A Sequential Quadratic Programming Approach to the Solution of Open-Loop Generalized Nash Equilibria

Dynamic games can be an effective approach to modeling interactive behavior between multiple non-cooperative agents and they provide a theoretical framework for simultaneous prediction and control in such scenarios. In this work, we propose a numerical method for the solution of local generalized Nash equilibria (GNE) for the class of open-loop general-sum dynamic games for agents with nonlinear dynamics and constraints. In particular, we formulate a sequential quadratic programming (SQP) approach which requires only the solution of a single convex quadratic program at each iteration. Central to the robustness of our approach is a non-monotonic line search method and a novel merit function for SQP step acceptance. We show that our method achieves linear convergence in the neighborhood of local GNE and we derive an update rule for the merit function which helps to improve convergence from a larger set of initial conditions. We demonstrate the effectiveness of the algorithm in the context of car racing, where we show up to 32\% improvement of success rate when comparing against a state-of-the-art solution approach for dynamic games. \url{https://github.com/zhu-edward/DGSQP}

Learning Model Predictive Control with Error Dynamics Regression for Autonomous Racing

This work presents a novel Learning Model Predictive Control (LMPC) strategy for autonomous racing at the handling limit that can iteratively explore and learn unknown dynamics in high-speed operational domains. We start from existing LMPC formulations and modify the system dynamics learning method. In particular, our approach uses a nominal, global, nonlinear, physics-based model with a local, linear, data-driven learning of the error dynamics. We conduct experiments in simulation, 1/10th scale hardware, and deployed the proposed LMPC on a full-scale autonomous race car used in the Indy Autonomous Challenge (IAC) with closed loop experiments at the Putnam Park Road Course in Indiana, USA. The results show that the proposed control policy exhibits improved robustness to parameter tuning and data scarcity. Incremental and safety-aware exploration toward the limit of handling and iterative learning of the vehicle dynamics in high-speed domains is observed both in simulations and experiments.Comment: Submitted to ICRA 202

Inclined Surface Locomotion Strategies for Spherical Tensegrity Robots

This paper presents a new teleoperated spherical tensegrity robot capable of performing locomotion on steep inclined surfaces. With a novel control scheme centered around the simultaneous actuation of multiple cables, the robot demonstrates robust climbing on inclined surfaces in hardware experiments and speeds significantly faster than previous spherical tensegrity models. This robot is an improvement over other iterations in the TT-series and the first tensegrity to achieve reliable locomotion on inclined surfaces of up to 24\degree. We analyze locomotion in simulation and hardware under single and multi-cable actuation, and introduce two novel multi-cable actuation policies, suited for steep incline climbing and speed, respectively. We propose compelling justifications for the increased dynamic ability of the robot and motivate development of optimization algorithms able to take advantage of the robot's increased control authority.Comment: 6 pages, 11 figures, IROS 201

Distributed Learning Model Predictive Control for Linear Systems

This paper presents a distributed learning model predictive control (DLMPC) scheme for distributed linear time invariant systems with coupled dynamics and state constraints. The proposed solution method is based on an online distributed optimization scheme with nearest-neighbor communication. If the control task is iterative and data from previous feasible iterations are available, local data are exploited by the subsystems in order to construct the local terminal set and terminal cost, which guarantee recursive feasibility and asymptotic stability, as well as performance improvement over iterations. In case a first feasible trajectory is difficult to obtain, or the task is non-iterative, we further propose an algorithm that efficiently explores the state-space and generates the data required for the construction of the terminal cost and terminal constraint in the MPC problem in a safe and distributed way. In contrast to other distributed MPC schemes which use structured positive invariant sets, the proposed approach involves a control invariant set as the terminal set, on which we do not impose any distributed structure. The proposed iterative scheme converges to the global optimal solution of the underlying infinite horizon optimal control problem under mild conditions. Numerical experiments demonstrate the effectiveness of the proposed DLMPC scheme

Structure and Kinetic Investigation of Streptococcus pyogenes Family GH38 α-Mannosidase

BACKGROUND: The enzymatic hydrolysis of alpha-mannosides is catalyzed by glycoside hydrolases (GH), termed alpha-mannosidases. These enzymes are found in different GH sequence-based families. Considerable research has probed the role of higher eukaryotic "GH38" alpha-mannosides that play a key role in the modification and diversification of hybrid N-glycans; processes with strong cellular links to cancer and autoimmune disease. The most extensively studied of these enzymes is the Drosophila GH38 alpha-mannosidase II, which has been shown to be a retaining alpha-mannosidase that targets both alpha-1,3 and alpha-1,6 mannosyl linkages, an activity that enables the enzyme to process GlcNAc(Man)(5)(GlcNAc)(2) hybrid N-glycans to GlcNAc(Man)(3)(GlcNAc)(2). Far less well understood is the observation that many bacterial species, predominantly but not exclusively pathogens and symbionts, also possess putative GH38 alpha-mannosidases whose activity and specificity is unknown. METHODOLOGY/PRINCIPAL FINDINGS: Here we show that the Streptococcus pyogenes (M1 GAS SF370) GH38 enzyme (Spy1604; hereafter SpGH38) is an alpha-mannosidase with specificity for alpha-1,3 mannosidic linkages. The 3D X-ray structure of SpGH38, obtained in native form at 1.9 A resolution and in complex with the inhibitor swainsonine (K(i) 18 microM) at 2.6 A, reveals a canonical GH38 five-domain structure in which the catalytic "-1" subsite shows high similarity with the Drosophila enzyme, including the catalytic Zn(2+) ion. In contrast, the "leaving group" subsites of SpGH38 display considerable differences to the higher eukaryotic GH38s; features that contribute to their apparent specificity. CONCLUSIONS/SIGNIFICANCE: Although the in vivo function of this streptococcal GH38 alpha-mannosidase remains unknown, it is shown to be an alpha-mannosidase active on N-glycans. SpGH38 lies on an operon that also contains the GH84 hexosaminidase (Spy1600) and an additional putative glycosidase. The activity of SpGH38, together with its genomic context, strongly hints at a function in the degradation of host N- or possibly O-glycans. The absence of any classical signal peptide further suggests that SpGH38 may be intracellular, perhaps functioning in the subsequent degradation of extracellular host glycans following their initial digestion by secreted glycosidases

Intergenomic and epistatic interactions control free radical mediated pancreatic β-cell damage.

Alloxan (AL)-generated Reactive Oxygen Species (ROS) selectively destroy insulin-producing pancreatic β-cells. A previous genome-wide scan (GWS) using a cohort of 296 F2 hybrids between NOD (AL-sensitive) and ALR (AL-resistant) mice identified linkages contributing to β-cell susceptibility or resistance to AL-induced diabetes on Chromosomes (Chr) 2, 3, 8, and a single nucleotide polymorphism i