Danger-aware Adaptive Composition of DRL Agents for Self-navigation

Self-navigation, referred as the capability of automatically reaching the goal while avoiding collisions with obstacles, is a fundamental skill required for mobile robots. Recently, deep reinforcement learning (DRL) has shown great potential in the development of robot navigation algorithms. However, it is still difficult to train the robot to learn goal-reaching and obstacle-avoidance skills simultaneously. On the other hand, although many DRL-based obstacle-avoidance algorithms are proposed, few of them are reused for more complex navigation tasks. In this paper, a novel danger-aware adaptive composition (DAAC) framework is proposed to combine two individually DRL-trained agents, obstacle-avoidance and goal-reaching, to construct a navigation agent without any redesigning and retraining. The key to this adaptive composition approach is that the value function outputted by the obstacle-avoidance agent serves as an indicator for evaluating the risk level of the current situation, which in turn determines the contribution of these two agents for the next move. Simulation and real-world testing results show that the composed Navigation network can control the robot to accomplish difficult navigation tasks, e.g., reaching a series of successive goals in an unknown and complex environment safely and quickly.Comment: 7 pages, 9 figure

Semi-Active Control of Dynamically Excited Structures Using Active Interaction Control

This thesis presents a family of semi-active control algorithms termed Active Interaction Control (AIC) used for response control of dynamically excited structures. The AIC approach has been developed as a semiactive means of protecting building structures against large earthquakes. The AIC algorithms include the Active Interface Damping (AID), Optimal Connection Strategy (OCS), and newly developed Tuned Interaction Damping (TID) algorithms. All of the AIC algorithms are founded upon the same basic instantaneous optimal control strategy that involves minimization of an energybased performance index at every time instant. A typical AIC system consists of a primary structure targeted for vibration control, a number of auxiliary structures, and interaction elements that connect the auxiliary structures to the primary structure. Through actively modulating the operating states of the interaction elements according to pre-specified control logic, control forces favorable to the control strategy are reactively developed within the interaction elements and the vibration of the primary structure is thus restrained. The merits of this structural control approach include both high control performance and minimal external power requirement for the operation of the control devices. The latter is important during large earthquakes when power blackouts are likely to occur. Most encouraging is that with currently available technology this control approach can be readily implemented in real structures. In this thesis, the cause for an overattachment problem in the original OCS system is clarified and corresponding counter-measures are proposed. The OCS algorithm is reformulated within an energy framework and therefore all of the AIC control algorithms are unified under the same instantaneous optimal control strategy. To implement the AIC algorithms into multi-degree-of-freedom systems, two approaches are formulated in this thesis: the Modal Control and Nodal Control approaches. The Modal Control approach directs the control effort to certain dominant response modes, and the Nodal Control approach directly controls the response quantities in physical space. It is found that the Modal Control approach is more efficient than the Nodal Control approach. The effectiveness of the AIC control algorithms is verified through numerical simulation results for three-story, nine-story and twenty-story steel-framed buildings. The statistical behavior of the AIC system is evaluated based on a Monte Carlo simulation

On Fourier restriction type problems on compact Lie groups

In this article, we obtain new results for Fourier restriction type problems on compact Lie groups. We first provide a sharp form of $L^p$ estimates of irreducible characters in terms of their Laplace-Beltrami eigenvalue and as a consequence provide some sharp $L^p$ estimates of joint eigenfunctions for the ring of invariant differential operators. Then we improve upon the previous range of exponent for scale-invariant Strichartz estimates for the Sch\"odinger equation, and prove $L^p$ bounds of Laplace-Beltrami eigenfunctions in terms of their eigenvalue matching the known bounds on tori. The main novelties in our approach consist of a barycentric-semiclassical subdivision of the Weyl alcove and sharp $L^p$ estimates on each component of this subdivision of some weight functions coming out of the Weyl denominator.Comment: v2: More references added to exempt proof of some lemmas; more eigenfunction bounds proved; added some joint eigenfunction bounds. v3: Part II of arXiv:2005.00429v1 moved here. v4: Corrected a few error