Reactive Navigation under Non-Parametric Uncertainty through Hilbert Space Embedding of Probabilistic Velocity Obstacles

The probabilistic velocity obstacle (PVO) extends the concept of velocity obstacle (VO) to work in uncertain dynamic environments. In this paper, we show how a robust model predictive control (MPC) with PVO constraints under non-parametric uncertainty can be made computationally tractable. At the core of our formulation is a novel yet simple interpretation of our robust MPC as a problem of matching the distribution of PVO with a certain desired distribution. To this end, we propose two methods. Our first baseline method is based on approximating the distribution of PVO with a Gaussian Mixture Model (GMM) and subsequently performing distribution matching using Kullback Leibler (KL) divergence metric. Our second formulation is based on the possibility of representing arbitrary distributions as functions in Reproducing Kernel Hilbert Space (RKHS). We use this foundation to interpret our robust MPC as a problem of minimizing the distance between the desired distribution and the distribution of the PVO in the RKHS. Both the RKHS and GMM based formulation can work with any uncertainty distribution and thus allowing us to relax the prevalent Gaussian assumption in the existing works. We validate our formulation by taking an example of 2D navigation of quadrotors with a realistic noise model for perception and ego-motion uncertainty. In particular, we present a systematic comparison between the GMM and the RKHS approach and show that while both approaches can produce safe trajectories, the former is highly conservative and leads to poor tracking and control costs. Furthermore, RKHS based approach gives better computational times that are up to one order of magnitude lesser than the computation time of the GMM based approach.

A Hierarchical Network for Diverse Trajectory Proposals

Autonomous explorative robots frequently encounter scenarios where multiple future trajectories can be pursued. Often these are cases with multiple paths around an obstacle or trajectory options towards various frontiers. Humans in such situations can inherently perceive and reason about the surrounding environment to identify several possibilities of either manoeuvring around the obstacles or moving towards various frontiers. In this work, we propose a 2 stage Convolutional Neural Network architecture which mimics such an ability to map the perceived surroundings to multiple trajectories that a robot can choose to traverse. The first stage is a Trajectory Proposal Network which suggests diverse regions in the environment which can be occupied in the future. The second stage is a Trajectory Sampling network which provides a finegrained trajectory over the regions proposed by Trajectory Proposal Network. We evaluate our framework in diverse and complicated real life settings. For the outdoor case, we use the KITTI dataset and our own outdoor driving dataset. In the indoor setting, we use an autonomous drone to navigate various scenarios and also a ground robot which can explore the environment using the trajectories proposed by our framework. Our experiments suggest that the framework is able to develop a semantic understanding of the obstacles, open regions and identify diverse trajectories that a robot can traverse. Our comparisons portray the performance gain of the proposed architecture over a diverse set of methods against which it is compared.

IVO: Inverse Velocity Obstacles for Real Time Navigation

In this paper, we present "IVO: Inverse Velocity Obstacles" an ego-centric framework that improves the real time implementation. The proposed method stems from the concept of velocity obstacle and can be applied for both single agent and multi-agent system. It focuses on computing collision free maneuvers without any knowledge or assumption on the pose and the velocity of the robot. This is primarily achieved by reformulating the velocity obstacle to adapt to an ego-centric framework. This is a significant step towards improving real time implementations of collision avoidance in dynamic environments as there is no dependency on state estimation techniques to infer the robot pose and velocity. We evaluate IVO for both single agent and multi-agent in different scenarios and show it's efficacy over the existing formulations. We also show the real time scalability of the proposed methodology.

Learning to Prevent Monocular SLAM Failure using Reinforcement Learning

Monocular SLAM refers to using a single camera to estimate robot ego motion while building a map of the environment. While Monocular SLAM is a well studied problem, automating Monocular SLAM by integrating it with trajectory planning frameworks is particularly challenging. This paper presents a novel formulation based on Reinforcement Learning (RL) that generates fail safe trajectories wherein the SLAM generated outputs do not deviate largely from their true values. Quintessentially, the RL framework successfully learns the otherwise complex relation between perceptual inputs and motor actions and uses this knowledge to generate trajectories that do not cause failure of SLAM. We show systematically in simulations how the quality of the SLAM dramatically improves when trajectories are computed using RL. Our method scales effectively across Monocular SLAM frameworks in both simulation and in real world experiments with a mobile robot.

Solving Chance Constrained Optimization under Non-Parametric Uncertainty Through Hilbert Space Embedding

In this paper, we present an efficient algorithm for solving a class of chance constrained optimization under non-parametric uncertainty. Our algorithm is built on the possibility of representing arbitrary distributions as functions in Reproducing Kernel Hilbert Space (RKHS). We use this foundation to formulate chance constrained optimization as one of minimizing the distance between a desired distribution and the distribution of the constraint functions in the RKHS. We provide a systematic way of constructing the desired distribution based on a notion of scenario approximation. Furthermore, we use the kernel trick to show that the computational complexity of our reformulated optimization problem is comparable to solving a deterministic variant of the chance-constrained optimization. We validate our formulation on two important robotic/control applications: (i) reactive collision avoidance of mobile robots in uncertain dynamic environments and (ii) inverse dynamics based path tracking of manipulators under perception uncertainty. In both these applications, the underlying chance constraints are defined over highly non-linear and non-convex functions of the uncertain parameters and possibly also decision variables. We also benchmark our formulation with the existing approaches in terms of sample complexity and the achieved optimal cost highlighting significant improvements in both these metrics.

Parameter Sharing Reinforcement Learning Architecture for Multi Agent Driving Behaviors

Multi-agent learning provides a potential framework for learning and simulating traffic behaviors. This paper proposes a novel architecture to learn multiple driving behaviors in a traffic scenario. The proposed architecture can learn multiple behaviors independently as well as simultaneously. We take advantage of the homogeneity of agents and learn in a parameter sharing paradigm. To further speed up the training process asynchronous updates are employed into the architecture. While learning different behaviors simultaneously, the given framework was also able to learn cooperation between the agents, without any explicit communication. We applied this framework to learn two important behaviors in driving: 1) Lane-Keeping and 2) Over-Taking. Results indicate faster convergence and learning of a more generic behavior, that is scalable to any number of agents. When compared the results with existing approaches, our results indicate equal and even better performance in some cases.

Model Predictive Control for Autonomous Driving considering Actuator Dynamics

In this paper, we propose a new model predictive control (MPC) formulation for autonomous driving. The novelty of our MPC stems from the following results. Firstly, we adopt an alternating minimization approach wherein linear velocities and angular accelerations are alternately optimized. We show that in contrast to the joint optimization, the alternating minimization exploits the structure of the problem better, which in turn translates to reduction in computation time. Secondly, our MPC explicitly incorporates the time dependent non-linear actuator dynamics that captures the transient response of the vehicle for a given commanded velocity. This added complexity improves the predictive component of MPC resulting in improved margin of inter-vehicle distance during maneuvers like overtaking, lane-change, etc. Although, past works have also incorporated actuator dynamics within MPC, there has been very few attempts towards coupling actuator dynamics to collision avoidance constraints through the non-holonomic motion model of the vehicle and analyzing the resulting behavior. We use a high fidelity simulator to benchmark our actuator dynamics augmented MPC with other related approaches in terms of metrics like inter-vehicle distance, trajectory smoothness, and velocity overshoot.

Beyond Pixels: Leveraging Geometry and Shape Cues for Online Multi-Object Tracking

This paper introduces geometry and object shape and pose costs for multi-object tracking in urban driving scenarios. Using images from a monocular camera alone, we devise pairwise costs for object tracks, based on several 3D cues such as object pose, shape, and motion. The proposed costs are agnostic to the data association method and can be incorporated into any optimization framework to output the pairwise data associations. These costs are easy to implement, can be computed in real-time, and complement each other to account for possible errors in a tracking-by-detection framework. We perform an extensive analysis of the designed costs and empirically demonstrate consistent improvement over the state-of-the-art under varying conditions that employ a range of object detectors, exhibit a variety in camera and object motions, and, more importantly, are not reliant on the choice of the association framework. We also show that, by using the simplest of associations frameworks (two-frame Hungarian assignment), we surpass the state-of-the-art in multi-object-tracking on road scenes. More qualitative and quantitative results can be found at the following URL: https://junaidcs032.github.io/Geometry_ObjectShape_MOT/.

Gradient Aware - Shrinking Domain based Control Design for Reactive Planning Frameworks used in Autonomous Vehicles

In this paper, we present a novel control law for longitudinal speed control of autonomous vehicles. The key contributions of the proposed work include the design of a control law that reactively integrates the longitudinal surface gradient of road into its operation. In contrast to the existing works, we found that integrating the path gradient into the control framework improves the speed tracking efficacy. Since the control law is implemented over a shrinking domain scheme, it minimizes the integrated error by recomputing the control inputs at every discretized step and consequently provides less reaction time. This makes our control law suitable for motion planning frameworks that are operating at high frequencies. Furthermore, our work is implemented using a generalized vehicle model and can be easily extended to other classes of vehicles. The performance of gradient aware-shrinking domain based controller is implemented and tested on a stock electric vehicle on which a number of sensors are mounted. Results from the tests show the robustness of our control law for speed tracking on a terrain with varying gradient while also considering stringent time constraints imposed by the planning framework.

Geometric Consistency for Self-Supervised End-to-End Visual Odometry

With the success of deep learning based approaches in tackling challenging problems in computer vision, a wide range of deep architectures have recently been proposed for the task of visual odometry (VO) estimation. Most of these proposed solutions rely on supervision, which requires the acquisition of precise ground-truth camera pose information, collected using expensive motion capture systems or high-precision IMU/GPS sensor rigs. In this work, we propose an unsupervised paradigm for deep visual odometry learning. We show that using a noisy teacher, which could be a standard VO pipeline, and by designing a loss term that enforces geometric consistency of the trajectory, we can train accurate deep models for VO that do not require ground-truth labels. We leverage geometry as a self-supervisory signal and propose "Composite Transformation Constraints (CTCs)", that automatically generate supervisory signals for training and enforce geometric consistency in the VO estimate. We also present a method of characterizing the uncertainty in VO estimates thus obtained. To evaluate our VO pipeline, we present exhaustive ablation studies that demonstrate the efficacy of end-to-end, self-supervised methodologies to train deep models for monocular VO. We show that leveraging concepts from geometry and incorporating them into the training of a recurrent neural network results in performance competitive to supervised deep VO methods.