Luis Pantoja-Garcia

This study presents the development of a robust second‐order sliding mode controller (SOSMC) that incorporates position error constraints into the control design. To achieve this, a barrier Lyapunov function (BLF) is employed, enabling the enforcement of predefined bounds on tracking errors throughout the system's evolution. This approach ensures that errors remain within previously known limits, thereby improving safety and reliability in practical applications, particularly robotic systems. The proposed control scheme guarantees the existence of a sliding mode and achieves exponential convergence of the tracking errors, even in the presence of bounded disturbances and model uncertainties. Hence, the main contribution of this study is the integration of the BLF into the SOSMC framework, which not only maintains robustness but also addresses the critical issue of constraint satisfaction. This is often overlooked in traditional sliding mode designs. The effectiveness and improved performance of the proposed controller are validated through simulation studies conducted on a three‐degree‐of‐freedom robotic manipulator and through experiments on a six‐degree‐of‐freedom robotic manipulator. Comparative results demonstrate that, unlike a conventional SOSMC without error constraints, the proposed controller successfully maintains position errors within the specified limits while preserving fast convergence and robustness. These findings highlight the significant benefits of incorporating barrier Lyapunov functions in sliding mode control strategies for systems with strict performance and safety requirements.

The paradigm of reinforcement learning (RL) refers to agents that learn iteratively through continuous interactions with their environment. However, when the value function is unknown, a neural network is used, which is typically encoded into an unknown temporal difference equation. When RL is implemented in physical systems, explicit convergence and stability analyses are required to guarantee the worst-case operations for any trial, even when the initial conditions are set to zero. In this paper, physical RL (p-RL) refers to the application of RL in dynamical systems that interact with their environments, such as robot manipulators in contact tasks and humanoid robots in cooperation or interaction tasks. Unfortunately, most p-RL schemes lack stability properties, which can even be dangerous for specific robot applications, such as those involving contact (constrained) tasks or interaction tasks. Considering an unknown and disturbed DAE2 robot, in this paper a p-RL approach is developed to guaranteeing robust stability throughout a continuous-time-adaptive actor–critic, with local exponential convergence of force–position tracking error. The novel adaptive mechanisms lead to robustness, while an integral sliding mode enforces tracking. Simulations are presented and discussed to show our proposal’s effectiveness, and some final remarks are addressed concerning the structural aspects.

Summary: Model‐based adaptive control suffers over parametrization from the many adaptive parameters compared to the order of system dynamics, leading to sluggish tracking with a poor adaptation transient without robustness. Likewise, adaptive model‐free neurocontrol that relies on the Stone–Weierstrass theorem also suffers from similar problems in addition to over‐fitting to approximate inverse dynamics. This article proposes a novel reinforced adaptive mechanism to guarantee a transient and robustness for the model‐free adaptive control of nonlinear Lagrangian systems. Inspired by the symbiosis of Actor‐Critic (AC) architecture and integral sliding modes, the reinforced stage neural network, analogous to the critic, injects excitation signals to reinforce the parametric learning of the adaptive stage neural network, analogous to the actor to improve the approximation of inverse dynamics. The underlying integral sliding surface error drives improved learning onto a low‐dimensional invariant manifold to guarantee local exponential convergence of tracking errors. Lyapunov stability substantiates the robustness with an improved transient response. Our proposal stands for a hybrid approach between AC and neurocontrol, where the reinforced stage does not require a value function nor reward to provide automatic reinforcement to the adaptive stage parametric adaptation. Dynamic simulations are presented for a nonlinear robot manipulator under different conditions.

Reinforcement learning (RL) is explored for motor control of a novel pneumatic-driven soft robot modeled after continuum media with a varying density. This model complies with closed-form Lagrangian dynamics, which fulfills the fundamental structural property of passivity, among others. Then, the question arises of how to synthesize a passivity-based RL model to control the unknown continuum soft robot dynamics to exploit its input–output energy properties advantageously throughout a reward-based neural network controller. Thus, we propose a continuous-time Actor–Critic scheme for tracking tasks of the continuum 3D soft robot subject to Lipschitz disturbances. A reward-based temporal difference leads to learning with a novel discontinuous adaptive mechanism of Critic neural weights. Finally, the reward and integral of the Bellman error approximation reinforce the adaptive mechanism of Actor neural weights. Closed-loop stability is guaranteed in the sense of Lyapunov, which leads to local exponential convergence of tracking errors based on integral sliding modes. Notably, it is assumed that dynamics are unknown, yet the control is continuous and robust. A representative simulation study shows the effectiveness of our proposal for tracking tasks.