Delay-Adaptive Control of a 7-DOF Robot Manipulator: Design and Experiments
Abstract
We present an analytical design and experimental verification of trajectory-tracking control of a 7-DOF robot manipulator with an unknown long actuator delay. To compensate for this unknown delay, we formulate a delay-adaptive prediction-based control strategy to simultaneously estimate the unknown delay while driving the robot manipulator toward the desired trajectory. To the best of the authors’ knowledge, this article is the first to present a delay-adaptive approach for a nonlinear system with multiple inputs. Through Lyapunov analysis, we first establish local input-to-state stability with respect to temporal derivatives of the reference trajectory, along with regulation of the tracking errors when the reference trajectory approaches a stationary configuration. Then, through both simulation and experiment, we demonstrate that the proposed controller is capable of tracking the desired trajectory with desirable performance despite a large initial delay mismatch, which would cause nonadaptive prediction-based controllers to become unstable.
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Implementation of nonlinear predictor feedbacks is thoroughly addressed in [17], and its practical feasibility is supported by experimental implementations [1], [32], [33].
“Implementation of nonlinear predictor feedbacks is thoroughly addressed in [17], while its practical feasibility is supported by experimental implementations [1], [32], [33].”
From Semiglobal Switched Predictor-Feedback Stabilization of Nonlinear Systems With Input Delay and State/Input Quantization (2026) · cites this paper as [1]
If x(t), u(t), and u̇(t) are uniformly bounded, and the initial estimation error |D̃(0)| < Dmax, then there exists H such that |ρ_D(t)| ≤ H and D̃(t)ρ_D(t) ≥ 0, ensuring the delay estimation error is monotonically non-increasing.
“Lemma 1 ( [21]): If x(t), u(t), and u(t) are uniformly bounded, and the initial estimation error D(0) = D -D(0), where D(t) ≜ D -D(t), is bounded by | D(0)| < Dmax , then there exists a parameter H ∈ R + such that |ρ D (t)| ≤ H, and the estimation error D(t) satisfies: D(t)ρ D (t) ≥ 0, which ensures that the delay estimation error is monotonically non-increasing.”
From Minimizing Conservatism in Safety-Critical Control for Input-Delayed Systems via Adaptive Delay Estimation (2024) · cites this paper as [21]
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“…with the initial condition given by x ( t − β ) , where β > 0 is a design parameter, using an estimated input delay, ˆ D [21]: where δ ∈ [0 , 1] is a distribution variable, and f 0 ( · , · ) takes form, We utilize property (3) to formulate the cost function [21]: where ˆ D = D is a minimizer of J .”
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- Authors
- Bertino, A., Naseradinmousavi, P., & Krstic, M.
- Affiliations
- San Diego State University (US)
- Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA, USA
- Venue
- IEEE Transactions on Control Systems Technology
- Published
- 2022-11
- Volume
- 30
- Issue
- 6
- Pages
- 2506-2521
- ISSN
- 1063-6536 (ISSN-L)
- 1558-0865
- 2374-0159
- OpenAlex
- W4214892943
- Cited by
- 33
- References
- 35
- Citations by year
- 2026: 7 · 2025: 10 · 2024: 6 · 2023: 5 · 2022: 5
- FWCI
- 2.62
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- Locations
- IEEE Transactions on Control Systems Technology (publishedVersion)
- Funders
- National Science Foundation (#1823951-1823983)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Adaptive Control of Nonlinear Systems
- Physical Sciences › Engineering › Mechanical Engineering › Teleoperation and Haptic Systems
- Keywords
- trajectory tracking, time delay estimation, predictive control, input-to-state stability, Lyapunov analysis, delay mismatch
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