Reachable Polyhedral Marching (RPM): An Exact Analysis Tool for Deep-Learned Control Systems

We present a tool for computing exact forward and backward reachable sets of deep neural networks with rectified linear unit (ReLU) activation. We then develop algorithms using this tool to compute invariant sets and regions of attraction (ROAs) for control systems with neural networks in the feedback loop. Our algorithm is unique in that it builds the reachable sets by incrementally enumerating polyhedral regions in the input space, rather than iterating layer-by-layer through the network as in other methods. When performing safety verification, if an unsafe region is found, our algorithm can return this result without completing the full reachability computation, thus giving an anytime property that accelerates safety verification. Furthermore, we introduce a method to accelerate the computation of ROAs in the case that deep learned components are homeomorphisms, which we find is surprisingly common in practice. We demonstrate our tool in several test cases. We compute a ROA for a learned van der Pol oscillator model. We find a control invariant set for a learned torque-controlled pendulum model. We also verify specific safety properties for multiple deep networks related to the ACAS Xu aircraft collision advisory system. Finally, we apply our algorithm to find ROAs for an image-based aircraft runway taxi problem. Algorithm source code: https://github.com/StanfordMSL/Neural-Network-Reach .

Intention Communication and Hypothesis Likelihood in Game-Theoretic Motion Planning

Game-theoretic motion planners are a potent solution for controlling systems of multiple highly interactive robots. Most existing game-theoretic planners unrealistically assume a priori objective function knowledge is available to all agents. To address this, we propose a fault-tolerant receding horizon game-theoretic motion planner that leverages inter-agent communication with intention hypothesis likelihood. Specifically, robots communicate their objective function incorporating their intentions. A discrete Bayesian filter is designed to infer the objectives in real-time based on the discrepancy between observed trajectories and the ones from communicated intentions. In simulation, we consider three safety-critical autonomous driving scenarios of overtaking, lane-merging and intersection crossing, to demonstrate our planner's ability to capitalize on alternative intention hypotheses to generate safe trajectories in the presence of faulty transmissions in the communication network.

NeRF-Loc: Transformer-Based Object Localization Within Neural Radiance Fields

Neural Radiance Fields (NeRFs) have been successfully used for scene representation. Recent works have also developed robotic navigation and manipulation systems using NeRF-based environment representations. As object localization is the foundation for many robotic applications, to further unleash the potential of NeRFs in robotic systems, we study object localization within a NeRF scene. We propose a transformer-based framework NeRF-Loc to extract 3D bounding boxes of objects in NeRF scenes. NeRF-Loc takes a pre-trained NeRF model and camera view as input, and produces labeled 3D bounding boxes of objects as output. Concretely, we design a pair of paralleled transformer encoder branches, namely the coarse stream and the fine stream, to encode both the context and details of target objects. The encoded features are then fused together with attention layers to alleviate ambiguities for accurate object localization. We have compared our method with the conventional transformer-based method and our method achieves better performance. In addition, we also present the first NeRF samples-based object localization benchmark NeRFLocBench.

Learning Deep SDF Maps Online for Robot Navigation and Exploration

We propose an algorithm to (i) learn online a deep signed distance function (SDF) with a LiDAR-equipped robot to represent the 3D environment geometry, and (ii) plan collision-free trajectories given this deep learned map. Our algorithm takes a stream of incoming LiDAR scans and continually optimizes a neural network to represent the SDF of the environment around its current vicinity. When the SDF network quality saturates, we cache a copy of the network, along with a learned confidence metric, and initialize a new SDF network to continue mapping new regions of the environment. We then concatenate all the cached local SDFs through a confidence-weighted scheme to give a global SDF for planning. For planning, we make use of a sequential convex model predictive control (MPC) algorithm. The MPC planner optimizes a dynamically feasible trajectory for the robot while enforcing no collisions with obstacles mapped in the global SDF. We show that our online mapping algorithm produces higher-quality maps than existing methods for online SDF training. In the WeBots simulator, we further showcase the combined mapper and planner running online -- navigating autonomously and without collisions in an unknown environment.

Game-Theoretic Planning for Autonomous Driving among Risk-Aware Human Drivers

We present a novel approach for risk-aware planning with human agents in multi-agent traffic scenarios. Our approach takes into account the wide range of human driver behaviors on the road, from aggressive maneuvers like speeding and overtaking, to conservative traits like driving slowly and conforming to the right-most lane. In our approach, we learn a mapping from a data-driven human driver behavior model called the CMetric to a driver's entropic risk preference. We then use the derived risk preference within a game-theoretic risk-sensitive planner to model risk-aware interactions among human drivers and an autonomous vehicle in various traffic scenarios. We demonstrate our method in a merging scenario, where our results show that the final trajectories obtained from the risk-aware planner generate desirable emergent behaviors. Particularly, our planner recognizes aggressive human drivers and yields to them while maintaining a greater distance from them. In a user study, participants were able to distinguish between aggressive and conservative simulated drivers based on trajectories generated from our risk-sensitive planner. We also observe that aggressive human driving results in more frequent lane-changing in the planner. Finally, we compare the performance of our modified risk-aware planner with existing methods and show that modeling human driver behavior leads to safer navigation.

Self-Supervised Traffic Advisors: Distributed, Multi-view Traffic Prediction for Smart Cities

Connected and Autonomous Vehicles (CAVs) are becoming more widely deployed, but it is unclear how to best deploy smart infrastructure to maximize their capabilities. One key challenge is to ensure CAVs can reliably perceive other agents, especially occluded ones. A further challenge is the desire for smart infrastructure to be autonomous and readily scalable to wide-area deployments, similar to modern traffic lights. The present work proposes the Self-Supervised Traffic Advisor (SSTA), an infrastructure edge device concept that leverages self-supervised video prediction in concert with a communication and co-training framework to enable autonomously predicting traffic throughout a smart city. An SSTA is a statically-mounted camera that overlooks an intersection or area of complex traffic flow that predicts traffic flow as future video frames and learns to communicate with neighboring SSTAs to enable predicting traffic before it appears in the Field of View (FOV). The proposed framework aims at three goals: (1) inter-device communication to enable high-quality predictions, (2) scalability to an arbitrary number of devices, and (3) lifelong online learning to ensure adaptability to changing circumstances. Finally, an SSTA can broadcast its future predicted video frames directly as information for CAVs to run their own post-processing for the purpose of control.

FIG-OP: Exploring Large-Scale Unknown Environments on a Fixed Time Budget

We present a method for autonomous exploration of large-scale unknown environments under mission time constraints. We start by proposing the Frontloaded Information Gain Orienteering Problem (FIG-OP) -- a generalization of the traditional orienteering problem where the assumption of a reliable environmental model no longer holds. The FIG-OP addresses model uncertainty by frontloading expected information gain through the addition of a greedy incentive, effectively expediting the moment in which new area is uncovered. In order to reason across multi-kilometre environments, we solve FIG-OP over an information-efficient world representation, constructed through the aggregation of information from a topological and metric map. Our method was extensively tested and field-hardened across various complex environments, ranging from subway systems to mines. In comparative simulations, we observe that the FIG-OP solution exhibits improved coverage efficiency over solutions generated by greedy and traditional orienteering-based approaches (i.e. severe and minimal model uncertainty assumptions, respectively).

Dojo: A Differentiable Simulator for Robotics

We present a differentiable rigid-body-dynamics simulator for robotics that prioritizes physical accuracy and differentiability: Dojo. The simulator utilizes an expressive maximal-coordinates representation, achieves stable simulation at low sample rates, and conserves energy and momentum by employing a variational integrator. A nonlinear complementarity problem, with nonlinear friction cones, models hard contact and is reliably solved using a custom primal-dual interior-point method. The implicit-function theorem enables efficient differentiation of an intermediate relaxed problem and computes smooth gradients from the contact model. We demonstrate the usefulness of the simulator and its gradients through a number of examples including: simulation, trajectory optimization, reinforcement learning, and system identification.

Maximum-Entropy Multi-Agent Dynamic Games: Forward and Inverse Solutions

In this paper, we study the problem of multiple stochastic agents interacting in a dynamic game scenario with continuous state and action spaces. We define a new notion of stochastic Nash equilibrium for boundedly rational agents, which we call the Entropic Cost Equilibrium (ECE). We show that ECE is a natural extension to multiple agents of Maximum Entropy optimality for single agents. We solve both the "forward" and "inverse" problems for the multi-agent ECE game. For the forward problem, we provide a Riccati algorithm to compute closed-form ECE feedback policies for the agents, which are exact in the Linear-Quadratic-Gaussian case. We give an iterative variant to find locally ECE feedback policies for the nonlinear case. For the inverse problem, we present an algorithm to infer the cost functions of the multiple interacting agents given noisy, boundedly rational input and state trajectory examples from agents acting in an ECE. The effectiveness of our algorithms is demonstrated in a simulated multi-agent collision avoidance scenario, and with data from the INTERACTION traffic dataset. In both cases, we show that, by taking into account the agents' game theoretic interactions using our algorithm, a more accurate model of agents' costs can be learned, compared with standard inverse optimal control methods.

Vision-Only Robot Navigation in a Neural Radiance World

Neural Radiance Fields (NeRFs) have recently emerged as a powerful paradigm for the representation of natural, complex 3D scenes. NeRFs represent continuous volumetric density and RGB values in a neural network, and generate photo-realistic images from unseen camera viewpoints through ray tracing. We propose an algorithm for navigating a robot through a 3D environment represented as a NeRF using only an on-board RGB camera for localization. We assume the NeRF for the scene has been pre-trained offline, and the robot's objective is to navigate through unoccupied space in the NeRF to reach a goal pose. We introduce a trajectory optimization algorithm that avoids collisions with high-density regions in the NeRF based on a discrete time version of differential flatness that is amenable to constraining the robot's full pose and control inputs. We also introduce an optimization based filtering method to estimate 6DoF pose and velocities for the robot in the NeRF given only an onboard RGB camera. We combine the trajectory planner with the pose filter in an online replanning loop to give a vision-based robot navigation pipeline. We present simulation results with a quadrotor robot navigating through a jungle gym environment, the inside of a church, and Stonehenge using only an RGB camera. We also demonstrate an omnidirectional ground robot navigating through the church, requiring it to reorient to fit through the narrow gap. Videos of this work can be found at https://mikh3x4.github.io/nerf-navigation/ .