In this paper we explore the relationship between dual decomposition and the consensus-based method for distributed optimization. The relationship is developed by examining the similarities between the two approaches and their relationship to gradient-based constrained optimization. By formulating each algorithm in continuous-time, it is seen that both approaches use a gradient method for optimization with one using a proportional control term and the other using an integral control term to drive the system to the constraint set. Therefore, a significant contribution of this paper is to combine these methods to develop a continuous-time proportional-integral distributed optimization method. Furthermore, we establish convergence using Lyapunov stability techniques and utilizing properties from the network structure of the multi-agent system. is solved by these methods. Specifically, we formulate both the mentioned dual-decomposition method and the consensus-based method in [8] in control theoretic terms to draw parallels and gain intuition behind why they can naturally be joined together. In fact, it will become apparent that dual-decomposition is very closely related to integral (I) control and the consensus method is closely related to proportional (P) control. Therefore, a significant contribution of this paper is to combine these two methods to form a new, proportional-integral (PI) distributed optimization method. This formulation will be similar to the PI distributed optimization method introduced in [9] and extended in [11,19]. However, due to the fact that we create the PI optimization method from the perspective of the dual-decomposition method, which involves a set of constraints associated with the interconnections of agents, it enables us to form a different type of integral control term and reduce the required communication.While much of the work on distributed optimization has been developed in discrete-time formulations, which are amenable for implementation, e.g. [7,10,12,20], a great deal of work recently has been made in continuous-time [8,9,11,13,14,21,19]. Continuous-time analysis has proven useful as it allows Lyapunov stability conditions to be directly applied to the update-equations for convergence analysis. It also allows for an intuitive connection between the optimization algorithm proposed in this paper and proportional-integral control. Moreover, a discretization of the framework proposed in this paper does not pose a significant contribution.The proportional element has been evaluated in discrete time in [10] and the integral element has been evaluated in discrete time in [12,13,14]. Furthermore, a closely related PI distributed optimization algorithm developed in [9,11,19] (discussed further in Section 5.1) was discretized in [9].The remainder of this paper will proceed as follows. We first introduce the necessary background material for the analysis of the distributed optimization algorithms, including the problem formulation, the graph-based multi-agent model of the network, and a ...

This paper presents a new method for injecting human inputs in mixed initiative interactions between humans and robots. The method is based on a model predictive control (MPC) formulation, which inevitably involves predicting the system (robot dynamics as well as human inputs) into the future. These predictions are complicated by the fact that the human is interacting with the robot, causing the prediction method itself to have an effect on future human inputs. We investigate and develop different prediction schemes, including fixed and variable horizon MPCs and human input estimators of different orders. Through a search-and-rescue-inspired human operator study, we arrive at the conclusion that the simplest prediction methods outperform the more complex ones, i.e., in this particular case, less is indeed more.Index Terms-human-robot interaction, model-predictive control, mixed initiative initeractions.

This work presents a novel cooperative path planning for formation keeping robots traversing along a road with obstacles and possible narrow passages. A unique challenge in this problem is a requirement for spatial and temporal coordination between vehicles while ensuring collision and obstacle avoidance. A two-step approach is used for fast realtime planning. The first step uses the A* search on a spatiotemporally extended graph to generate an obstacle-free path for the agent while the second step refines this path through local optimization to comply with dynamic and other vehicle constraints. This approach keeps robots close to their intended formation while giving them flexibility to negotiate narrow passages and obstacles, adhering to any given constraints.

Whenever the control task involves the tracking of a reference signal the performance is typically improved if one knows the future behavior of this reference. However, in many applications, this is typically not the case, e.g., when the reference signal is generated by a human operator, and a remedy to this can be to try and model the reference signal over a short time horizon. In this paper, we address the problem of selecting this horizon in an adaptive fashion by minimizing a cost that takes into account the performance of the underlying control problem (that prefers longer time horizons) and the effectiveness of the reference signal model (that prefers shorter time horizons). The result is an adaptive time horizon controller that operates in a manner reminiscent of Model Predictive Control (MPC).

In this paper, a novel, dual-mode model predictive control framework is introduced that combines the dynamic window approach to navigation with reference tracking controllers. This adds a deliberative component to the obstacle avoidance guarantees present in the dynamic window approach as well as allow for the inclusion of complex robot models. The proposed algorithm allows for guaranteed convergence to a goal location while navigating through an unknown environment at relatively high speeds. The framework is applied in both simulation and hardware implementation to demonstrate the computational feasibility and the ability to cope with dynamic constraints and stability concerns. *

This paper investigates proportional-integral distributed optimization when the underlying information exchange network is dynamic. Proportional-integral distributed optimization is a technique which combines consensus-based methods and dual-decomposition methods to form a method which has the convergence guarantees of dual-decomposition and the damped response of the consensus methods. This paper extends PI distributed optimization to allow for dynamic communication networks, permitting agents to change who they can communicate with, without sacrificing convergence to the collective optimum.

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Snake robots are controlled by implementing gaits inspired from their biological counterparts. However, transitioning between these gaits often produces undesired oscillations which cause net movements that are difficult to predict. In this paper we present a framework for implementing gaits which will allow for smooth transitions. We also present a method to determine the optimal time for each module of the snake to switch between gaits in a decentralized fashion. This will allow for each module to participate in minimizing a cost by communicating with a set of modules in a local neighborhood. Both of these developments will help to maintain desired properties of the gaits during transition.