a network to support their operation, i.e., where not all sensing, computation, and memory is integrated into a standalone system. This survey is organized around four potential benefits of the Cloud: 1) Big Data: access to libraries of images, maps, trajectories, and descriptive data; 2) Cloud Computing: access to parallel grid computing on demand for statistical analysis, learning, and motion planning; 3) Collective Robot Learning: robots sharing trajectories, control policies, and outcomes; and 4) Human Computation: use of crowdsourcing to tap human skills for analyzing images and video, classification, learning, and error recovery. The Cloud can also improve robots and automation systems by providing access to: a) datasets, publications, models, benchmarks, and simulation tools; b) open competitions for designs and systems; and c) open-source software. This survey includes over 150 references on results and open challenges. A website with new developments and updates is available at: http://goldberg.berkeley.edu/cloud-robotics/.

This paper considers grasp planning in the presence of shape uncertainty and explores how cloud computing can facilitate parallel Monte Carlo sampling of combination actions and shape perturbations to estimate a lower bound on the probability of achieving force closure. We focus on parallel-jaw push grasping for the class of parts that can be modeled as extruded 2-D polygons with statistical tolerancing. We describe an extension to model part slip and experimental results with an adaptive sampling algorithm that can reduce sample size by 90%. We show how the algorithm can also bound part tolerance for a given grasp quality level and report a sensitivity analysis on algorithm parameters. We test a cloud-based implementation with varying numbers of nodes, obtaining a 515 × speedup with 500 nodes in one case, suggesting the algorithm can scale linearly when all nodes are reliable. Code and data are available at: http://automation.berkeley.edu/cloud-based-grasping.

We present an approach for planning ensembles of channels, ribbons, within 3D printed implants for facilitating radiation therapy treatment of cancer. The ribbons are traced out by sweeping a constant width rigid body (cuboid) along spatial curves. We propose a method for planning multiple disjoint and mutually collision-free ribbons of finite thickness along curvature and torsion constrained curves in 3D space. This is equivalent to planning motions for the cross section of the ribbon along a spatial curve such that the cross section is oriented along the unit binormal to the curve defined according to the Frenet-Serret frame. We propose a two-stage planning approach. In the first stage, a customized sampling-based planner uses rapidly exploring random trees (RRTs) to generate feasible curvature and torsion constrained ribbons. In the second stage, the curvature and torsion along each ribbon is locally optimized using sequential quadratic programming (SQP). We use this approach to design curved radiation delivery channels inside custom 3D printed implants that allow temporary insertion of a high-dose radioactive source that is threaded through the channels using a wire and allowed to dwell for specified times to expose cancerous tumors for intracavitary brachytherapy treatment. Constraints on the curvature and torsion are required for 3D printing (to allow flushing of sacrificial material) and for smooth insertion of radioactive sources. In simulation experiments, this approach achieves an improvement of 46% in tumor coverage compared with a greedy approach that generates channels sequentially.

As sampling-based motion planners become faster, they can be re-executed more frequently by a robot during task execution to react to uncertainty in robot motion, obstacle motion, sensing noise, and uncertainty in the robot's kinematic model. We investigate and analyze high-frequency replanning (HFR), where, during each period, fast sampling-based motion planners are executed in parallel as the robot simultaneously executes the first action of the best motion plan from the previous period. We consider discrete-time systems with stochastic nonlinear (but linearizable) dynamics and observation models with noise drawn from zero mean Gaussian distributions. The objective is to maximize the probability of success (i.e., avoid collision with obstacles and reach the goal) or to minimize path length subject to a lower bound on the probability of success. We show that, as parallel computation power increases, HFR offers asymptotic optimality for these objectives during each period for goal-oriented problems. We then demonstrate the effectiveness of HFR for holonomic and nonholonomic robots including car-like vehicles and steerable medical needles.

3D curvature-constrained motion planning finds applications in a wide variety of domains, including motion planning for flexible, bevel-tip medical needles, planning curvature-constrained channels in 3D printed implants for targeted brachytherapy dose delivery or channels for cooling turbine blades, and path planning for unmanned aerial vehicles (UAVs). In this work, we present a motion planning technique using sequential convex optimization for computing locally optimal, curvature-constrained trajectories to desired targets while avoiding obstacles in 3D environments. We report two main contributions in this work: (i) curvature-constrained trajectory optimization in 6D pose (position and orientation) space, and (ii) planning multiple trajectories that are mutually collision-free. We demonstrate the performance of our approach on two clinically motivated applications. Our experiments indicate that our approach can compute high-quality plans for medical needle steering in 1.6 seconds on a commodity PC, enabling re-planning during execution to correct for perturbations. Our approach can also be used for designing optimized channel layouts within 3D printed implants for intracavitary brachytherapy.

Autonomous robot execution of surgical sub-tasks has the potential to reduce surgeon fatigue and facilitate supervised tele-surgery. This paper considers the sub-task of surgical debridement: removing dead or damaged tissue fragments to allow the remaining healthy tissue to heal. We present an autonomous multilateral surgical debridement system using the Raven, an open-architecture surgical robot with two cable-driven 7 DOF arms. Our system combines stereo vision for 3D perception with trajopt, an optimization-based motion planner, and model predictive control (MPC). Laboratory experiments involving sensing, grasping, and removal of 120 fragments suggest that an autonomous surgical robot can achieve robustness comparable to human performance. Our robot system demonstrated the advantage of multilateral systems, as the autonomous execution was 1.5× faster with two arms than with one; however, it was two to three times slower than a human. Execution speed could be improved with better state estimation that would allow more travel between MPC steps and fewer MPC replanning cycles. The three primary contributions of this paper are: (1) introducing debridement as a sub-task of interest for surgical robotics, (2) demonstrating the first reliable autonomous robot performance of a surgical sub-task using the Raven, and (3) reporting experiments that highlight the importance of accurate state estimation for future research. Further information including code, photos, and video is available at: http://rll.berkeley.edu/raven.

Percutaneous needle insertions are commonly performed for diagnostic and therapeutic purposes. Accurate placement of the needle tip is important to the success of many needle procedures. The current needle steering systems depend on needle-tissue-specific data, such as maximum curvature, that is unavailable prior to an interventional procedure. In this paper, we present a novel three-dimensional adaptive steering method for flexible bevel-tipped needles that is capable of performing accurate tip placement without previous knowledge about needle curvature. The method steers the needle by integrating duty-cycled needle steering, online curvature estimation, ultrasound-based needle tracking, and sampling-based motion planning. The needle curvature estimation is performed online and used to adapt the path and duty cycling. We evaluated the method using experiments in a homogenous gelatin phantom, a two-layer gelatin phantom, and a biological tissue phantom composed of a gelatin layer and in vitro chicken tissue. In all experiments, virtual obstacles and targets move in order to represent the disturbances that might occur due to tissue deformation and physiological processes. The average targeting error using our new adaptive method is 40% lower than using the conventional non-adaptive duty-cycled needle steering method.

Discontinuities in sensing domains are common when planning for many robotic navigation and manipulation tasks. For cameras and 3D sensors, discontinuities may be inherent in sensor field of view or may change over time due to occlusions that are created by moving obstructions and movements of the sensor. The associated gaps in sensor information due to missing measurements pose a challenge for belief space and related optimization-based planning methods since there is no gradient information when the system state is outside the sensing domain. We address this in a belief space context by considering the signed distance to the sensing region. We smooth out sensing discontinuities by assuming that measurements can be obtained outside the sensing region with noise levels depending on a sigmoid function of the signed distance. We sequentially improve the continuous approximation by increasing the sigmoid slope over an outer loop to find plans that cope with sensor discontinuities. We also incorporate the information contained in not obtaining a measurement about the state during execution by appropriately truncating the Gaussian belief state. We present results in simulation for tasks with uncertainty involving navigation of mobile robots and reaching tasks with planar robot arms. Experiments suggest that the approach can be used to cope with discontinuities in sensing domains by effectively re-planning during execution.

Steerable needles have the potential to improve the effectiveness of needle-based clinical procedures such as biopsy and drug delivery by improving targeting accuracy and reaching previously inaccessible targets that are behind sensitive or impenetrable anatomical regions. We present a new needle steering system capable of automatically reaching targets in 3-D environments while avoiding obstacles and compensating for real-world uncertainties. Given a specification of anatomical obstacles and a clinical target (e.g., from preoperative medical images), our system plans and controls needle motion in a closed-loop fashion under sensory feedback to optimize a clinical metric. We unify planning and control using a new fast algorithm that continuously replans the needle motion. Our rapid replanning approach is enabled by an efficient sampling-based rapidly exploring random tree (RRT) planner that achieves orders-of-magnitude reduction in computation time compared with prior 3-D approaches by incorporating variable curvature kinematics and a novel distance metric for planning. Our system uses an electromagnetic tracking system to sense the state of the needle tip during the procedure. We experimentally evaluate our needle steering system using tissue phantoms and animal tissue ex vivo. We demonstrate that our rapid replanning strategy successfully guides the needle around obstacles to desired 3-D targets with an average error of less than 3 mm.

In many home and service applications, an emerging class of articulated robots such as the Raven and Baxter trade off precision in actuation and sensing to reduce costs and to reduce the potential for injury to humans in their workspaces. For planning and control of such robots, planning in belief ssigma hullpace, i.e., modeling such problems as POMDPs, has shown great promise but existing belief space planning methods have primarily been applied to cases where robots can be approximated as points or spheres. In this paper, we extend the belief space framework to treat articulated robots where the linkage can be decomposed into convex components. To allow planning and collision avoidance in Gaussian belief spaces, we introduce the concept of sigma hulls: convex hulls of robot links transformed according to the sigma standard deviation boundary points generated by the Unscented Kalman filter (UKF). We characterize the signed distances between sigma hulls and obstacles in the workspace to formulate efficient collision avoidance constraints compatible with the Gilbert-Johnson-Keerthi (GKJ) and Expanding Polytope Algorithms (EPA) within an optimization-based planning framework. We report results in simulation for planning motions for a 4-DOF planar robot and a 7-DOF articulated robot with imprecise actuation and inaccurate sensors. These experiments suggest that the sigma hull framework can significantly reduce the probability of collision and is computationally efficient enough to permit iterative re-planning for model predictive control.

We introduce a highly efficient method for solving continuous partially-observable Markov decision processes (POMDPs) in which beliefs can be modeled using Gaussian distributions over the state space. Our method enables fast solutions to sequential decision making under uncertainty for a variety of problems involving noisy or incomplete observations and stochastic actions. We present an efficient approach to compute locally-valid approximations to the value function over continuous spaces in time polynomial (O[n^4]) in the dimension n of the state space. To directly tackle the intractability of solving general POMDPs, we leverage the assumption that beliefs are Gaussian distributions over the state space, approximate the belief update using an extended Kalman filter (EKF), and represent the value function by a function that is quadratic in the mean and linear in the variance of the belief. Our approach iterates towards a linear control policy over the state space that is locally-optimal with respect to a user defined cost function, and is approximately valid in the vicinity of a nominal trajectory through belief space. We demonstrate the scalability and potential of our approach on problems inspired by robot navigation under uncertainty for state spaces of up to 128 dimensions.

We present a fast, analytical method for estimating the probability of collision of a motion plan for a mobile robot operating under the assumptions of Gaussian motion and sensing uncertainty. Estimating the probability of collision is an integral step in many algorithms for motion planning under uncertainty and is crucial for characterizing the safety of motion plans. Our method is computationally fast, enabling its use in online motion planning, and provides conservative estimates to promote safety. To improve accuracy, we use a novel method to truncate estimated a priori state distributions to account for the fact that the probability of collision at each stage along a plan is conditioned on the previous stages being collision free. Our method can be directly applied within a variety of existing motion planners to improve their performance and the quality of computed plans. We apply our method to a car-like mobile robot with second order dynamics and to a steerable medical needle in 3D and demonstrate that our method for estimating the probability of collision is orders of magnitude faster than naïve Monte Carlo sampling methods and reduces estimation error by more than 25% compared to prior methods.

Computing globally optimal motion plans requires exploring the configuration space to identify reachable free space regions as well as refining understanding of already explored regions to find better paths. We present the rapidly-exploring roadmap (RRM), a new method for single-query optimal motion planning that allows the user to explicitly consider the trade-off between exploration and refinement. RRM initially explores the configuration space like a rapidly exploring random tree (RRT). Once a path is found, RRM uses a user-specified parameter to weigh whether to explore further or to refine the explored space by adding edges to the current roadmap to find higher quality paths in the explored space. Unlike prior methods, RRM does not focus solely on exploration or refine prematurely. We demonstrate the performance of RRM and the trade-off between exploration and refinement using two examples, a point robot moving in a plane and a concentric tube robot capable of following curved trajectories inside patient anatomy for minimally invasive medical procedures.

We present a new sampling-based method for planning optimal, collision-free, curvature-constrained paths for nonholonomic robots to visit multiple goals in any order. Rather than sampling configurations as in standard sampling-based planners, we construct a roadmap by sampling circles of constant curvature and then generating feasible transitions between the sampled circles. We provide a closed-form formula for connecting the sampled circles in 2D and generalize the approach to 3D workspaces. We then formulate the multi-goal planning problem as finding a minimum directed Steiner tree over the roadmap. Since optimally solving the multi-goal planning problem requires exponential time, we propose greedy heuristics to efficiently compute a path that visits multiple goals. We apply the planner in the context of medical needle steering where the needle tip must reach multiple goals in soft tissue, a common requirement for clinical procedures such as biopsies, drug delivery, and brachytherapy cancer treatment. We demonstrate that our multi-goal planner significantly decreases tissue that must be cut when compared to sequential execution of single-goal plans.

We present a novel approach to direct and control virtual crowds using navigation fields. Our method guides one or more agents toward desired goals based on guidance fields. The system allows the user to specify these fields by either sketching paths directly in the scene via an intuitive authoring interface or by importing motion flow fields extracted from crowd video footage. We propose a novel formulation to blend input guidance fields to create singularity-free, goal-directed navigation fields. Our method can be easily combined with the most current local collision avoidance methods and we use two such methods as examples to highlight the potential of our approach. We illustrate its performance on several simulation scenarios.

Robotic surgical assistants are enhancing physician performance, enabling physicians to perform more delicate and precise minimally invasive surgery. However, these devices are currently tele-operated and lack autonomy. In this paper, we present initial steps toward automating a commonly performed surgical task, tissue retraction, which involves grasping and lifting a thin layer of tissue to expose an underlying area. Given a model of tissues in the vicinity, our method computes a motion plan for a 6-DOF gripper that grasps a tissue flap at an optimal location and retracts it such that an underlying target is fully visible. The planner considers three optimization objectives relevant to medical applications: minimizing the maximum deformation energy, minimizing maximum stress, and minimizing the control effort in lifting the tissue flap. The planner can be used to locally improve physician specified retraction trajectories based on the optimization criteria or to compute a de novo plan. We use a physically-based simulation to compute equilibrium configurations of the tissue flap subject to manipulation constraints. These configurations are used with a sampling-based planner to explore the space of deformations and compute an optimal plan subject to discretization and modeling error. Our experimental results illustrate the ability of the method to compute retractions for heterogeneous tissues while avoiding obstacles and minimizing tissue damage.

We present a novel approach for interactive navigation and planning of multiple agents in crowded scenes with moving obstacles. Our formulation uses a precomputed roadmap that provides macroscopic, global connectivity for wayfinding and combines it with fast and localized navigation for each agent. At runtime, each agent senses the environment independently and computes a collision-free path based on an extended "Velocity Obstacles" concept. Furthermore, our algorithm ensures that each agent exhibits no oscillatory behaviors. We have tested the performance of our algorithm in several challenging scenarios with a high density of virtual agents. In practice, the algorithm performance scales almost linearly with the number of agents and can run at interactive rates on multi-core processors.

This paper presents empirical results to support the use of vibrotactile cues as a means of improving user performance on a spatial task. In a building-clearing exercise, directional vibrotactile cues were employed to alert subjects to areas of the building that they had not yet cleared, but were currently exposed to. Compared with performing the task without vibrotactile cues, subjects were exposed to uncleared areas a smaller percentage of time, and cleared more of the overall space, when given the added vibrotactile stimulus. The average length of each exposure was also significantly less when vibrotactile cues were present.