In this work, we present an application of a policy gradient algorithm to a real-time robotic learning problem, where the goal is to maximize the average lift generation of a dynamically scaled robotic wing at a constant Reynolds number (Re). Compared to our previous work, the merit of this work is two-fold. First, a central pattern generator (CPG) model was used as the motion controller, which provided a smooth generation and transition of rhythmic wing motion patterns while the CPG was being updated by the policy gradient, thereby accelerating the sample generation and reducing the total learning time. Second, the kinematics included three degrees of freedom (stroke, deviation, pitching) and were also free of half-stroke symmetry constraint, together they yielded a larger kinematic space which later explored by the policy gradient to maximize the lift generation. The learned wing kinematics used the full range of stroke and deviation to maximize the lift generation, implying that the wing trajectories with larger disk area and lower frequencies were preferred for high lift generation at constant Re. Furthermore, the wing pitching amplitude converged to values between 45°-49° regardless of what the other parameters were. Notably, the learning agent was able to find two locally optimal wing motion patterns, which had distinct shapes of wing trajectory but generated similar cycle-averaged lift.

In this work, we present a successful application of a policy search algorithm to a real-time robotic learning problem, where the goal is to maximize the efficiency of lift generation on a dynamically scaled flapping robotic wing. The robotic wing has two degrees-of-freedom, i.e., stroke and pitch, and operates in a tank filled with mineral oil. For all experiments, the Reynolds number is maintained constant at 1000, where learning is performed for different prescribed stroke amplitudes to find the optimal wing pitching amplitude and the stroke-pitch phase difference that maximize the power loading (PL) of lift generation, a measure of aerodynamic efficiency. For the investigated stroke amplitude range (30°-90°), the efficiency is observed to increase with the stroke amplitude and the lift is mainly generated through the delayed stall, a quasi-steady aerodynamic mechanism. Furthermore, the wing rotation becomes more asymmetric with respect to stroke reversal as the stroke amplitude decreases, indicating an increased use of unsteady lift generation mechanisms at lower stroke amplitudes.

Clock gating is an effective method of reducing power dissipation of a high-performance circuit. However, deployment of gated cells increases the difficulty of optimizing a clock tree. In this paper, we propose a delay-matching approach to addressing this problem. Delay-matching uses gated cells whose timing characteristics are similar to that of their clock buffer (inverter) counterparts. It attains better slew and much smaller latency with comparable clock skew and less area when compared to type-matching. The skew of a delay-matching gated tree, just like the one generated by type-matching, is insensitive to process and operating corner variations. Besides, delay-matching ECO of a gated tree excels in preserving the original timing characteristics of the gated tree.