Towards Fine-Grained Online Adaptive Approximation Control for Dense SLAM on Embedded GPUs

Dense SLAM is an important application on an embedded environment. However, embedded platforms usually fail to provide enough computation resources for high-accuracy real-time dense SLAM, even with high-parallelism architecture such as GPUs. To tackle this problem, one solution is to design proper approximation techniques for dense SLAM on embedded GPUs. In this work, we propose two novel approximation techniques, critical data identification and redundant branch elimination. We also analyze the error characteristics of the other two techniques—loop skipping and thread approximation. Then, we propose SLaPP, an online adaptive approximation controller, which aims to control the error to be under an acceptable threshold. The evaluation shows SLaPP can achieve 2.0× performance speedup and 30% energy saving on average compared to the case without approximation.

Asymptotics of $L_p$-error for adaptive approximation of $n$-variable functions by harmonic splines

For a twice continuously differentiable function, defined on $n$-dimensional unit cube, we obtain sharp asymptotics of $L_p$-error for approximation by harmonic splines, and construct the asymptotically optimal sequence of partitions.

Proxy-Based Sliding Mode Vibration Control with an Adaptive Approximation Compensator for Euler-Bernoulli Smart Beams

Proxy-based sliding mode control PSMC is an improved version of PID control that combines the features of PID and sliding mode control SMC with continuously dynamic behaviour. However, the stability of the control architecture maybe not well addressed. Consequently, this work is focused on modification of the original version of the proxy-based sliding mode control PSMC by adding an adaptive approximation compensator AAC term for vibration control of an Euler-Bernoulli beam. The role of the AAC term is to compensate for unmodelled dynamics and make the stability proof more easily. The stability of the proposed control algorithm is systematically proved using Lyapunov theory. Multi-modal equation of motion is derived using the Galerkin method. The state variables of the multi-modal equation are expressed in terms of modal amplitudes that should be regulated via the proposed control system. The proposed control structure is implemented on a simply supported beam with two piezo-patches. The simulation experiments are performed using MATLAB/SIMULINK package. The locations of piezo-transducers are optimally placed on the beam. A detailed comparison study is implemented including three scenarios. Scenario 1 includes disturbing the smart beam while no feedback loop is established (open-loop system). In scenario 2, a PD controller is applied on the vibrating beam. Whereas, scenario 3 includes implementation of the PSMC+AAC. For all previously mentioned scenarios, two types of disturbances are applied separately: 1) an impulse force of 1 N peak and 1 s pulse width, and 2) a sinusoidal disturbance with 0.5 N amplitude and 20 Hz frequency. For impulse disturbance signals, the results show the superiority of the PSMC+AAC in comparison with the conventional PD control. Whereas, both the PSMC+ACC and the PD control work well in the case of a sinusoidal disturbance signal and the superiority of the PSMC is not clear.