We investigate how to distribute large quantity of sensors in such a way that workload is evenly shared by sensors. These techniques can also be used for regulating agile mobile sensors, such as UAVs, when the workload of sensors rather than the energy for mobility is the primarily concern. An algorithm is developed for partitioning sensing field such that different partitions have different sensor densities. The goal is to minimize unevenness of the workload to sensor density ratio. The output of the algorithm proved to be the global optimum for serving this purpose.

We present a framework for reduction between different observation properties of discrete event systems modeled by automata under language-based dynamic observations defined in [1]. This framework encapsulates the reduction from coobservability to codiagnosability in [1] and from k-codiagnosability to coobservability in [2]. Under this framework, we show a reduction from observability to diagnosability, but a general reduction in the opposite direction does not exist.

Search-based planning that uses a state lattice has been successfully applied in many applications but its utility is limited when confronted with complex problems represented by a lattice with many nodes and edges with high branching factor. However, in many seemingly complex problems, proper “form-fitting” can reduce the number of nodes and edges needed to represent the problems, provides a concise state lattice and therefore simplifies the computation. This paper proposes a planning framework which strikes to identify concise representations of problems, creates such “form-fitting” state lattice on which a more concise search can take place. In a sense, we take a conventional state lattice and map it onto a deformed space, and then the motion primitives and heuristics follow. Since the contribution of the paper is not the search approach but rather the means by which the lattice is deformed, any search-based planner can then be easily changed to a corresponding deformed version with no increase in time complexity. This paper demonstrate the benifits of the approach which includes 1) planned path can be followed with few changes in motion primitives and thus can provide global smoothness of planned path; 2) fewer states are expanded and thus shorter time to search solution in state space is required, and 3) fewer states are expanded and thus less memory is required to save the state lattice. We demonstrate the benefit of the proposed approach in illustrative toy examples, as well as robot experiments.

Biologically inspired robots perform many interesting and useful behaviors, but to effectively emulate their biological counterparts, robots often need to possess many degrees of freedom, complicating their mechanical design and making it difficult to apply standard control and motion planning strategies. To address this complexity, the robotics community has derived low-dimensional parameter-based controllers that naturally coordinate many degrees of freedom such as the serpenoid curves used to control snake robots. Controllers utilizing this parameterization for snake robots have been able to induce behaviors similar to that of the robots' biological counterparts. A similar concept, called a control template, is used in the study of animal movements. However, much of the prior work on control templates has been limited to in-plane motion. In this work, we extend the usage of control templates to three dimensions to both better model and understand biology, as well as to help us gain better intuition into how we can use pre-existing control paradigms to create new behaviors for biologically inspired robots.

Our research group has started a collaboration that analyzes data collected from biological snakes to provide insight on how to better program snake robots. Most data collected on biological snakes views the snakes from above and thus can only detect motion in the horizontal plane. However, both our robots and biological snakes are capable of generating motions both in the horizontal and vertical planes. Vertical waves naturally play a major role in limbless locomotion in that they simultaneously provide thrust motion and make-and-break contact between the mechanism and environment. Analysis on the data, collected from sidewinder rattle snakes, revealed that disparate modes of locomotion emerged from different contact patterns. We conclude that the same horizontal undulation can cause dramatically different motions for both the biological and robotic snakes depending upon the choice of contacts. With this knowledge, we introduce contact scheduling, a technique that plans positions of contacts along the body to design gaits for snake robots. Contact scheduling results in a novel turning gait, which can reorient a snake robot more than 90 degrees in one gait cycle.

Limbless locomotion, evidenced by both biological and robotic snakes, capitalizes on these systems' redundant degrees of freedom to negotiate complicated environments. While the versatility of locomotion methods provided by a snake-like form is of great advantage, the difficulties in both representing the high dimensional workspace configuration and implementing the desired translations and orientations makes difficult further development of autonomous behaviors for snake robots. Based on a previously defined average body frame and set of motion primitives, this work proposes locomotive reduction, a simplifying methodology which reduces the complexity of controlling a redundant snake robot to that of navigating a differential-drive vehicle. We verify this technique by controlling a 16-DOF snake robot using locomotive reduction combined with a visual tracking system. The simplicity resulting from the proposed locomotive reduction method allows users to apply established autonomous navigation techniques previously developed for differential-drive cars to snake robots. Best of all, locomotive reduction preserves the advantages of a snake robot's ability to perform a variety of locomotion modes when facing complicated mobility challenges.

Successful deployment of a snake robot in search and rescue tasks requires the capability of generating controls which can adapt to unknown environments in real-time. However, available motion generation techniques can be computationally expensive and lack the ability to adapt to the surroundings. This work considers modeling the rolling motion of a snake robot by applying the Bellows model with computation reduction techniques. One benefit of this is that controllers are defined with physically meaningful parameters, which in turn allows for higher level control of the robot. Another benefit is that it allows controllers to be defined by “composing shapes”, which enables developing controllers that can adapt to the surroundings. Using shape composition, we implemented a novel gait, named rolling hump, which forms a contour-fitting hump to negotiate obstacles. The efficacy of a snake robot climbing over obstacles by using the rolling hump is experimentally evaluated. An autonomous control strategy is presented and realized in simulation.

Snake robots are uniquely qualified to investigate a large variety of settings including archaeological sites, natural disaster zones, and nuclear power plants. For these applications, modular snake robots have been tele-operated to perform specific tasks using images returned to it from an onboard camera in the robots head. In order to give the operator an even richer view of the environment and to enable the robot to perform autonomous tasks we developed a structured light sensor that can make three-dimensional maps of the environment. This paper presents a sensor that is uniquely qualified to meet the severe constraints in size, power and computational footprint of snake robots. Using range data, in the form of 3D pointclouds, we show that it is possible to pair high-level planning with mid-level control to accomplish complex tasks without operator intervention.

We derive and demonstrate a new capability for snake robots in which two behaviors-one for locomotion and the other for manipulation-are executed simultaneously on the same robot. This is done in two steps: 1) inverse kinematics via numerical optimization and 2) gait-based locomotion via modal decomposition. The result is an analytical representation of a multiple mode behavior that reduces online execution to simple parameterized control. This representation makes it possible to derive a feedback control law that enables reliable visual servoing using a snake robot while climbing a pole.

Sidewinding is an efficient gait adopted by biological and robotic snakes for locomoting on various terrains. The mechanics of this motion on flat ground and steady state terrains have been thoroughly investigated, while its capability to adapt to changing environments is not as well studied. We demonstrate the capability of a snake robot to automatically adjust gait parameters to optimally move up and down slopes of varying angle. This capability is achieved by three components. First, an efficient offline learning algorithm finds a policy mapping the estimated slope angle to the optimal gait parameters. Next, a robust online state estimation technique infers the local terrain characteristics. Finally, the precomputed policy is consulted online to select the optimal gait parameters for this slope. The efficacy of this approach is verified by robot experiments.

Sidewinding is an efficient translational gait used by biological snakes to locomote over flat ground. Prior work has identified the fact that it is possible to steer the moving direction of sidewinding. The previously proposed virtual tread model reveals the working principal of sidewinding from a geometric point of view. Unfortunately, the implementation of the virtual tread model relied on a computationally expensive numerical fitting algorithm that impeded online applications. Motivated by this limitation, in this work we propose a novel approach to develop analytical expressions for snake robot gaits based on the study of the corresponding geometric model. This approach is rooted in the identification of dominant frequency components afforded by the two-dimensional Fast Fourier Transformation (FFT). Applying this method to the virtual tread model for conical sidewinding, we derive an analytical expression between the parameters that describe the gait's motion and the turning radius of the system moving in the world. This analytical expression, which we call the extended gait equation, is verified by experimental results.

Highly articulated robot locomotion systems, such as snake robots, present special motion planning challenges. They possess many degrees of freedom, and therefore are modeled by a high dimensional configuration space which must be searched to plan a path. Kinematic and dynamic constraints further complicate the selection of effective controls. Finally, snake robots often have multiple modes of interaction with the terrain as contacts are made and broken, leading to complex and imperfect motion models. We believe that the space of useful controls that provides desirable motions, however, is much smaller. Useful net motions for such systems are often generated via gaits, or cyclic motions in the shape space. Gaits transform a high-dimensional continuum search into a relatively tractable discrete search. In this paper, we put forward a framework which allows a planner to generate paths in a low dimensional work space and select among gaits, pre-planned motions in the robot's shape space. The contribution of this paper rests on the “virtual chassis” which is a choice of body frame for the snake robot that allows the planner to efficiently select among and plan with gaits to direct the robot along the work space path. We demonstrate this planner running on a simulated snake robot navigating through a variety of clutter scenarios. The virtual chassis also has the benefit of allowing us to generalize notions of controllability to gait motions.

Sidewinding is an efficient translation gait used by snakes and snake robots over flat ground, and resembles a helical tread moving over a core cylindrical geometry. Most sidewinding research has focused on straight-line translation of the snake, and less on steering capabilities. Here, we offer a new, geometrically intuitive method for steering this gait: Tapering the core cylinder into a cone, such that one end moves faster than the other, changing the heading of the robot as it drives forward. We present several design tools for working with this cone, along with experimental results on a physical robot turning at different rates.

In this paper, we present a novel algorithm for deterministically mapping an undirected graph-like world with multiple synchronized agents. The application of this algorithm is the collective mapping of an indoor environment with multiple mobile robots while leveraging an embedded topological decomposition of the environment. Our algorithm relies on a group of agents that all depart from the same initial vertex in the graph and spread out to explore the graph. A centralized tree of graph hypotheses is maintained to consider loop-closure, which is deterministically verified when agents observe each other at a common vertex. To achieve efficient mapping, we introduce an active exploration method in which agents dynamically request rendezvous tasks from other available agents to validate graph hypotheses.