Mo Chen

Somil Bansal, Mo Chen, Sylvia Herbert et al.

Hamilton-Jacobi (HJ) reachability analysis is an important formal verification method for guaranteeing performance and safety properties of dynamical systems; it has been applied to many small-scale systems in the past decade. Its advantages include compatibility with general nonlinear system dynamics, formal treatment of bounded disturbances, and the availability of well-developed numerical tools. The main challenge is addressing its exponential computational complexity with respect to the number of state variables. In this tutorial, we present an overview of basic HJ reachability theory and provide instructions for using the most recent numerical tools, including an efficient GPU-parallelized implementation of a Level Set Toolbox for computing reachable sets. In addition, we review some of the current work in high-dimensional HJ reachability to show how the dimensionality challenge can be alleviated via various general theoretical and application-specific insights.

Pedram Agand, Allison Kennedy, Trevor Harris et al.

As the importance of eco-friendly transportation increases, providing an efficient approach for marine vessel operation is essential. Methods for status monitoring with consideration to the weather condition and forecasting with the use of in-service data from ships requires accurate and complete models for predicting the energy efficiency of a ship. The models need to effectively process all the operational data in real-time. This paper presents models that can predict fuel consumption using in-service data collected from a passenger ship. Statistical and domain-knowledge methods were used to select the proper input variables for the models. These methods prevent over-fitting, missing data, and multicollinearity while providing practical applicability. Prediction models that were investigated include multiple linear regression (MLR), decision tree approach (DT), an artificial neural network (ANN), and ensemble methods. The best predictive performance was from a model developed using the XGboost technique which is a boosting ensemble approach. \rvv{Our code is available on GitHub at \url{https://github.com/pagand/model_optimze_vessel/tree/OE} for future research.

Pedram Agand, Mohammad Mahdavian, Manolis Savva et al.

In end-to-end autonomous driving, the utilization of existing sensor fusion techniques and navigational control methods for imitation learning proves inadequate in challenging situations that involve numerous dynamic agents. To address this issue, we introduce LeTFuser, a lightweight transformer-based algorithm for fusing multiple RGB-D camera representations. To perform perception and control tasks simultaneously, we utilize multi-task learning. Our model comprises of two modules, the first being the perception module that is responsible for encoding the observation data obtained from the RGB-D cameras. Our approach employs the Convolutional vision Transformer (CvT) \cite{wu2021cvt} to better extract and fuse features from multiple RGB cameras due to local and global feature extraction capability of convolution and transformer modules, respectively. Encoded features combined with static and dynamic environments are later employed by our control module to predict waypoints and vehicular controls (e.g. steering, throttle, and brake). We use two methods to generate the vehicular controls levels. The first method uses a PID algorithm to follow the waypoints on the fly, whereas the second one directly predicts the control policy using the measurement features and environmental state. We evaluate the model and conduct a comparative analysis with recent models on the CARLA simulator using various scenarios, ranging from normal to adversarial conditions, to simulate real-world scenarios. Our method demonstrated better or comparable results with respect to our baselines in term of driving abilities. The code is available at \url{https://github.com/pagand/e2etransfuser/tree/cvpr-w} to facilitate future studies.

Mo Chen, Jennifer C. Shih, Claire J. Tomlin

Multi-agent differential games are important and useful tools for analyzing many practical problems. With the recent surge of interest in using UAVs for civil purposes, the importance and urgency of developing tractable multi-agent analysis techniques that provide safety and performance guarantees is at an all-time high. Hamilton-Jacobi (HJ) reachability has successfully provided safety guarantees to small-scale systems and is flexible in terms of system dynamics. However, the exponential complexity scaling of HJ reachability prevents its direct application to large scale problems when the number of vehicles is greater than two. In this paper, we overcome the scalability limitations of HJ reachability by using a mixed integer program that exploits the properties of HJ solutions to provide higher-level control logic. Our proposed method provides safety guarantee for three-vehicle systems -- a previously intractable task for HJ reachability -- without incurring significant additional computation cost. Furthermore, our method is scalable beyond three vehicles and performs significantly better by several metrics than an extension of pairwise collision avoidance to multi-vehicle collision avoidance. We demonstrate our proposed method in simulations.

Mo Chen, Qie Hu, Casey Mackin et al.

Recently, there has been immense interest in using unmanned aerial vehicles (UAVs) for civilian operations such as package delivery, firefighting, and fast disaster response. As a result, UAV traffic management systems are needed to support potentially thousands of UAVs flying simultaneously in the airspace, in order to ensure their liveness and safety requirements are met. Hamilton-Jacobi (HJ) reachability is a powerful framework for providing conditions under which these requirements can be met, and for synthesizing the optimal controller for meeting them. However, due to the curse of dimensionality, HJ reachability is only tractable for a small number of vehicles if their set of maneuvers is unrestricted. In this paper, we define a platoon to be a group of UAVs in a single-file formation. We model each vehicle as a hybrid system with modes corresponding to its role in the platoon, and specify the set of allowed maneuvers in each mode to make the analysis tractable. We propose several liveness controllers based on HJ reachability, and wrap a safety controller, also based on HJ reachability, around the liveness controllers. For a single altitude range, our approach guarantees safety for one safety breach; in the unlikely event of multiple safety breaches, safety can be guaranteed over multiple altitude ranges. We demonstrate the satisfaction of liveness and safety requirements through simulations of three common scenarios.

Mo Chen, Somil Bansal, Ken Tanabe et al.

Provably safe and scalable multi-vehicle path planning is an important and urgent problem due to the expected increase of automation in civilian airspace in the near future. Hamilton-Jacobi (HJ) reachability is an ideal tool for analyzing such safety-critical systems and has been successfully applied to several small-scale problems. However, a direct application of HJ reachability to large scale systems is often intractable because of its exponentially-scaling computation complexity with respect to system dimension, also known as the "curse of dimensionality". To overcome this problem, the sequential path planning (SPP) method, which assigns strict priorities to vehicles, was previously proposed; SPP allows multi-vehicle path planning to be done with a linearly-scaling computation complexity. In this work, we demonstrate the potential of SPP algorithm for large-scale systems. In particular, we simulate large-scale multi-vehicle systems in two different urban environments, a city environment and a multi-city environment, and use the SPP algorithm for trajectory planning. SPP is able to efficiently design collision-free trajectories in both environments despite the presence of disturbances in vehicles' dynamics. To ensure a safe transition of vehicles to their destinations, our method automatically allocates space-time reservations to vehicles while accounting for the magnitude of disturbances such as wind in a provably safe way. Our simulation results show an intuitive multi-lane structure in airspace, where the number of lanes and the distance between the lanes depend on the size of disturbances and other problem parameters.

Payam Nikdel, Mohammad Mahdavian, Mo Chen

Human motion prediction is a fundamental part of many human-robot applications. Despite the recent progress in human motion prediction, most studies simplify the problem by predicting the human motion relative to a fixed joint and/or only limit their model to predict one possible future motion. While due to the complex nature of human motion, a single output cannot reflect all the possible actions one can do. Also, for any robotics application, we need the full human motion including the user trajectory not a 3d pose relative to the hip joint. In this paper, we try to address these two issues by proposing a transformer-based generative model for forecasting multiple diverse human motions. Our model generates \textit{N} future possible motion by querying a history of human motion. Our model first predicts the pose of the body relative to the hip joint. Then the \textit{Hip Prediction Module} predicts the trajectory of the hip movement for each predicted pose frame. To emphasize on the diverse future motions we introduce a similarity loss that penalizes the pairwise sample distance. We show that our system outperforms the state-of-the-art in human motion prediction while it can predict diverse multi-motion future trajectories with hip movements

Somil Bansal, Mo Chen, Claire J. Tomlin

Provably safe and scalable multi-vehicle trajectory planning is an important and urgent problem. Hamilton-Jacobi (HJ) reachability is an ideal tool for analyzing such safety-critical systems and has been successfully applied to several small-scale problems. However, a direct application of HJ reachability to multi-vehicle trajectory planning is often intractable due to the "curse of dimensionality." To overcome this problem, the sequential trajectory planning (STP) method, which assigns strict priorities to vehicles, was proposed, STP allows multi-vehicle trajectory planning to be done with a linearly-scaling computation complexity. However, if a vehicle not in the set of STP vehicles enters the system, or even worse, if this vehicle is an adversarial intruder, the previous formulation requires the entire system to perform replanning, an intractable task for large-scale systems. In this paper, we make STP more practical by providing a new algorithm where replanning is only needed only for a fixed number of vehicles, irrespective of the total number of STP vehicles. Moreover, this number is a design parameter, which can be chosen based on the computational resources available during run time. We demonstrate this algorithm in a representative simulation of an urban airspace environment.

Pedram Agand, Mo Chen, Hamid D. Taghirad

Although the Bayesian paradigm offers a formal framework for estimating the entire probability distribution over uncertain parameters, its online implementation can be challenging due to high computational costs. We suggest the Adaptive Recursive Markov Chain Monte Carlo (ARMCMC) method, which eliminates the shortcomings of conventional online techniques while computing the entire probability density function of model parameters. The limitations to Gaussian noise, the application to only linear in the parameters (LIP) systems, and the persistent excitation (PE) needs are some of these drawbacks. In ARMCMC, a temporal forgetting factor (TFF)-based variable jump distribution is proposed. The forgetting factor can be presented adaptively using the TFF in many dynamical systems as an alternative to a constant hyperparameter. By offering a trade-off between exploitation and exploration, the specific jump distribution has been optimised towards hybrid/multi-modal systems that permit inferences among modes. These trade-off are adjusted based on parameter evolution rate. We demonstrate that ARMCMC requires fewer samples than conventional MCMC methods to achieve the same precision and reliability. We demonstrate our approach using parameter estimation in a soft bending actuator and the Hunt-Crossley dynamic model, two challenging hybrid/multi-modal benchmarks. Additionally, we compare our method with recursive least squares and the particle filter, and show that our technique has significantly more accurate point estimates as well as a decrease in tracking error of the value of interest.

Zhewen Zheng, Wenjing Cao, Hongkang Yu et al.

Parameter tuning in real-world experiments is constrained by the limited evaluation budget available on hardware. The path-following controller studied in this paper reflects a typical situation in nonlinear geometric controller, where multiple gains influence the dynamics through coupled nonlinear terms. Such interdependence makes manual tuning inefficient and unlikely to yield satisfactory performance within a practical number of trials. To address this challenge, we propose a Bayesian optimization (BO) framework that treats the closed-loop system as a black box and selects controller gains using a Gaussian-process surrogate. BO offers model-free exploration, quantified uncertainty, and data-efficient search, making it well suited for tuning tasks where each evaluation is costly. The framework is implemented on Honda's AI-Formula three-wheeled robot and assessed through repeated full-lap experiments on a fixed test track. The results show that BO improves controller performance within 32 trials, including 15 warm-start initial evaluations, indicating that it can efficiently locate high-performing regions of the parameter space under real-world conditions. These findings demonstrate that BO provides a practical, reliable, and data-efficient tuning approach for nonlinear path-following controllers on real robotic platforms.

Saba Akhyani, Mehryar Abbasi Boroujeni, Mo Chen et al.

Robots and artificial agents that interact with humans should be able to do so without bias and inequity, but facial perception systems have notoriously been found to work more poorly for certain groups of people than others. In our work, we aim to build a system that can perceive humans in a more transparent and inclusive manner. Specifically, we focus on dynamic expressions on the human face, which are difficult to collect for a broad set of people due to privacy concerns and the fact that faces are inherently identifiable. Furthermore, datasets collected from the Internet are not necessarily representative of the general population. We address this problem by offering a Sim2Real approach in which we use a suite of 3D simulated human models that enables us to create an auditable synthetic dataset covering 1) underrepresented facial expressions, outside of the six basic emotions, such as confusion; 2) ethnic or gender minority groups; and 3) a wide range of viewing angles that a robot may encounter a human in the real world. By augmenting a small dynamic emotional expression dataset containing 123 samples with a synthetic dataset containing 4536 samples, we achieved an improvement in accuracy of 15% on our own dataset and 11% on an external benchmark dataset, compared to the performance of the same model architecture without synthetic training data. We also show that this additional step improves accuracy specifically for racial minorities when the architecture's feature extraction weights are trained from scratch.

Mohammad Mahdavian, Payam Nikdel, Mahdi TaherAhmadi et al.

In this paper, we develop a neural network model to predict future human motion from an observed human motion history. We propose a non-autoregressive transformer architecture to leverage its parallel nature for easier training and fast, accurate predictions at test time. The proposed architecture divides human motion prediction into two parts: 1) the human trajectory, which is the hip joint 3D position over time and 2) the human pose which is the all other joints 3D positions over time with respect to a fixed hip joint. We propose to make the two predictions simultaneously, as the shared representation can improve the model performance. Therefore, the model consists of two sets of encoders and decoders. First, a multi-head attention module applied to encoder outputs improves human trajectory. Second, another multi-head self-attention module applied to encoder outputs concatenated with decoder outputs facilitates learning of temporal dependencies. Our model is well-suited for robotic applications in terms of test accuracy and speed, and compares favorably with respect to state-of-the-art methods. We demonstrate the real-world applicability of our work via the Robot Follow-Ahead task, a challenging yet practical case study for our proposed model.

Mohammad Mahdavian, KangKang Yin, Mo Chen

We propose a Visual Teach and Repeat (VTR) algorithm using semantic landmarks extracted from environmental objects for ground robots with fixed mount monocular cameras. The proposed algorithm is robust to changes in the starting pose of the camera/robot, where a pose is defined as the planar position plus the orientation around the vertical axis. VTR consists of a teach phase in which a robot moves in a prescribed path, and a repeat phase in which the robot tries to repeat the same path starting from the same or a different pose. Most available VTR algorithms are pose dependent and cannot perform well in the repeat phase when starting from an initial pose far from that of the teach phase. To achieve more robust pose independency, the key is to generate a 3D semantic map of the environment containing the camera trajectory and the positions of surrounding objects during the teach phase. For specific implementation, we use ORB-SLAM to collect the camera poses and the 3D point clouds of the environment, and YOLOv3 to detect objects in the environment. We then combine the two outputs to build the semantic map. In the repeat phase, we relocalize the robot based on the detected objects and the stored semantic map. The robot is then able to move toward the teach path, and repeat it in both forward and backward directions. We have tested the proposed algorithm in different scenarios and compared it with two most relevant recent studies. Also, we compared our algorithm with two image-based relocalization methods. One is purely based on ORB-SLAM and the other combines Superglue and RANSAC. The results show that our algorithm is much more robust with respect to pose variations as well as environmental alterations. Our code and data are available at the following Github page: https://github.com/mmahdavian/semantic_visual_teach_repeat.

Mohammad Mahdavian, Mo Chen, Yu Zhang

In this paper, we propose a tracking-based HD mapping algorithm for top-down road images, referred to as tile images. While HD maps traditionally rely on perspective camera images, our approach shows that tile images can also be effectively utilized, offering valuable contributions to this research area as it can be start of a new path in HD mapping algorithms. We modified the BEVFormer layers to generate BEV masks from tile images, which are then used by the model to generate divider and boundary lines. Our model was tested with both color and intensity images, and we present quantitative and qualitative results to demonstrate its performance.

Salar Asayesh, Mo Chen, Mehran Mehrandezh et al.

Multi-agent collision-free trajectory planning and control subject to different goal requirements and system dynamics has been extensively studied, and is gaining recent attention in the realm of machine and reinforcement learning. However, in particular when using a large number of agents, constructing a least-restrictive collision avoidance policy is of utmost importance for both classical and learning-based methods. In this paper, we propose a Least-Restrictive Collision Avoidance Module (LR-CAM) that evaluates the safety of multi-agent systems and takes over control only when needed to prevent collisions. The LR-CAM is a single policy that can be wrapped around policies of all agents in a multi-agent system. It allows each agent to pursue any objective as long as it is safe to do so. The benefit of the proposed least-restrictive policy is to only interrupt and overrule the default controller in case of an upcoming inevitable danger. We use a Long Short-Term Memory (LSTM) based Variational Auto-Encoder (VAE) to enable the LR-CAM to account for a varying number of agents in the environment. Moreover, we propose an off-policy meta-reinforcement learning framework with a novel reward function based on a Hamilton-Jacobi value function to train the LR-CAM. The proposed method is fully meta-trained through a ROS based simulation and tested on real multi-agent system. Our results show that LR-CAM outperforms the classical least-restrictive baseline by 30 percent. In addition, we show that even if a subset of agents in a multi-agent system use LR-CAM, the success rate of all agents will increase significantly.

Mo Chen, Sylvia L. Herbert, Haimin Hu et al.

Real-time, guaranteed safe trajectory planning is vital for navigation in unknown environments. However, real-time navigation algorithms typically sacrifice robustness for computation speed. Alternatively, provably safe trajectory planning tends to be too computationally intensive for real-time replanning. We propose FaSTrack, Fast and Safe Tracking, a framework that achieves both real-time replanning and guaranteed safety. In this framework, real-time computation is achieved by allowing any trajectory planner to use a simplified \textit{planning model} of the system. The plan is tracked by the system, represented by a more realistic, higher-dimensional \textit{tracking model}. We precompute the tracking error bound (TEB) due to mismatch between the two models and due to external disturbances. We also obtain the corresponding tracking controller used to stay within the TEB. The precomputation does not require prior knowledge of the environment. We demonstrate FaSTrack using Hamilton-Jacobi reachability for precomputation and three different real-time trajectory planners with three different tracking-planning model pairs.

Minh Bui, Michael Lu, Reza Hojabr et al.

Hamilton-Jacobi reachability analysis is a powerful technique used to verify the safety of autonomous systems. This method is very good at handling non-linear system dynamics with disturbances and flexible set representations. A drawback to this approach is that it suffers from the curse of dimensionality, which prevents real-time deployment on safety-critical systems. In this paper, we show that a customized hardware design on a Field Programmable Gate Array (FPGA) could accelerate 4D grid-based Hamilton-Jacobi (HJ) reachability analysis up to 16 times compared to an optimized implementation and 142 times compared to MATLAB ToolboxLS on a 16-thread CPU. Our design can overcome the complex data access pattern while taking advantage of the parallel nature of the HJ PDE computation. Because of this, we are able to achieve real-time formal verification with a 4D car model by re-solving the HJ PDE at a frequency of 5Hz on the FPGA as the environment changes. The latency of our computation is deterministic, which is crucial for safetycritical systems. Our approach presented here can be applied to different systems dynamics, and moreover, potentially leveraged for higher dimensions systems. We also demonstrate obstacle avoidance with a robot car in a changing environment.

Karen Leung, Edward Schmerling, Mengxuan Zhang et al.

Action anticipation, intent prediction, and proactive behavior are all desirable characteristics for autonomous driving policies in interactive scenarios. Paramount, however, is ensuring safety on the road -- a key challenge in doing so is accounting for uncertainty in human driver actions without unduly impacting planner performance. This paper introduces a minimally-interventional safety controller operating within an autonomous vehicle control stack with the role of ensuring collision-free interaction with an externally controlled (e.g., human-driven) counterpart while respecting static obstacles such as a road boundary wall. We leverage reachability analysis to construct a real-time (100Hz) controller that serves the dual role of (i) tracking an input trajectory from a higher-level planning algorithm using model predictive control, and (ii) assuring safety by maintaining the availability of a collision-free escape maneuver as a persistent constraint regardless of whatever future actions the other car takes. A full-scale steer-by-wire platform is used to conduct traffic weaving experiments wherein two cars, initially side-by-side, must swap lanes in a limited amount of time and distance, emulating cars merging onto/off of a highway. We demonstrate that, with our control stack, the autonomous vehicle is able to avoid collision even when the other car defies the planner's expectations and takes dangerous actions, either carelessly or with the intent to collide, and otherwise deviates minimally from the planned trajectory to the extent required to maintain safety.

Anjian Li, Liting Sun, Wei Zhan et al.

Safety is an important topic in autonomous driving since any collision may cause serious injury to people and damage to property. Hamilton-Jacobi (HJ) Reachability is a formal method that verifies safety in multi-agent interaction and provides a safety controller for collision avoidance. However, due to the worst-case assumption on the cars future behaviours, reachability might result in too much conservatism such that the normal operation of the vehicle is badly hindered. In this paper, we leverage the power of trajectory prediction and propose a prediction-based reachability framework to compute safety controllers. Instead of always assuming the worst case, we cluster the car's behaviors into multiple driving modes, e.g. left turn or right turn. Under each mode, a reachability-based safety controller is designed based on a less conservative action set. For online implementation, we first utilize the trajectory prediction and our proposed mode classifier to predict the possible modes, and then deploy the corresponding safety controller. Through simulations in a T-intersection and an 8-way roundabout, we demonstrate that our prediction-based reachability method largely avoids collision between two interacting cars and reduces the conservatism that the safety controller brings to the car's original operation.

Payam Nikdel, Richard Vaughan, Mo Chen

This paper investigates a hybrid solution which combines deep reinforcement learning (RL) and classical trajectory planning for the following in front application. Here, an autonomous robot aims to stay ahead of a person as the person freely walks around. Following in front is a challenging problem as the user's intended trajectory is unknown and needs to be estimated, explicitly or implicitly, by the robot. In addition, the robot needs to find a feasible way to safely navigate ahead of human trajectory. Our deep RL module implicitly estimates human trajectory and produces short-term navigational goals to guide the robot. These goals are used by a trajectory planner to smoothly navigate the robot to the short-term goals, and eventually in front of the user. We employ curriculum learning in the deep RL module to efficiently achieve a high return. Our system outperforms the state-of-the-art in following ahead and is more reliable compared to end-to-end alternatives in both the simulation and real world experiments. In contrast to a pure deep RL approach, we demonstrate zero-shot transfer of the trained policy from simulation to the real world.

Xubo Lyu, Site Li, Seth Siriya et al.

In this paper, a novel optimal control-based baseline function is presented for the policy gradient method in deep reinforcement learning (RL). The baseline is obtained by computing the value function of an optimal control problem, which is formed to be closely associated with the RL task. In contrast to the traditional baseline aimed at variance reduction of policy gradient estimates, our work utilizes the optimal control value function to introduce a novel aspect to the role of baseline -- providing guided exploration during policy learning. This aspect is less discussed in prior works. We validate our baseline on robot learning tasks, showing its effectiveness in guided exploration, particularly in sparse reward environments.

Zhitian Zhang, Jimin Rhim, Taher Ahmadi et al.

This article describes a dataset collected in a set of experiments that involves human participants and a robot. The set of experiments was conducted in the computing science robotics lab in Simon Fraser University, Burnaby, BC, Canada, and its aim is to gather data containing common gestures, movements, and other behaviours that may indicate humans' navigational intent relevant for autonomous robot navigation. The experiment simulates a shopping scenario where human participants come in to pick up items from his/her shopping list and interact with a Pepper robot that is programmed to help the human participant. We collected visual data and motion capture data from 108 human participants. The visual data contains live recordings of the experiments and the motion capture data contains the position and orientation of the human participants in world coordinates. This dataset could be valuable for researchers in the robotics, machine learning and computer vision community.

Anjian Li, Somil Bansal, Georgios Giovanis et al.

In Bansal et al. (2019), a novel visual navigation framework that combines learning-based and model-based approaches has been proposed. Specifically, a Convolutional Neural Network (CNN) predicts a waypoint that is used by the dynamics model for planning and tracking a trajectory to the waypoint. However, the CNN inevitably makes prediction errors which often lead to collisions in cluttered and tight spaces. In this paper, we present a novel Hamilton-Jacobi (HJ) reachability-based method to generate supervision for the CNN for waypoint prediction in an unseen environment. By modeling CNN prediction error as "disturbances" in robot's dynamics, our generated waypoints are robust to these disturbances, and consequently to the prediction errors. Moreover, using globally optimal HJ reachability analysis leads to predicting waypoints that are time-efficient and avoid greedy behavior. Through simulations and hardware experiments, we demonstrate the advantages of the proposed approach on navigating through cluttered, narrow indoor environments.

Xubo Lyu, Mo Chen

Model-free reinforcement learning (RL) is a powerful approach for learning control policies directly from high-dimensional state and observation. However, it tends to be data-inefficient, which is especially costly in robotic learning tasks. On the other hand, optimal control does not require data if the system model is known, but cannot scale to models with high-dimensional states and observations. To exploit benefits of both model-free RL and optimal control, we propose time-to-reach-based (TTR-based) reward shaping, an optimal control-inspired technique to alleviate data inefficiency while retaining advantages of model-free RL. This is achieved by summarizing key system model information using a TTR function to greatly speed up the RL process, as shown in our simulation results. The TTR function is defined as the minimum time required to move from any state to the goal under assumed system dynamics constraints. Since the TTR function is computationally intractable for systems with high-dimensional states, we compute it for approximate, lower-dimensional system models that still captures key dynamic behaviors. Our approach can be flexibly and easily incorporated into any model-free RL algorithm without altering the original algorithm structure, and is compatible with any other techniques that may facilitate the RL process. We evaluate our approach on two representative robotic learning tasks and three well-known model-free RL algorithms, and show significant improvements in data efficiency and performance.

Karen Leung, Edward Schmerling, Mo Chen et al.

Action anticipation, intent prediction, and proactive behavior are all desirable characteristics for autonomous driving policies in interactive scenarios. Paramount, however, is ensuring safety on the road --- a key challenge in doing so is accounting for uncertainty in human driver actions without unduly impacting planner performance. This paper introduces a minimally-interventional safety controller operating within an autonomous vehicle control stack with the role of ensuring collision-free interaction with an externally controlled (e.g., human-driven) counterpart. We leverage reachability analysis to construct a real-time (100Hz) controller that serves the dual role of (1) tracking an input trajectory from a higher-level planning algorithm using model predictive control, and (2) assuring safety through maintaining the availability of a collision-free escape maneuver as a persistent constraint regardless of whatever future actions the other car takes. A full-scale steer-by-wire platform is used to conduct traffic weaving experiments wherein the two cars, initially side-by-side, must swap lanes in a limited amount of time and distance, emulating cars merging onto/off of a highway. We demonstrate that, with our control stack, the autonomous vehicle is able to avoid collision even when the other car defies the planner's expectations and takes dangerous actions, either carelessly or with the intent to collide, and otherwise deviates minimally from the planned trajectory to the extent required to maintain safety.

Sumeet Singh, Mo Chen, Sylvia L. Herbert et al.

In the pursuit of real-time motion planning, a commonly adopted practice is to compute a trajectory by running a planning algorithm on a simplified, low-dimensional dynamical model, and then employ a feedback tracking controller that tracks such a trajectory by accounting for the full, high-dimensional system dynamics. While this strategy of planning with model mismatch generally yields fast computation times, there are no guarantees of dynamic feasibility, which hampers application to safety-critical systems. Building upon recent work that addressed this problem through the lens of Hamilton-Jacobi (HJ) reachability, we devise an algorithmic framework whereby one computes, offline, for a pair of "planner" (i.e., low-dimensional) and "tracking" (i.e., high-dimensional) models, a feedback tracking controller and associated tracking bound. This bound is then used as a safety margin when generating motion plans via the low-dimensional model. Specifically, we harness the computational tool of sum-of-squares (SOS) programming to design a bilinear optimization algorithm for the computation of the feedback tracking controller and associated tracking bound. The algorithm is demonstrated via numerical experiments, with an emphasis on investigating the trade-off between the increased computational scalability afforded by SOS and its intrinsic conservativeness. Collectively, our results enable scaling the appealing strategy of planning with model mismatch to systems that are beyond the reach of HJ analysis, while maintaining safety guarantees.

Benoit Landry, Mo Chen, Scott Hemley et al.

Reach-avoid problems involve driving a system to a set of desirable configurations while keeping it away from undesirable ones. Providing mathematical guarantees for such scenarios is challenging but have numerous potential practical applications. Due to the challenges, analysis of reach-avoid problems involves making trade-offs between generality of system dynamics, generality of problem setups, optimality of solutions, and computational complexity. In this paper, we combine sum-of-squares optimization and dynamic programming to address the reach-avoid problem, and provide a conservative solution that maintains reaching and avoidance guarantees. Our method is applicable to polynomial system dynamics and to general problem setups, and is more computationally scalable than previous related methods. Through a numerical example involving two single integrators, we validate our proposed theory and compare our method to Hamilton-Jacobi reachability. Having validated our theory, we demonstrate the computational scalability of our method by computing the reach-avoid set of a system involving two kinematic cars.

Boris Ivanovic, James Harrison, Apoorva Sharma et al.

Model-free Reinforcement Learning (RL) offers an attractive approach to learn control policies for high-dimensional systems, but its relatively poor sample complexity often forces training in simulated environments. Even in simulation, goal-directed tasks whose natural reward function is sparse remain intractable for state-of-the-art model-free algorithms for continuous control. The bottleneck in these tasks is the prohibitive amount of exploration required to obtain a learning signal from the initial state of the system. In this work, we leverage physical priors in the form of an approximate system dynamics model to design a curriculum scheme for a model-free policy optimization algorithm. Our Backward Reachability Curriculum (BaRC) begins policy training from states that require a small number of actions to accomplish the task, and expands the initial state distribution backwards in a dynamically-consistent manner once the policy optimization algorithm demonstrates sufficient performance. BaRC is general, in that it can accelerate training of any model-free RL algorithm on a broad class of goal-directed continuous control MDPs. Its curriculum strategy is physically intuitive, easy-to-tune, and allows incorporating physical priors to accelerate training without hindering the performance, flexibility, and applicability of the model-free RL algorithm. We evaluate our approach on two representative dynamic robotic learning problems and find substantial performance improvement relative to previous curriculum generation techniques and naive exploration strategies.

Somil Bansal, Mo Chen, Jaime F. Fisac et al.

Multi-UAV systems are safety-critical, and guarantees must be made to ensure no unsafe configurations occur. Hamilton-Jacobi (HJ) reachability is ideal for analyzing such safety-critical systems; however, its direct application is limited to small-scale systems of no more than two vehicles due to an exponentially-scaling computational complexity. Previously, the sequential path planning (SPP) method, which assigns strict priorities to vehicles, was proposed; SPP allows multi-vehicle path planning to be done with a linearly-scaling computational complexity. However, the previous formulation assumed that there are no disturbances, and that every vehicle has perfect knowledge of higher-priority vehicles' positions. In this paper, we make SPP more practical by providing three different methods to account for disturbances in dynamics and imperfect knowledge of higher-priority vehicles' states. Each method has different assumptions about information sharing. We demonstrate our proposed methods in simulations.

Frank Jiang, Glen Chou, Mo Chen et al.

To sidestep the curse of dimensionality when computing solutions to Hamilton-Jacobi-Bellman partial differential equations (HJB PDE), we propose an algorithm that leverages a neural network to approximate the value function. We show that our final approximation of the value function generates near optimal controls which are guaranteed to successfully drive the system to a target state. Our framework is not dependent on state space discretization, leading to a significant reduction in computation time and space complexity in comparison with dynamic programming-based approaches. Using this grid-free approach also enables us to plan over longer time horizons with relatively little additional computation overhead. Unlike many previous neural network HJB PDE approximating formulations, our approximation is strictly conservative and hence any trajectories we generate will be strictly feasible. For demonstration, we specialize our new general framework to the Dubins car model and discuss how the framework can be applied to other models with higher-dimensional state spaces.