An arXiv preprint reports close synchronization between two simulated teleoperation robots operating with uncertain dynamics and a fixed communication delay. In the main run, the slave caught up with the master in about 2–3 seconds: an initial joint-1 error of about 0.74 radians died out by roughly 2 seconds, while the errors between force steps were around 10−3 radians.
The result comes from a mathematical model and simulation. The model contained one master and one slave, each a two-degree-of-freedom revolute-joint manipulator. The MATLAB/Simulink simulations included friction, an external disturbance, operator force and a 0.1-second communication delay.
The paper asks whether a compact adaptive radial-basis-function neural-network controller, or RBFNN, can maintain stability and synchronization when both robots have uncertain dynamics and communication is delayed. The supplied metadata identifies it as arXiv preprint version 1, dated 20 Aug. 2026.
A compact way to handle uncertainty
The controller’s adaptive structure uses two scalar quantities. One estimates the size of the ideal RBF weight vector; the other supplies an adaptive bound for friction, external disturbances and errors left by the RBF approximation.
The stability argument places neural adaptation and delay effects inside one Lyapunov–Krasovskii analysis, a framework for systems whose present behavior depends on earlier states. From that analysis, the authors derive delay-dependent linear matrix inequalities, or LMIs, using free-weighting matrices. The LMIs are the test the paper uses to ask whether the required stability conditions can be satisfied for a given delay.
When those LMIs are feasible, the paper states that the sliding variables, synchronization errors and adaptive estimates are uniformly ultimately bounded. In plain language, the claim is that these quantities remain within bounded ranges after the system’s transient behavior under the stated conditions; it is a boundedness result for the model, not a claim that every error becomes exactly zero.
The delay limit was model-specific
The LMI check produced a clear boundary in the tested cases. The conditions were feasible at delays of 0.05, 0.10, 0.15 and 0.20 seconds. Feasibility was at the boundary near 0.256 seconds, while the test at 0.30 seconds was infeasible.
Those numbers are selected mathematical tests, not statistical uncertainty intervals. They describe the point at which this model and its chosen parameters met the paper’s matrix conditions; they do not by themselves establish a universal communication-delay limit.
The main simulation used a 0.1-second delay, which sits within the tested feasible range. It also included friction, an external disturbance and operator force.
In the reported run, the adaptive estimates were described as nondivergent, with only minor short-lived spikes after force steps. The simulated torques stayed within ±200 N·m, reaching the stated limit at startup and at force steps at 12 and 18 seconds. High-frequency chattering was most visible in the first few seconds and after those force changes.
The middle gain setting performed best in this run
The paper then compared three fixed gain settings: low, baseline and high. The sliding gains were diag(30, 30), diag(100, 100) and diag(300, 300), while the corresponding robust gains were 2.5, 5 and 10.
On the paper’s two main measures—mean absolute joint-1 error and settling time, the reported time for the error to settle—the baseline setting came out best. Its mean absolute error was 0.015 rad and its settling time was 1.1 seconds, compared with 0.047 rad and 5.8 seconds for the low setting, and 0.018 rad and 3.8 seconds for the high setting.
The torque numbers rose with the gain setting in the root-mean-square, or RMS, measure of typical control effort. RMS master joint-1 torque was 18 N·m with low gains, 30 N·m at baseline and 37 N·m at high gains. Peak torque was 189, 200 and 200 N·m, respectively.
That pattern is why the authors interpret the baseline as a balance between tracking and effort, while viewing higher gains as mainly increasing chattering and control effort. The comparison remains descriptive: only three fixed settings were tested, so it shows the pattern in these reported runs rather than establishing a general rule for gain selection.
A narrow claim, not a hardware result
The paper’s conclusion is deliberately narrower than a claim about teleoperation in general. The supplied analysis limits it to constant, known-bounded communication delays, a compact RBF input set, a stability analysis that does not include actuator saturation, and simulation of one 2-DOF master–slave pair without measurement noise.
The ±200 N·m figure is a simulation result; actuator saturation was not included in the stability analysis.
The compact input-set assumption also narrows the neural-network claim. The supplied analysis does not establish that the RBF approximation remains valid outside that set, so it does not establish a global result for every possible input.
Nor does the simulation answer how the controller would behave outside the fixed, noise-free, single-pair conditions used here or on physical hardware. Those questions remain open because the evidence is limited to one modeled robot pair under the stated settings.
Taken together, the work is a feasibility report for a particular modeled system. Its central result is that the proposed two-scalar adaptive structure was paired with a delay-dependent stability test, and the simulation showed close synchronization under the proposed controller. Whether that result survives broader operating conditions remains unanswered.
Paper data and sources
Original title: Adaptive RBFNN Control of Uncertain Bilateral Teleoperation Systems with Delay-Dependent LMI Stability Conditions
Authors: Mohammadali Ghaemifar, Arshia Goshtasbi, Arian Hajizadeh et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text