Yancy Diaz-Mercado

Multirobot Control Using Time-Varying Density Functions

An approach is presented for influencing teams of robots by means of time-varying density functions, representing rough references for where the robots should be located. A continuous-time coverage algorithm is proposed and distributed approximations are given whereby the robots only need to access information from adjacent robots. Robotic experiments show that the proposed algorithms work in practice, as well as in theory.

Optimal trajectory generation for next generation flight management systems

Next generation flight management systems require the compliance of temporal and spatial constraints on navigation performance. The problem of generating fuel-efficient trajectories for aircrafts that comply with the required navigation performance is approached from an optimal control framework. By deriving the necessary conditions for optimality, nominal optimal control signals can be generated in a computationally efficient manner. These control signals can be used to generate nominal trajectories for an aircraft model. Using the nominal control and nominal trajectory, a feedforward-feedback control scheme can be implemented to robustify the systems response in the presence of uncertainty and disturbances to still achieve the required navigation performance. The feasibility of the approach is demonstrated through simulation and Monte Carlo runs.

Distributed dynamic density coverage for human-swarm interactions

This paper presents two approaches to externally influence a team of robots by means of time-varying density functions. These density functions represent rough references for where the robots should be located. Recently developed continuous-time algorithms move the robots so as to provide optimal coverage of a given the time-varying density functions. This makes it possible for a human operator to abstract away the number of robots and focus on the general behavior of the team of robots as a whole. Using a distributed approximation to this algorithm whereby the robots only need to access information from adjacent robots allows these algorithms to scale well with the number of robots. Simulations and robotic experiments show that the desired behaviors are achieved.

Multi-robot mixing using braids

This paper presents a method for automatically achieving multi-robot mixing in the sense that the robots follow predefined paths in a somewhat loose sense while ensuring that their actual movements are rich enough. In particular, we focus on the mixing problem, where the robots have to interweave their movements, for example to ensure sufficiently rich pairwise interactions or to cover an area along the path. By formally specifying mixing levels through strings over the Braid Group, the resulting hybrid system can execute a geometric interpretation of these strings, where the level of mixing is dictated by the string length. The feasibility of the proposed approach is illustrated on a particular class of multi-robot systems that cooperatively have to achieve the desired mixing levels.

An integrated undergraduate research experience in control, power electronics, and design using a Micromouse

This paper presents a Micromouse project-integrated with the power electronics undergraduate curriculum — as part of a complete undergraduate research experience. The project had several objectives: a) challenge the programming skills of the students, b) teach team integration for an efficient hardware and software development, c) solve engineering problems in order to have a better Micromouse design. Undergraduate student participation is further ensured by linking the Micromouse project to microprocessor programming, electromechanical applications, and other classes. After this research experience the undergraduate students will expand their knowledge on software, hardware, and design using an entertaining but fairly complicated project. Finally, the project will benefit the department in enhancing classroom instruction as well as student retention, graduate school recruitment, and a hands-on experience.

Shortest Paths Through 3-Dimensional Cluttered Environments

This paper investigates the problem of finding shortest paths through 3-dimensional cluttered environments. In particular, an algorithm is presented that determines the shortest path between two points in an environment with obstacles which can be implemented on robots with capabilities of detecting obstacles in the environment. As knowledge of the environment is increasing while the vehicle moves around, the algorithm provides not only the global minimizer - or shortest path - with increasing probability as time goes by, but also provides a series of local minimizers. The feasibility of the algorithm is demonstrated on a quadrotor robot flying in an environment with obstacles.

Multi-robot mixing of nonholonomic mobile robots

In this paper we investigate how much “mixing” one can impose on a team of nonholonomic unicycle robots. This notion is encoded through braids, and a controller is proposed that executes the braids while ensuring that the team is collision-free. Mixing bounds, the bounds on the amount of mixing possible under this braid controller, are also provided. Results are validated when they are implemented on a team of mobile robots which are cooperatively achieving desired mixing levels.

Multirobot Mixing via Braid Groups

This paper presents a framework for multirobot motion planning that characterizes pairwise interactions between agents, e.g., crossing paths while en route to a destination. Mixing is identified as the number of pairwise crossings exhibited by the robot motion. Mixing patterns specified through elements of the braid group provide sufficient level of abstraction to describe interactions without concern for the geometry of the motion. Controllers are constructed explicitly reasoning about the spatial collocation of robots to execute mixing patterns, achieving rich motion in a shared space, e.g., to exchange inter-robot information. We do not focus on achieving a particular pattern, but rather on the problem of being able to execute a whole class of them (e.g., all patterns with at most

Optimal trajectory generation for NextGen flight management systems

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Human–Swarm Interactions via Coverage of Time-Varying Densities

pairwise interactions). The result is a hybrid system driven by symbolic inputs that are mapped onto paths, realizing desired mixing levels. Controllers derived from optimal control provide theoretical bounds on the achievable amount of mixing, satisfaction of spatio-temporal constraints, and collision-free trajectories. Designs are carried to implementation on real robot platforms.