Srinivas Akella

Coordinating Multiple Robots with Kinodynamic Constraints Along Specified Paths

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.

Performance Characterization of a Reconfigurable Planar-Array Digital Microfluidic System

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 systems 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.

Posing polygonal objects in the plane by pushing

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.<<ETX>>

Folding cartons with fixtures: a motion planning approach

Packaging products such as telephones and two-way radios after assembly is a common manufacturing task. Carton folding is a packaging operation typically performed by human operators or with fixed automation. We present a flexible method to fold cardboard cartons using fixtures; a carton blank is folded by moving it through a fixture with a robot. This method uses interchangeable fixtures to enable rapid changeovers between product models. We outline an approach to design a fixture given a carton and a folding sequence. We present an implemented motion planning algorithm that generates all folding sequences for a carton by modeling it kinematically as a many degree-of-freedom robot manipulator with revolute joints and branching links. Folding fixtures constrain the carton motion to paths consisting of line segments in its configuration space. We characterize the set of valid paths for these carton robots and generate them using the motion planner. To illustrate the method, we selected a folding sequence for an example carton, designed a fixture, and demonstrated folding of the carton from blanks with an industrial robot.

Coordinating the motions of multiple robots with specified trajectories

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.

Parts Feeding on a Conveyor with a One Joint Robot

Abstract. This paper explores a method of manipulating a planar rigid part on a conveyor belt using a robot with just one joint. This approach has the potential of offering a simple and flexible method for feeding parts in industrial automation applications. In this paper we develop a model of this system and of a variation which requires no sensing. We have been able to characterize these systems and to prove that they can serve as parts feeding devices for planar polygonal parts. We present the planners for these systems and describe our implementations.

Posing Polygonal Objects in the Plane by Pushing

This paper studies the use of pushing actions to orient and trans late objects in the plane. The authors use linear normal pushes, which are straight-line pushes in a direction normal to the pushing fence. These pushes are specified by the fence orientation and push distance. The authors show that a set of linear normal pushes can always be found to move any polygonal object from any initial con figuration to any goal configuration in the obstacle-free plane. The object configuration is specified by its pose; that is, its position and orientation. The authors formulate the search for such a sequence of pushes as a linear programming problem. They then describe an implemented pose planner that uses this formulation to identify a sequence of linear normal pushes given any polygonal object, any initial pose, and any goal pose. This planner is proven to be com plete and to have polynomial time complexity. The planner, which uses an analysis of the mechanics of pushing an object, generates open-loop plans that do not require sensing. The authors describe experiments that demonstrate the validity of the generated plans.

Coordinating Multiple Droplets in Planar Array Digital Microfluidic Systems

In this paper we present an approach to coordinate the motions of droplets in digital microfluidic systems, a new class of lab-on-a-chip systems for biochemical analysis. A digital microfluidic system typically consists of a planar array of cells with electrodes that control the droplets. The primary challenge in using droplet-based systems is that they require the simultaneous coordination of a potentially large number of droplets on the array as the droplets move, mix, and split. In this paper we describe a general-purpose system that uses simple algorithms and yet is versatile. First, we present a semi-automated approach to generate the array layout in terms of components. Next, we discuss simple algorithms to select destination components for the droplets and a decentralized scheme for components to route the droplets on the array. These are then combined into a reconfigurable system that has been simulated in software to perform analyses such as the DNA polymerase chain reaction. The algorithms have been able to successfully coordinate hundreds of droplets simultaneously and perform one or more chemical analyses in parallel. Because it is challenging to analytically characterize the behavior of such systems, simulation methods to detect potential system instability are proposed.

Planar Manipulation on a Conveyor with a One Joint Robot

This paper explores a method of manipulating a planar rigid body on a conveyor belt using a robot with just one joint. This approach has the potential of offering a simple and flexible method for feeding parts in industrial automation applications. In this paper we outline our approach, develop some of the theoretical properties, present a planner for the robot, and describe an initial implementation.

Proximity Queries Between Convex Objects: An Interior Point Approach for Implicit Surfaces

This paper presents a general method for exact distance computation between convex objects represented as intersections of implicit surfaces. Exact distance computation algorithms are particularly important for applications involving objects that make intermittent contact, such as in dynamic simulations and in haptic interactions. They can also be used in the narrow phase of hierarchical collision detection. In contrast to geometric approaches developed for polyhedral objects, we formulate the distance computation problem as a convex optimization problem. We use an interior point method to solve the optimization problem and demonstrate that, for general convex objects represented as implicit surfaces, interior point approaches are globally convergent, and fast in practice. Further, they provide polynomial-time guarantees for implicit surface objects when the implicit surfaces have self-concordant barrier functions. We use a primal-dual interior point algorithm that solves the Karush-Kuhn-Tucker (KKT) conditions obtained from the convex programming formulation. For the case of polyhedra and quadrics, we establish a theoretical time complexity of O(n1.5), where n is the number of constraints. We present implementation results for example implicit surface objects, including polyhedra, quadrics, and generalizations of quadrics such as superquadrics and hyperquadrics, as well as intersections of these surfaces. We demonstrate that in practice, the algorithm takes time linear in the number of constraints, and that distance computation rates of about 1 kHz can be achieved. We also extend the approach to proximity queries between deforming convex objects. Finally, we show that continuous collision detection for linearly translating objects can be performed by solving two related convex optimization problems. For polyhedra and quadrics, we establish that the computational complexity of this problem is also O(n1.5).