Contact-Implicit Trajectory Optimization Based on a Variable Smooth Contact Model and Successive Convexification

In this paper, we propose a contact-implicit trajectory optimization (CITO) method based on a variable smooth contact model (VSCM) and successive convexification (SCvx). The VSCM facilitates the convergence of gradient-based optimization without compromising physical fidelity. On the other hand, the proposed SCvx-based approach combines the advantages of direct and shooting methods for CITO. For evaluations, we consider non-prehensile manipulation tasks. The proposed method is compared to a version based on iterative linear quadratic regulator (iLQR) on a planar example. The results demonstrate that both methods can find physically-consistent motions that complete the tasks without a meaningful initial guess owing to the VSCM. The proposed SCvx-based method outperforms the iLQR-based method in terms of convergence, computation time, and the quality of motions found. Finally, the proposed SCvx-based method is tested on a standard robot platform and shown to perform efficiently for a real-world application.Comment: Accepted for publication in ICRA 201

Maximizing Profit with Convex Costs in the Random-order Model

Suppose a set of requests arrives online: each request gives some value v_i if accepted, but requires using some amount of each of d resources. Our cost is a convex function of the vector of total utilization of these d resources. Which requests should be accept to maximize our profit, i.e., the sum of values of the accepted demands, minus the convex cost? We consider this problem in the random-order a.k.a. secretary model, and show an O(d)-competitive algorithm for the case where the convex cost function is also supermodular. If the set of accepted demands must also be independent in a given matroid, we give an O(d^3 alpha)-competitive algorithm for the supermodular case, and an improved O(d^2 alpha) if the convex cost function is also separable. Here alpha is the competitive ratio of the best algorithm for the submodular secretary problem. These extend and improve previous results known for this problem. Our techniques are simple but use powerful ideas from convex duality, which give clean interpretations of existing work, and allow us to give the extensions and improvements

Regional groupings among microstates

Forming a regional grouping with neighboring nations may be one way for microstates to overcome a major problem: Because of their weak bargaining power and high fixed costs of negotiation, microstates are at a severe disadvantage in dealing with the rest of the world. They don't have the human and physical resources to unilaterally conduct the various bilateral and multilateral negotiations a developing nation typically conducts. The authors present a model in which the decision to form, expand, or join a regional club is based on reduced negotiating costs and increased bargaining power, rather than on the traditional costs and benefits of trade integration (which might be miniscule for a microstate and might even generate welfare losses). Under various conditions for entry, the model is used to determine the equilibrium group size, which is shown to be positively correlated with the number of issues to be tackled, the degree of similarity among countries, and the per-issue costs of international negotiation. They use the case of the Caribbean Community (CARICOM) to show the model's relevance in the real world. The countries that belong to CARICOM pooled their negotiating resources and formulated common policy stances. Despite its relatively limited impact on trade and investments, CARICOM served as a political instrument in joint negotiations on trade and investment with larger countries and regional trade blocs. By establishing a union, the CARICOM countries succeeded in making their voices heard on a variety of issues in a way none of them could have done alone.Economic Theory&Research,Health Systems Development&Reform,Environmental Economics&Policies,Decentralization,Scientific Research&Science Parks,Economic Theory&Research,Trade and Regional Integration,Environmental Economics&Policies,Scientific Research&Science Parks,Science Education

Social Exchange and Common Agency in Organizations

We study the relation between formal incentives and social exchange in organizations where employees work for several managers and reciprocate a manager’s attention with higher effort. To this end we develop a common agency model with two-sided moral hazard. We show that when effort is contractible but attention is not, the first-best can be achieved through granting autonomy of effort choice to employees and giving bonus pay to both managers and employees. When neither effort nor attention are contractible, an ‘attention race’ arises, as each manager tries to sway the employee’s effort his way. While this may result in too much social exchange, the attention race may also be a blessing because it alleviates managers’ moral-hazard problem in attention provision. Lastly, we derive the implications of these contract imperfections for optimal organizational design.social exchange, reciprocity, incentive contracts, common agency, organizational design