This paper introduces a novel motion planning algorithm designed for a team of curvature-constrained tethered robots operating on sloped 3D terrains. Our approach addresses the critical issues of tether-terrain interaction, robot stability, and tether entanglement avoidance. The study focuses on a two-robot system, where stability is primarily dependent on tether tension, which is in turn limited by wheel traction. We propose a path-planning method that strategically utilizes terrain features (e.g., rocks) to augment tether tension through additional friction, thereby enhancing overall system stability. Our algorithm employs a modified tangent graph as the underlying structure for a hybrid A* search, incorporating stability constraints throughout the planning process. The proposed method is extensively evaluated through various simulation experiments, demonstrating its effectiveness in planning safe and efficient paths.

Motivated by human-chains in rescue missions, this paper proposes a scalable path planning algorithm for multiple mobile robots that are tethered to one another in a chain topology with finite-length tethers. Specifically, our approach trades off optimality for scalability and computational tractability by adding some simplifying, yet realistic constraints that can significantly reduce computation. In particular, by maintaining the existence of tether configurations that coincide with collision-free, feasible paths for the robots, we remove the need to check that the tether configurations are collision-free, which is often a bottleneck since the tethers are infinite-dimensional. Our proposed path planning framework for tethered robot chains builds upon sampling-based algorithms such as RRT*, BIT*, and ABIT*. Finally, we prove the probabilistic completeness of the approach, ensuring reliable path generation, and demonstrate the effectiveness of our approach in simulation experiments.

In this paper, we propose a variant of the anytime hybrid A* algorithm that generates a fast but suboptimal solution before progressively optimizing the paths to find the shortest winding-constrained paths for a pair of tethered robots under curvature constraints. Specifically, our proposed algorithm uses a tangent graph as its underlying search graph and leverages an anytime A* search framework with appropriately defined cost metrics in order to reduce the overall computation and to ensure that a winding angle constraint is satisfied. Moreover, we prove the completeness and optimality of the algorithm for finding the shortest winding-constrained paths in an anytime fashion. The effectiveness of the proposed algorithm is demonstrated via simulation experiments.

In this paper, a variant of hybrid A* is developed to find the shortest path for a curvature-constrained robot, that is tethered at its start position, such that the tether satisfies user-defined winding angle constraints. A variant of tangent graphs is used as an underlying graph for searching a path using A*in order to reduce the overall computation and define appropriate cost metrics to ensure winding angle constraints are satisfied. Conditions are provided under which the proposed algorithm is guaranteed to find a winding angle constrained path. The effectiveness and performance of the proposed algorithm are studied in simulation.

In the absence of a tether attachment mechanism that can provide infinitely large tension to the tethered robots moving on extreme planetary terrains, there is a limit on how much tension can be realistically generated or supported by the tether. In this paper, we consider a team of two robots tethered together moving on extreme terrains. The traction on the wheels of the robot and the friction between the tether and the tether attachment surfaces/objects (e.g., rocks) is the only way to support the tether tension. Given a path for the robots to navigate, we provide a systematic algorithm to check if the robots will be stable along the given path while considering the maximum constraints on the tension generated or supported by the tether. The results are validated via simulation experiments.

This paper presents path-dependent feedback controllers and estimators with bounded tracking and estimation error guarantees for discrete-time affine systems with time-varying delayed and missing data, where the set of all temporal patterns for the missing or delayed data is constrained by a fixed-length language. In particular, we propose two controller/estimator synthesis approaches based on output feedback and output error feedback parameterizations such that the tracking or estimation errors satisfy a property known as equalized recovery, where the errors are guaranteed to satisfy a recovery level at the start and the end of a finite time horizon, but may temporarily increase (by a bounded amount) within the horizon. To achieve this, we introduce a mapping of the fixed-length delayed/missing data language onto a reduced event-based language, and present designs with feedback gain matrices that adapt based on the observed path in the reduced language, resulting in improved performance. Furthermore, we propose a word observer that finds the set of words (i.e., the delayed/missing data patterns) in the original fixed-length language that are compatible with the observed path. The effectiveness of the proposed approaches when compared to existing approaches is demonstrated using several illustrative examples.

When deployed into real environments, control systems need to be able to operate when their sensor data can become 'missing' (e.g., a vehicle's radar system may incorrectly detect a falling leaf as a vehicle on the road, or a distributed control system may lose sensor data packets while attempting to transmit). Guaranteeing safety of such systems can be handled by enforcing boundedness of the state or the estimated state of a system during operation. The form of boundedness that we use within this work is called equalized recovery and the goal of this work is to find controllers or estimators that satisfy equalized recovery in the presence of missing data. Equalized recovery relaxes the notion of invariance and allows the system states to be in a larger set during missing data events as long as the states can be steered back to the original set. Prefix-based controllers and estimators are introduced to solve this problem and methods to synthesize them are presented.

In this article, we consider the problem of attack-resilient state estimation, that is, to reliably estimate the true system states despite two classes of attacks: (i) attacks on the switching mechanisms and (ii) false data injection attacks on actuator and sensor signals, in the presence of stochastic process and measurement noise signals. We model the systems under attack as hidden mode stochastic switched linear systems with unknown inputs and propose the use of a multiple-model inference algorithm to tackle these security issues. Moreover, we characterize fundamental limitations to resilient estimation (e.g., upper bound on the number of tolerable signal attacks) and discuss the topics of attack detection, identification, and mitigation under this framework. Simulation examples of switching and false data injection attacks on a benchmark system and an IEEE 68-bus test system show the efficacy of our approach to recover resilient (i.e., asymptotically unbiased) state estimates as well as to identify and mitigate the attacks.

We consider an approach-evasion differential game where the inputs of one of the players are upper bounded by a random variable. The game enjoys the order preserving property where a larger relaxation of the random variable induces a smaller value function. Two numerical computation algorithms are proposed to asymptotically recover the expected value function. The performance of the proposed algorithms is compared via a stochastically parametric homicidal chauffeur game. The algorithms are also applied to the scenario of merging lanes in urban transportation.