Navigation in dynamic environments requires autonomous systems to reason about uncertainties in the behavior of other agents. In this paper, we introduce a unified framework that combines trajectory planning with multimodal predictions and active probing to enhance decision-making under uncertainty. We develop a novel risk metric that seamlessly integrates multimodal prediction uncertainties through mixture models. When these uncertainties follow a Gaussian mixture distribution, we prove that our risk metric admits a closed-form solution, and is always finite, thus ensuring analytical tractability. To reduce prediction ambiguity, we incorporate an active probing mechanism that strategically selects actions to improve its estimates of behavioral parameters of other agents, while simultaneously handling multimodal uncertainties. We extensively evaluate our framework in autonomous navigation scenarios using the MetaDrive simulation environment. Results demonstrate that our active probing approach successfully navigates complex traffic scenarios with uncertain predictions. Additionally, our framework shows robust performance across diverse traffic agent behavior models, indicating its broad applicability to real-world autonomous navigation challenges.

Safe and efficient path planning in parking scenarios presents a significant challenge due to the presence of cluttered environments filled with static and dynamic obstacles. To address this, we propose a novel and computationally efficient planning strategy that seamlessly integrates the predictions of dynamic obstacles into the planning process, ensuring the generation of collision-free paths. Our approach builds upon the conventional Hybrid A star algorithm by introducing a time-indexed variant that explicitly accounts for the predictions of dynamic obstacles during node exploration in the graph, thus enabling dynamic obstacle avoidance. We integrate the time-indexed Hybrid A star algorithm within an online planning framework to compute local paths at each planning step, guided by an adaptively chosen intermediate goal. The proposed method is validated in diverse parking scenarios, including perpendicular, angled, and parallel parking. Through simulations, we showcase our approach's potential in greatly improving the efficiency and safety when compared to the state of the art spline-based planning method for parking situations.

We propose a Dynamical System (DS) approach to learn complex, possibly periodic motion plans from kinesthetic demonstrations using Neural Ordinary Differential Equations (NODE). To ensure reactivity and robustness to disturbances, we propose a novel approach that selects a target point at each time step for the robot to follow, by combining tools from control theory and the target trajectory generated by the learned NODE. A correction term to the NODE model is computed online by solving a quadratic program that guarantees stability and safety using control Lyapunov functions and control barrier functions, respectively. Our approach outperforms baseline DS learning techniques on the LASA handwriting dataset and complex periodic trajectories. It is also validated on the Franka Emika robot arm to produce stable motions for wiping and stirring tasks that do not have a single attractor, while being robust to perturbations and safe around humans and obstacles. The project’s web-page is https://sites.google.com/view/lfd-neural-ode/home.

Robots interacting with humans must be safe, reactive and adapt online to unforeseen environmental and task changes. Achieving these requirements concurrently is a challenge as interactive planners lack formal safety guarantees, while safe motion planners lack flexibility to adapt. To tackle this, we propose a modular control architecture that generates both safe and reactive motion plans for human-robot interaction by integrating temporal logic-based discrete task level plans with continuous Dynamical System (DS)-based motion plans. We formulate a reactive temporal logic formula that enables users to define task specifications through structured language, and propose a planning algorithm at the task level that generates a sequence of desired robot behaviors while being adaptive to environmental changes. At the motion level, we incorporate control Lyapunov functions and control barrier functions to compute stable and safe continuous motion plans for two types of robot behaviors: (i) complex, possibly periodic motions given by autonomous DS and (ii) time-critical tasks specified by Signal Temporal Logic (STL). Our methodology is demonstrated on the Franka robot arm performing wiping tasks on a whiteboard and a mannequin that is compliant to human interactions and adaptive to environmental changes.