Vijay Kumar

In this work, we address the design of tracking controllers that drive a mechanical system's state asymptotically towards a reference trajectory. Motivated by aerospace and robotics applications, we consider fully-actuated systems evolving on the broad class of homogeneous spaces (encompassing all vector spaces, Lie groups, and spheres of any dimension). In this setting, the transitive action of a Lie group on the configuration manifold enables an intrinsic description of the tracking error as an element of the state space, even in the absence of a group structure on the configuration manifold itself (e.g., for ). Such an error state facilitates the design of a generalized control policy depending smoothly on state and time that drives this geometric tracking error to a designated origin from almost every initial condition, thereby guaranteeing almost global convergence to the reference trajectory. Moreover, the proposed controller simplifies naturally when specialized to a Lie group or the -sphere. In summary, we propose a unified, intrinsic controller guaranteeing almost global asymptotic trajectory tracking for fully-actuated mechanical systems evolving on a broader class of manifolds. We apply the method to an axisymmetric satellite and an omnidirectional aerial robot.

In this letter, we address the problem of exploration and metric-semantic mapping of multi-floor GPS-denied indoor environments using swap constrained aerial robots. Most previous work in exploration assumes that robot localization is solved. However, neglecting the state uncertainty of the agent can ultimately lead to cascading errors both in the resulting map and in the state of the agent itself. Furthermore, actions that reduce localization errors may be at direct odds with the exploration task. We develop a framework that balances the efficiency of exploration with actions that reduce the state uncertainty of the agent. In particular, our algorithmic approach for active metric-semantic SLAM is built upon sparse information abstracted from raw problem data, to make it suitable for swap-constrained robots. Furthermore, we integrate this framework within a fully autonomous aerial robotic system that achieves autonomous …

This paper presents a novel learning-based trajectory planning framework for quadrotors that combines model-based optimization techniques with deep learning. Specifically, we formulate the trajectory optimization problem as a quadratic programming (QP) problem with dynamic and collision-free constraints using piecewise trajectory segments through safe flight corridors [1]. We train neural networks to directly learn the time allocation for each segment to generate optimal smooth and fast trajectories. Furthermore, the constrained optimization problem is applied as a separate implicit layer for backpropagation in the network, for which the differential loss function can be obtained. We introduce an additional penalty function to penalize time allocations which result in solutions that violate the constraints to accelerate the training process and increase the success rate of the original optimization problem. To this end …

The problem of multi-robot target tracking asks for actively planning the joint motion of robots to track targets. In this article, we focus on such target tracking problems in adversarial environments, where attacks or failures may deactivate robots' sensors and communications. In contrast to the previous works that consider no attacks or sensing attacks only, we formalize the first robust multi-robot tracking framework that accounts for any fixed numbers of worst-case sensing and communication attacks. To secure against such attacks, we design the first robust planning algorithm, named Robust Active Target Tracking ( RATT ), which approximates the communication attacks to equivalent sensing attacks and then optimizes against the approximated and original sensing attacks. We show that RATT provides provable suboptimality bounds on the tracking quality for any non-decreasing objective function. Our analysis …

We consider a path guarding problem in dynamic Defender-Attacker Blotto games (dDAB), where a team of robots must defend a path in a graph against adversarial agents. Multi-robot systems are particularly well suited to this application, as recent work has shown the effectiveness of these systems in related areas such as perimeter defense and surveillance. When designing a defender policy that guarantees the defense of a path, information about the adversary and the environment can be helpful and may reduce the number of resources required by the defender to achieve a sufficient level of security. In this work, we characterize the necessary and sufficient number of assets needed to guarantee the defense of a shortest path between two nodes in dDAB games when the defender can only detect assets within k-hops of a shortest path. By characterizing the relationship between sensing horizon and required …

Traditional approaches for active mapping focus on building geometric maps. For most real-world applications, however, actionable information is related to semantically meaningful objects in the environment. We propose an approach to the active metric-semantic mapping problem that enables multiple heterogeneous robots to collaboratively build a map of the environment. The robots actively explore to minimize the uncertainties in both semantic (object classification) and geometric (object modeling) information. We represent the environment using informative but sparse object models, each consisting of a basic shape and a semantic class label, and characterize uncertainties empirically using a large amount of real-world data. Given a prior map, we use this model to select actions for each robot to minimize uncertainties. The performance of our algorithm is demonstrated through multi-robot experiments in …

We propose a new formulation for the multi-robot task planning and allocation problem that incorporates (a) precedence relationships between tasks; (b) coordination for tasks allowing multiple robots to achieve increased efficiency; and (c) cooperation through the formation of robot coalitions for tasks that cannot be performed by individual robots alone. In our formulation, the tasks and the relationships between the tasks are specified by a task graph. We define a set of reward functions over the task graph's nodes and edges. These functions model the effect of robot coalition size on task performance while incorporating the influence of one task's performance on a dependent task. Solving this problem optimally is NP-hard. However, using the task graph formulation allows us to leverage min-cost network flow approaches to obtain approximate solutions efficiently. Additionally, we explore a mixed integer …

We address the problem of efficient 3-D exploration in indoor environments for micro aerial vehicles with limited sensing capabilities and payload/power constraints. We develop an indoor exploration framework that uses learning to predict the occupancy of unseen areas, extracts semantic features, samples viewpoints to predict information gains for different exploration goals, and plans informative trajectories to enable safe and smart exploration. Extensive experimentation in simulated and real-world environments shows the proposed approach outperforms the state-of-the-art exploration framework by 24% in terms of the total path length in a structured indoor environment and with a higher success rate during exploration.