Robotic control systems are increasingly relying on distributed feedback controllers to tackle complex sensing and decision problems such as those found in highly articulated human-centered robots. These demands come at the cost of a growing computational burden and, as a result, larger controller latencies. To maximize robustness to mechanical disturbances by maximizing control feedback gains, this paper emphasizes the necessity for compromise between high- and low-level feedback control effort in distributed controllers. Specifically, the effect of distributed impedance controllers is studied where damping feedback effort is executed in close proximity to the control plant and stiffness feedback effort is executed in a latency-prone centralized control process. A central observation is that the stability of high impedance distributed controllers is very sensitive to damping feedback delay but much less to stiffness feedback delay. This study pursues a detailed analysis of this observation that leads to a physical understanding of the disparity. Then a practical controller breakdown gain rule is derived to aim at enabling control designers to consider the benefits of implementing their control applications in a distributed fashion. These considerations are further validated through the analysis, simulation and experimental testing on high performance actuators and on an omnidirectional mobile base.
The field of haptics @cite_17 , networked control @cite_12 @cite_11 and teleoperation @cite_15 have also thoroughly studied delays and filtering effects. Specifically, haptics is more related to our work because it is a special case of distributed control in which the master and slave devices require separate feedback controllers. Due to the destabilizing effects of time delays, significant effort has been put forth to ensure systems are stable by enforcing passivity criteria @cite_17 . Other works @cite_23 @cite_10 @cite_19 further relax this constraint and focus on how delay and filtering affect stability. Related work has been performed considering additional real-world effects such as quantization and coulomb friction on system stability @cite_32 . Once more, theses studies do not analyze nor exploit the large sensitivity discrepancy between stiffness and damping feedback loops nor propose solutions to increase performance based on this discrepancy.
@cite_17 @cite_32 @cite_19 @cite_23 @cite_15 @cite_10 @cite_12 @cite_11
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Rendering stiff virtual objects remains a core challenge in the field of haptics. A study of this problem is presented, which relates the maximum achievable object stiffness to the elements of the control loop. In particular, we examine how the sampling rate, quantization, computational delay, and amplifier dynamics interact with the inertia, natural viscous, and Coulomb damping of the haptic device. Nonlinear effects create distinct stability regions, and many common devices operate stably, yet in violation of passivity criteria. An energy-based approach provides theoretical insights, supported by simulations, experimental data, and a describing function analysis. The presented results subsume previously known stability conditions In this paper, we consider a robust network control problem. We consider linear unstable and uncertain discrete time plants with a network between the sensor and controller and the controller and plant. We investigate the effect of data drop out in the form of packet losses. Four distinct control schemes are explored and sufficient conditions to ensure almost sure stability of the closed loop system are derived for each of them in terms of minimum packet arrival rate and the maximum uncertainty. I. INTRODUCTION In the past decade, networked control systems (NCS) have gained much attention from both the control com- munity and the network and communication community. When compared with classical feedback control system, networked control systems have several advantages. For example, they can reduce the system wiring, make the system easy to operate and maintain and later diagnose in case of malfunctioning, and increase system agility (20). Although NCS have advantages, inserting a network in between the plant and the controller introduces many problems as well. For instance, zero-delayed sensing and actuation, perfect information and synchronization are no longer guaranteed in the new system architecture as only finite bandwidth is available and data packet drops and delays may occur due to network traffic conditions. These must be revisited and analyzed before networked control systems become prevalent. Recently, many researchers have spent effort on these issues and some significant results were obtained and many are in progress. Many of the aforementioned issues are studied separately. Tatikonda (19) and Sahai (13) have presented some interesting results in the area of control under communication constraints. Specifically, Tatikonda gave a necessary and sufficient condition on the channel data rate such that a noiseless LTI system in the closed loop is asymptotically stable. He also gave rate results for stabilizing a noisy LTI system over a digital channel. Sahai proposed the notion of anytime capacity to deal with real time estimation and control for a networked control system. In our paper (17), the authors have considered various rate issues under finite bandwidth, packet drops and finite controls. An optimal bit allocation scheme is given in (16) under the networked setting. The effect of pacekt drops on state estimation was studied by Sinopoli, et. al. in (3). It has further been investigated by many researchers including the present authors in (15) and (6). In this paper, the stability of a Networked Control System (NCS) with time-varying delays is analyzed. A discrete-time state-space model is used to analyze the dynamics of the NCS. The delay is introduced by the network itself and is assumed to be upperbounded by a fraction of the sample-time. A typical motion control example is presented in which the time-variation of the delay results in an unstable system, although for each fixed delay the system is stable. Conditions in terms of LMIs are presented guaranteeing the robust asymptotic stability of the discrete-time system, given bounds on the uncertain time-varying delay. Moreover, it is shown that the robust stability conditions also guarantee asymptotic stability of the intersample behavior. Additionally, LMIs are presented to synthesize a feedback controller that stabilizes the system for the uncertain time-varying delay. The results are illustrated on an example concerning a mechanical model of a motor driving a roller in a printer. Shared compliant control has been incorporated into an advanced six-degree-of-freedom force-reflecting telemanipulation system. With this system the authors have investigated the effect of time delay on human telemanipulation task performance. Time delays of between 2 and 4096 ms were introduced between master and slave arms, and high-precision peg-in-hole tasks were performed by six test operators with two modes of control: kinesthetic force feedback (KFF) and shared compliant control (SCC). Task performance was quantified in terms of the completion time (CT) and the sum of square forces (SOSF). The experimental results demonstrate the superiority of SCC over KFF for time-delayed telemanipulation. SCC has significantly lower rates of increase than KFF in both CT and SOSF with time delay. Only SCC enabled task performance at delays above 1 s. Constant force maintenance tasks were also performed to investigate the effect of time delay on the stability of force reflection. SCC also has beneficial effects on telemanipulation without time delay. >