There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Simulations are attractive environments for training agents as they provide an abundant source of data and alleviate certain safety concerns during the training process. But the behaviours developed by agents in simulation are often specific to the characteristics of the simulator. Due to modeling error, strategies that are successful in simulation may not transfer to their real world counterparts. In this paper, we demonstrate a simple method to bridge this “reality gap”. By randomizing the dynamics of the simulator during training, we are able to develop policies that are capable of adapting to very different dynamics, including ones that differ significantly from the dynamics on which the policies were trained. This adaptivity enables the policies to generalize to the dynamics of the real world without any training on the physical system. Our approach is demonstrated on an object pushing task using a robotic arm. Despite being trained exclusively in simulation, our policies are able to maintain a similar level of performance when deployed on a real robot, reliably moving an object to a desired location from random initial configurations. We explore the impact of various design decisions and show that the resulting policies are robust to significant calibration error.

Sim-to-Real Transfer of Robotic Control with Dynamics Randomization

The suitability of electrowetting-on-dielectric (EWD) microfluidics for true lab-on-a-chip applications is discussed. The wide diversity in biomedical applications can be parsed into manageable components and assembled into architecture that requires the advantages of being programmable, reconfigurable, and reusable. This capability opens the possibility of handling all of the protocols that a given laboratory application or a class of applications would require. And, it provides a path toward realizing the true lab-on-a-chip. However, this capability can only be realized with a complete set of elemental fluidic components that support all of the required fluidic operations. Architectural choices are described along with the realization of various biomedical fluidic functions implemented in on-chip electrowetting operations. The current status of this EWD toolkit is discussed. However, the question remains: which applications can be performed on a digital microfluidic platform? And, are there other advantages offered by electrowetting technology, such as the programming of different fluidic functions on a common platform (reconfigurability)? To understand the opportunities and limitations of EWD microfluidics, this paper looks at the development of lab-on-chip applications in a hierarchical approach. Diverse applications in biotechnology, for example, will serve as the basis for the requirements for electrowetting devices. These applications drive a set of biomedical fluidic functions required to perform an application, such as cell lysing, molecular separation, or analysis. In turn, each fluidic function encompasses a set of elemental operations, such as transport, mixing, or dispensing. These elemental operations are performed on an elemental set of components, such as electrode arrays, separation columns, or reservoirs. Examples of the incorporation of these principles in complex biomedical applications are described.

/pdf/digital-microfluidics-is-a-true-lab-on-a-chip-possible-2w1y39xegp.pdf

Digital microfluidics: is a true lab-on-a-chip possible?

This paper focuses on the collision-free coordination of multiple robots with kinodynamic constraints along specified paths. We present an approach to generate continuous velocity profiles for multiple robots; these velocity profiles satisfy the dynamics constraints, avoid collisions, and minimize the completion time. The approach, which combines techniques from optimal control and mathematical programming, consists of identifying collision segments along each robot's path, and then optimizing the robots' velocities along the collision and collision-free segments. First, for each path segment for each robot, the minimum and maximum possible traversal times that satisfy the dynamics constraints are computed by solving the corresponding two-point boundary value problems. The collision avoidance constraints for pairs of robots can then be combined to formulate a mixed integer nonlinear programming (MINLP) problem. Since this nonconvex MINLP model is difficult to solve, we describe two related mixed integer linear programming (MILP) formulations, which provide schedules that give lower and upper bounds on the optimum; the upper bound schedule is designed to provide continuous velocity trajectories that are feasible. The approach is illustrated with coordination of multiple robots, modeled as double integrators subject to velocity and acceleration constraints. An application to coordination of nonholonomic car-like robots is described, along with implementation results for 12 robots.

https://link.springer.com/content/pdf/10.1007%2F978-3-540-45058-0_14.pdf

Coordinating Multiple Robots with Kinodynamic Constraints Along Specified Paths

This paper describes a computational approach to designing a digital microfluidic system (DMFS) that can be rapidly reconfigured for new biochemical analyses. Such a “lab-on-a-chip” system for biochemical analysis, based on electrowetting or dielectrophoresis, must coordinate the motions of discrete droplets or biological cells using a planar array of electrodes. The authors have earlier introduced a layout-based system and demonstrated its flexibility through simulation, including the system's ability to perform multiple assays simultaneously. Since array-layout design and droplet-routing strategies are closely related in such a DMFS, their goal is to provide designers with algorithms that enable rapid simulation and control of these DMFS devices. In this paper, the effects of variations in the basic array-layout design, droplet-routing control algorithms, and droplet spacing on system performance are characterized. DMFS arrays with hardware limited row-column addressing are considered, and a polynomial-time algorithm for coordinating droplet movement under such hardware limitations is developed. To demonstrate the capabilities of our system, we describe example scenarios, including dilution control and minimalist layouts, in which our system can be successfully applied.

Performance Characterization of a Reconfigurable Planar-Array Digital Microfluidic System

Implementing building-level SARS-CoV-2 wastewater surveillance on a university campus.

The authors study the use of pushing actions with a fence to orient and translate objects in the plane. They describe a planner which a guaranteed to construct a sequence of pushing actions to move any polygonal object from any initial configuration to any final configuration. This planner, which utilizes an analysis of the mechanics of pushing an object, generates open-loop plans which do not require feedback sensing. These plans are guaranteed to succeed provided certain physical assumptions are met. Results of experiments conducted to demonstrate the generated plans are presented. >

Posing polygonal objects in the plane by pushing

Coordinating the motions of multiple robots operating in a shared workspace without collisions is an important capability. We address the task of coordinating the motions of multiple robots when their trajectories (defined by both the path and velocity along the path) are specified. This problem of collision-free trajectory coordination arises in welding and painting workcells in the automotive industry. We identify sufficient and necessary conditions for collision-free coordination of the robots when only the robot start times can be varied, and define corresponding optimization problems. We develop mixed integer programming formulations of these problems to automatically generate minimum time solutions. This method is applicable to both mobile robots and articulated arms, and places no restrictions on the number of degrees of freedom of the robots. The primary advantage of this method is its ability to coordinate the motions of several robots, with as many as 20 robots being considered. We show that, even when the robot trajectories are specified, minimum time coordination of multiple robots is NP-hard.

/pdf/coordinating-the-motions-of-multiple-robots-with-specified-5dxeop6qty.pdf

Srinivas Akella

Papers

Coordinating Multiple Robots with Kinodynamic Constraints Along Specified Paths

Performance Characterization of a Reconfigurable Planar-Array Digital Microfluidic System

Implementing building-level SARS-CoV-2 wastewater surveillance on a university campus.

Posing polygonal objects in the plane by pushing

Coordinating the motions of multiple robots with specified trajectories