Jason C. Derenick

Convex Optimization Strategies for Coordinating Large-Scale Robot Formations

This paper investigates convex optimization strategies for coordinating a large-scale team of fully actuated mobile robots. Our primary motivation is both algorithm scalability as well as real-time performance. To accomplish this, we employ a formal definition from shape analysis for formation representation and repose the motion planning problem to one of changing (or maintaining) the shape of the formation. We then show that optimal solutions, minimizing either the total distance or minimax distance the nodes must travel, can be achieved through second-order cone programming techniques. We further prove a theoretical complexity for the shape problem of O(m1.5) as well as O(m) complexity in practice, where m denotes the number of robots in the shape configuration. Solutions for large-scale teams (1000s of robots) can be calculated in real time on a standard desktop PC. Extensions integrating both workspace and vehicle motion constraints are also presented with similar complexity bounds. We expect these results can be generalized for additional motion planning tasks, and will prove useful for improving the performance and extending the mission lives of large-scale robot formations as well as mobile ad hoc networks.

On the deployment of a hybrid free-space optic/radio frequency (FSO/RF) mobile ad-hoc network

The hybrid free-space optics/radio frequency (FSO/RF) network paradigm promises new levels of throughput for sensor and mobile ad-hoc networks. However, several challenges must be addressed before such a network model can be realized. These include a means by which deployed robots can autonomously establish optical links over sufficiently long distances as well as the formulation of a mobile network architecture that can exploit high throughput FSO channels. In this paper, we offer solutions to these problems in the form of hierarchical link acquisition and routing protocols. The heart of our link acquisition system (LAS) is a vision-based alignment phase for locating robot link partners via high zoom camera systems. Identification is accomplished in real-time using a multi-resolution image representation and normalized intensity distribution (NID) as a similarity metric. Our routing protocol relies upon the hierarchical state routing (HSR) model adapted to the FSO/RF paradigm. Experimental results from a large set of link acquisition trials as well as a small scale FSO/RF deployment are provided to support our approach.

An Optimal Approach to Collaborative Target Tracking with Performance Guarantees

In this paper, we present a discrete-time optimization framework for target tracking with multi-agent systems. The “target tracking” problem is formulated as a generic semidefinite program (SDP) that when paired with an appropriate objective yields an optimal robot configuration over a given time step. The framework affords impressive performance guarantees to include full target coverage (i.e. each target is tracked by at least a single team member) as well as maintenance of network connectivity across the formation. Key to this work is the result from spectral graph theory that states the second-smallest eigenvalue—λ2—of a weighted graph’s Laplacian (i.e. its inter-connectivity matrix) is a measure of connectivity for the associated graph. Our approach allows us to articulate agent-target coverage and inter-agent communication constraints as linear-matrix inequalities (LMIs). Additionally, we present two key extensions to the framework by considering alternate tracking problem formulations. The first allows us to guarantee k-coverage of targets, where each target is tracked by k or more agents. In the second, we consider a relaxed formulation for the case when network connectivity constraints are superfluous. The problem is modeled as a second-order cone program (SOCP) that can be solved significantly more efficiently than its SDP counterpart—making it suitable for large-scale teams (e.g. 100’s of nodes in real-time). Methods for enforcing inter-agent proximity constraints for collision avoidance are also presented as well as simulation results for multi-agent systems tracking mobile targets in both ℝ2 and ℝ3.

Homological sensing for mobile robot localization

In this paper, we consider a multi-phased, minimalistic approach to mobile robot localization that constrains the robots ability to sense its environment to a binary detection of uniquely identifiable landmarks having unknown position (e.g., a WiFi transceiver detecting network SSIDs). Central to the proposed solution are dual landmark and observation complexes (instances of simplicial nerve complexes), which can be iteratively built through local observations without any metric or time-sequenced information. We have shown that these complexes approximate the topology of the underlying physical environment. Specifically, the notion of a “hole” (i.e., a topological invariant) within these complexes naturally represents a physical structure (e.g., a building) that limits landmark visibility/communication with respect to the robots location. Taking advantage of this property, we formulate a homological sensing model that operates on these constructs enabling the robot to “count” the number of structures in its vicinity using local homology computations as a pseudo-metric surrogate sensor. Our homological sensor is highlighted in the context of a Monte-Carlo localization algorithm that resolves robot location by correlating the measured number of topological invariants with an unlabeled, metric map location.

Energy-aware coverage control with docking for robot teams

In this paper, we formulate a distributed, energy-aware control policy aimed at enabling persistent surveillance of a specified region of interest by teams of networked robots. Central to our formulation is the fundamental idea that as an agent participating in coverage approaches a low energy reserve the team should cooperatively adjust the coverage formation to allow the agent to return to a designated base station, where it can recharge before rejoining the effort. Towards this end, we build upon recent efforts in employing Centroidal Voronoi Tessellation (CVT)-based coverage control laws by defining a policy that exploits a power-dependent weighting scheme that embeds an agents trade-off to achieve its coverage mission and to maintain a desired energy reserve to guarantee its own safety. Stability of the proposed approach is considered, and we show that coupling our continuous controller with a straightforward switching mechanism guarantees every agent will return to its base station safely. Simulation results are presented to verify and demonstrate the utility of the proposed control scheme.

Localization using ambiguous bearings from radio signal strength

In this paper, we consider the problem of localizing a mobile robot team capable of measuring ambiguous bearing estimates using received signal strength indicators (RSSI) from radio transceivers (e.g., ZigBee). More precisely, we formulate a robust bearing estimator that leverages anisotropic but symmetric radiation profiles to identify π-periodic bearing estimates between pairs of communicating agents. Utilizing these ambiguous bearing estimates along with compass and odometric measurements, we present a Multi-hypothesis Extended Kalman Filter-based framework that exploits agent motion to resolve the resulting state ambiguity and achieve localization up to translation. Despite the combinatoric nature of our problem, for teams exhibiting certain topological properties, we show that only two initial hypotheses need consideration to recover state. Experimental results from a small team of differential drive robots are presented to demonstrate the utility of our approach. Simulation results are also presented that explore our frameworks convergence properties for larger team sizes.

Hybrid Free-Space Optics/Radio Frequency (FSO/RF) Networks for Mobile Robot Teams

In this paper, we introduce a hybrid free-space optics/radio frequency (FSO/RF) networking paradigm for mobile robot teams. We believe that such a model will emerge as a consequence of inherent limitations of RF based approaches. FSO technology has the potential to provide tremendous increases in per-node throughput for a mobile ad-hoc network (MANET). To motivate this paradigm, we first provide a brief background on FSO and discuss potential applications where its capabilities could be well leveraged. We then provide initial experimental results from autonomous deployments of a hybrid FSO/RF MANET with real-time video data routed across both optical and RF links.

A semidefinite programming framework for controlling multi-robot systems in dynamic environments

In this paper, a discrete-time, semidefinite programming (SDP) framework is synthesized for controlling mobile robot teams operating in dynamic environments. Given an initially feasible configuration, the proffered framework embeds formation shape control and guarantees inter-agent and agent-obstacle collision avoidance and network interconnectivity across the formation given a sufficiently small Δt - provided that a feasible solution exists. Additionally, it affords goal-directed behaviors, which are explored, most notably, in terms of its application to directional coverage control, where the objective is to ensure that a set of mobile targets are being observed by at least a single member of the team at any given time. Central to our formulation is melding the recent application of shape theoretic constructs to globally optimal shape planning with state-dependent graphs whose enforced connectivity (gauged via their Fiedler value) implies satisfaction of the aforementioned constraints. Simulation results are presented to highlight the utility of our approach.

Towards simplicial coverage repair for mobile robot teams

In this note, we present initial results towards developing a distributed algorithm for repairing topological holes in the sensor cover of a mobile robot team. Central to our approach is the melding of recent advances in the application of computational homology (a sub-discipline of algebraic topology) to static sensor networks with relative metric information (i.e. relative pose). More precisely, we consider a greedy, hybrid (discrete-continuous) algorithm whereby a desired Cěch complex, the simplicial complex that captures the underlying topology of the sensing cover, is iteratively generated using local rules (between multi-hop neighbors) and agents are driven towards achieving this topology via a gradient-ascent simplicial control law. Convergence of the proposed algorithm is established as a function of the convergence of the underlying simplicial control law, and the relationship of the latter to the spectrum of the combinatorial Laplacian is considered. Simulation results for teams operating in ℝ2 are presented.

Efficient Motion Planning Strategies for Large-Scale Sensor Networks

In this paper, we develop a suite of motion planning strategies suitable for large-scale sensor networks. These solve the problem of reconfiguring the network to a new shape while minimizing either the total distance traveled by the nodes or the maximum distance traveled by any node. Three network paradigms are investigated: centralized, computationally distributed, and decentralized. For the centralized case, optimal solutions are obtained in O(m) time in practice using a logarithmic-barrier method. Key to this complexity is transforming the Karush-Kuhn-Tucker (KKT) matrix associated with the Newton step sub-problem into a mono-banded system solvable in O(m) time. These results are then extended to a distributed approach that allows the computation to be evenly partitioned across the m nodes in exchange for O(m) messages in the overlay network. Finally, we offer a decentralized, hierarchical approach whereby follower nodes are able to solve for their objective positions in O(1) time from observing the headings of a small number (2-4) of leader nodes. This is akin to biological systems (e.g. schools of fish, flocks of birds, etc.) capable of complex formation changes using only local sensor feedback. We expect these results will prove useful in extending the mission lives of large-scale mobile sensor networks.