Safe autonomous driving critically depends on how well the ego-vehicle can predict the trajectories of neighboring vehicles. To this end, several trajectory prediction algorithms have been presented in the existing literature. Many of these approaches output a multi-modal distribution of obstacle trajectories instead of a single deterministic prediction to account for the underlying uncertainty. However, existing planners cannot handle the multi-modality based on just sample-level information of the predictions. With this motivation, this paper proposes a trajectory optimizer that can leverage the distributional aspects of the prediction in a computationally tractable and sample-efficient manner. Our optimizer can work with arbitrarily complex distributions and thus can be used with output distribution represented as a deep neural network. The core of our approach is built on embedding distribution in Reproducing Kernel Hilbert Space (RKHS), which we leverage in two ways. First, we propose an RKHS embedding approach to select probable samples from the obstacle trajectory distribution. Second, we rephrase chance-constrained optimization as distribution matching in RKHS and propose a novel sampling-based optimizer for its solution. We validate our approach with hand-crafted and neural network-based predictors trained on real-world datasets and show improvement over the existing stochastic optimization approaches in safety metrics.

Efficient navigation in unknown and dynamic environments is crucial for expanding the application domain of mobile robots. The core challenge stems from the nonavailability of a feasible global path for guiding optimization-based local planners. As a result, existing local planners often get trapped in poor local minima. In this paper, we present a novel optimizer that can explore multiple homotopies to plan high-quality trajectories over long horizons while still being fast enough for real-time applications. We build on the gradient-free paradigm by augmenting the trajectory sampling strategy with a projection optimization that guides the samples toward a feasible region. As a result, our approach can recover from the frequently encountered pathological cases wherein all the sampled trajectories lie in the high-cost region. Furthermore, we also show that our projection optimization has a highly parallelizable structure that can be easily accelerated over GPUs. We push the state-of-the-art in the following respects. Over the navigation stack of the Robot Operating System (ROS), we show an improvement of 7-13% in success rate and up to two times in total travel time metric. On the same benchmarks and metrics, our approach achieves up to 44% improvement over MPPI and its recent variants. On simple point-to-point navigation tasks, our optimizer is up to two times more reliable than SOTA gradient-based solvers, as well as sampling-based approaches such as the Cross-Entropy Method (CEM) and VPSTO. Codes: https://github.com/fatemeh-rastgar/PRIEST

This paper presents a scalable online algorithm to generate safe and kinematically feasible trajectories for quadrotor swarms. Existing approaches rely on linearizing Euclidean distance-based collision constraints and on axis-wise decoupling of kinematic constraints to reduce the trajectory optimization problem for each quadrotor to a quadratic program (QP). This conservative approximation often fails to find a solution in cluttered environments. We present a novel alternative that handles collision constraints without linearization and kinematic constraints in their quadratic form while still retaining the QP form. We achieve this by reformulating the constraints in a polar form and applying an Alternating Minimization algorithm to the resulting problem. Through extensive simulation results, we demonstrate that, as compared to Sequential Convex Programming (SCP) baselines, our approach achieves on average a 72% improvement in success rate, a 36% reduction in mission time, and a 42 times faster per-agent computation time. We also show that collision constraints derived from discrete-time barrier functions (BF) can be incorporated, leading to different safety behaviours without significant computational overhead. Moreover, our optimizer outperforms the state-of-the-art optimal control solver ACADO in handling BF constraints with a 31 times faster per-agent computation time and a 44% reduction in mission time on average. We experimentally validated our approach on a Crazyflie quadrotor swarm of up to 12 quadrotors. The code with supplementary material and video are released for reference.

-- Autonomous driving has a natural bi-level structure. The goal of the upper behavioural layer is to provide appropriate lane change, speeding up, and braking decisions to optimize a given driving task. However, this layer can only indirectly influence the driving efficiency through the lower-level trajectory planner, which takes in the behavioural inputs to produce motion commands. Existing sampling-based approaches do not fully exploit the strong coupling between the behavioural and planning layer . On the other hand, end-to-end Reinforcement Learning (RL) can learn a behavioural layer while incorporating feedback from the lower-level planner . However, purely data-driven approaches often fail in safety metrics in unseen environments. This paper presents a novel alternative; a parameterized bi-level optimization that jointly computes the optimal behavioural decisions and the resulting downstream trajectory. Our approach runs in real-time using a custom GPU-accelerated batch optimizer, and a Conditional V ariational Autoencoder learnt warm-start strategy. Extensive simulations show that our approach outperforms state-of-the-art model predictive control and RL approaches in terms of collision rate while being competitive in driving efficiency. Motion planning for autonomous driving can be divided into two hierarchical components. At the top level, the behavioural layer computes decisions such as lane change, speeding up and braking based on the traffic scenario and the driving task. The behavioural inputs can be conveniently parameterized as set-points for longitudinal velocity, lateral offsets from the centre line, goal positions, etc. The advantage of such representation is that it naturally integrates with the lower-level optimal trajectory planner [1], [2], [3], [4] [5], [6].

Modern autonomous vehicles (AVs) often rely on vision, LIDAR, and even radar-based simultaneous localization and mapping (SLAM) frameworks for precise localization and navigation. However, modern SLAM frameworks often lead to unacceptably high levels of drift (i.e., localization error) when AVs observe few visually distinct features or encounter occlusions due to dynamic obstacles. This paper argues that minimizing drift must be a key desiderata in AV motion planning, which requires an AV to take active control decisions to move towards feature-rich regions while also minimizing conventional control cost. To do so, we first introduce a novel data-driven perception module that observes LIDAR point clouds and estimates which features/regions an AV must navigate towards for drift minimization. Then, we introduce an interpretable model predictive controller (MPC) that moves an AV toward such feature-rich regions while avoiding visual occlusions and gracefully trading off drift and control cost. Our experiments on challenging, dynamic scenarios in the state-of-the-art CARLA simulator indicate our method reduces drift up to 76.76% compared to benchmark approaches.