A Delay-free Control Method Based On Function Approximation And Broadcast For Robotic Surface And Multiactuator Systems

TL;DR

This work tackles the time-delay bottleneck in large robotic surface arrays by introducing a broadcast-based control scheme where a central computer distributes shape-approximation coefficients and each actuator computes its input locally. By employing function-approximation strategies—namely discrete cosine transform (DCT) and matching pursuit (MP)—the method achieves system-size-independent delays ($\tau \propto N^{\alpha}$ with $\alpha=0$) while maintaining shape accuracy. Experimental validation on a $4\times 4$ pin array shows that the broadcast approach preserves timing even with actuator dynamics, and MP can efficiently capture localized patterns with fewer messages than DCT or sequential control. The results demonstrate the feasibility of scalable, high-resolution robotic surfaces and provide a foundation for applying the approach to more complex multi-actuator systems and manipulative tasks.

Abstract

Robotic surface consisting of many actuators can change shape to perform tasks, such as facilitating human-machine interactions and transporting objects. Increasing the number of actuators can enhance the robot's capacity, but controlling them requires communication bandwidth to increase equally in order to avoid time delays. We propose a novel control method that has constant time delays no matter how many actuators are in the robot. Having a distributed nature, the method first approximates target shapes, then broadcasts the approximation coefficients to the actuators, and relies on themselves to compute the inputs. We build a robotic pin array and measure the time delay as a function of the number of actuators to confirm the system size-independent scaling behavior. The shape-changing ability is achieved based on function approximation algorithms, i.e. discrete cosine transform or matching pursuit. We perform experiments to approximate target shapes and make quantitative comparison with those obtained from standard sequential control method. A good agreement between the experiments and theoretical predictions is achieved, and our method is more efficient in the sense that it requires less control messages to generate shapes with the same accuracy. Our method is also capable of dynamic tasks such as object manipulation.

Figures (7)

• Figure 1: (a) The 4$\times$4 pin array; (b) time delay scaling exponent $\alpha$ is plotted vs. the number of actuators. Our work is highlighted in a yellow star.
• Figure 2: An illustration of our control method. At time $t$, the control message $\gamma_t$ is broadcast to all modules. In the n'th module, the control input is calculated via a function $f$ and its arguments $\gamma_t$ and $x_n$.
• Figure 3: (a) A picture of a single linear actuation module. The rectangular cover is removed to expose mechanical components; (b) block diagram of the electronic system. The arrows indicate information flows.
• Figure 4: Experimental time delay scaling without actuator dynamics. (a) The control inputs of two actuators when using sequential control method. The yellow (blue) line is the first (last) actuator in a two-actuator system; (b) the control inputs of the same actuators when using our control method; (c) averaged time delay is plotted as a function of the number of actuators for the two control methods and at different communication rates (expressed in $T_{\rm msg}$). Each point is an average of at least $20$ time delay values observed in (a) or (b). Darker color represents larger $T_{\rm msg}$. The triangles (circles) are experimentally measured time delays with the sequential (our) control method, and the dashed lines are theoretical predictions.
• Figure 5: Experimental time delay scaling with actuator dynamics. (a) The motor shaft angular position when using the sequential control method. The yellow (blue) trace is the first (last) actuator in a 16-actuator system, with their time delay indicated in dashed line; (b) the shaft position of the same actuators when using our control method; (c) time delay is plotted as a function of the number of actuators for the two control methods. The triangles and circles are experimentally measured time delays with the sequential and our control method, respectively. Each point is an average of at least 6 time delays, and the errorbar is one standard deviation. The dashed lines are theoretical predictions.