Underactuated Robotic Systems Research Articles

Experimental Evaluation of a Takagi–Sugeno Fuzzy Controller for an EV3 Ballbot System

In this paper, experimental results about the performance of a Takagi–Sugeno Fuzzy Controller (TSFC) for an EV3 Ballbot Robotic System (EV3BRS) are reported. The physical configuration of the EV3BRS has the form of an inverted pendulum mounted on a ball. The EV3BRS is an underactuated robotic system with four outputs and two control torques. In this work, following the Takagi–Sugeno (TS) fuzzy control design methodology, the Parallel Distributed Compensation (PDC) approach is used in the design of the TSFC. The EV3BRS’s TS Fuzzy Model (TSFM) design comes from linearization of the nonlinear model around two operation points near the upright position of EV3BRS’s body. The Linear Matrix Inequality (LMI) approach was used to obtain the feedback gains for every local linear controller, guaranteeing, via a conservative stability condition, the global asymptotic stability of the overall fuzzy control system. The main goal of the control task consists of maintaining the EV3BRS’s body at its upright position. Measurement and control data from and to the EV3BRS are transferred via telecontrol and telemetry. The appropriate performance of the controller design is corroborated via experimentation.

Adaptive Hierarchical Sliding Mode Control Based on Extended State Observer for Underactuated Robotic System

Adaptive Hierarchical Sliding Mode Control Based on Extended State Observer for Underactuated Robotic System

Concurrent Learning-Based Adaptive Control of Underactuated Robotic Systems With Guaranteed Transient Performance for Both Actuated and Unactuated Motions.

With the wide applications of underactuated robotic systems, more complex tasks and higher safety demands are put forward. However, it is still an open issue to utilize "fewer" control inputs to satisfy control accuracy and transient performance with theoretical and practical guarantee, especially for unactuated variables. To this end, for underactuated robotic systems, this article designs an adaptive tracking controller to realize exponential convergence results, rather than only asymptotic stability or boundedness; meanwhile, unactuated states exponentially converge to a small enough bound, which is adjustable by control gains. The maximum motion ranges and convergence speed of all variables both exhibit satisfactory performance with higher safety and efficiency. Here, a data-driven concurrent learning (CL) method is proposed to compensate for unknown dynamics/disturbances and improve the estimate accuracy of parameters/weights, without the need for persistency of excitation or linear parametrization (LP) conditions. Then, a disturbance judgment mechanism is utilized to eliminate the detrimental impacts of external disturbances. As far as we know, for general underactuated systems with uncertainties/disturbances, it is the first time to theoretically and practically ensure transient performance and exponential convergence speed for unactuated states, and simultaneously obtain the exponential tracking result of actuated motions. Both theoretical analysis and hardware experiment results illustrate the effectiveness of the designed controller.

Adaptive optimal control of under-actuated robotic systems using a self-regulating nonlinear weight-adjustment scheme: Formulation and experimental verification.

This paper formulates an innovative model-free self-organizing weight adaptation that strengthens the robustness of a Linear Quadratic Regulator (LQR) for inverted pendulum-like mechatronic systems against perturbations and parametric uncertainties. The proposed control procedure is devised by using an online adaptation law to dynamically adjust the state weighting factors of LQR's quadratic performance index via pre-calibrated state-error-dependent hyperbolic secant functions (HSFs). The updated state-weighting factors re-compute the optimal control problem to modify the state-compensator gains online. The novelty of the proposed article lies in adaptively adjusting the variation rates of the said HSFs via an auxiliary model-free online self-regulation law that uses dissipative and anti-dissipative terms to flexibly re-calibrate the nonlinear function's waveforms as the state errors vary. This augmentation increases the controller's design flexibility and enhances the system's disturbance rejection capacity while economizing control energy expenditure under every operating condition. The proposed self-organizing LQR is analyzed via customized hardware-in-loop (HIL) experiments conducted on the Quanser's single-link rotational inverted pendulum. As compared to the fixed-gain LQR, the proposed SR-EM-STC delivers an improvement of 52.2%, 16.4%, 55.2%, and 42.7% in the pendulum's position regulation behavior, control energy expenditure, transient recovery duration, and peak overshoot, respectively. The experimental outcomes validate the superior robustness of the proposed scheme against exogenous disturbances.

Cross-backstepping control with prescribed performance for input-coupled underactuated systems under arbitrary initial conditions

Underactuated robotic systems with input coupling are widely applied in practice. However, designing controllers for such systems poses significant challenges due to the complexities arising from input coupling. To address this issue, this paper proposes a novel cross-backstepping control strategy based on a composite error transformation. The transformation compresses the system’s initial error into a definable range to deal with the issue of initial value dependency of prescribed performance control, while maintaining the transient and steady state of the system. Based on such a technique, a cross-backstepping controller is proposed whose core idea lies in constructing a virtual term that crosses with coupled states to generate a unified form, which serves as a bridge between multiple coupled states and a single actual control input. Furthermore, a nonlinear disturbance observer is introduced to improve the robustness of the system. The stability of the closed-loop system is proved according to the Lyapunov theorem, and two numerical examples of underactuated robotic systems with coupled inputs are presented to demonstrate the effectiveness of the proposed approach.

Gyroscopic Balancer-Enhanced Motion Control of an Autonomous Bikebot

Abstract Bikebot (i.e., bicycle-based robot) is a class of underactuated balance robotic systems that require simultaneous trajectory tracking and balance control tasks. We present a tracking and balance control design of an autonomous bikebot. The external-internal convertible structure of the bikebot dynamics is used to design a causal feedback control to achieve both the tracking and balance tasks. A balance equilibrium manifold is used to define and capture the platform balance profiles and coupled interaction with the trajectory tracking performance. To achieve fully autonomous navigation, a gyrobalancer actuation is integrated with the steering and velocity control for stationary platform balance and stationary-moving switching. Stability and convergence analyses are presented to guarantee the control performance. Extensive experiments are presented to validate and demonstrate the autonomous control design. We also compare the autonomous control performance with human riding experiments and similar action strategies are found between them.

Backstepping-Based Tracking Control of Underactuated Aquatic Robots

Increased interest in the use of autonomous aquatic robots in a variety of applications has led to the need for efficient and precise control of these robots. In particular, accurate trajectory control has become of importance in many of these applications. However, the highly nonlinear and underactuated dynamics of many aquatic robots present significant challenges in control. In this work, we propose a trajectory-tracking control approach for a general class of underactuated aquatic robotic systems undergoing planar motion. We demonstrate how a backstepping-based control scheme can be synthesized to ultimately bound three tracking errors (2-D position and orientation), despite the underactuated nature of the system. Via multi-time-scale analysis of singularly perturbed systems, we prove how the control scheme achieves boundedness and convergence of the tracking errors to a neighborhood of the origin. Finally, we implement the proposed scheme on a robotic fish and demonstrate its efficacy via experimental results. This article is complemented with a video: https://youtu.be/7007tUQd3KI.

Opposite Treatment on Null Space: A Unified Control Framework for a Class of Underactuated Robotic Systems With Null Space Avoidance

Design of feedback control for underactuated robotic systems (URSs) is often complex and nonintuitive due to the inherent incapability of generating arbitrary velocities or accelerations at each moment. Researchers have designed various controllers; however, there are few unified intuitive feedback stabilization controllers for a wide range of URSs. In this article, we propose a real-time and unified control framework for a class of URSs with three states and two inputs based on the intuition of avoiding null space. To control diverse URSs, unlike transforming them to canonical forms, we approach them from an inverse perspective based on a Jacobian-like mapping matrix and disclose a fundamental issue, null space attraction, which fails all Jacobian-based standard kinematics control. An opposite treatment on null space, avoiding null space, is applied to oppose null space attraction, allowing the standard kinematics controllers to keep control authority. Overall, the proposed control framework consisting of a standard kinematics controller and a null space avoidance controller can fundamentally solve point-to-point stabilization for the class of driftless URSs and also render <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula> -neighborhood stabilization for URSs with a nonvanishing and constant drift. Both the convergence properties are rigorously analyzed. Simulations and applications are conducted to demonstrate the generality, effectiveness, and robustness of our controllers.

Energy based control of a bi-stable and underactuated soft robotic system based on dielectric elastomer actuators*

In this paper, we propose an energy based control approach for a class of underactuated soft robotic systems. The considered case study consists of an elastic structure driven by soft dielectric elastomer actuators, and is able to achieve large bending displacement thanks to a bi-stable design concept. The bi-stability feature, however, causes the system to exhibit an unstable behavior in open-loop. After providing a port-Hamiltonian description of the soft robotic system, sufficient conditions for the existence of an energy based stabilizing controller are provided. A linear matrix inequality approach is then proposed to practically address the design of the controller gain. The effectiveness of the method is verified by means of simulation studies, conducted on an experimentally validated model of the real-life device.

Active space control of underactuated robots: From adaptation to robustness to optimality

SummaryThis article develops a controller for the active space control of underactuated robotic systems with the ability to adapt to unknown parameters, be robust to unmodeled dynamics and disturbances, and generate optimal control policies in a pointwise fashion. To achieve the set forth objectives, the model dynamics are first partitioned into active and passive spaces. As a remedy for nonlinear coupling between these spaces, the system's acceleration is estimated for use in the control algorithm. The modeling uncertainty associated with both unknown system parameters and unknown control map is then estimated by proposing a concurrent learning adaptive approach. An online quadratic program (QP) is synthesized utilizing an intelligent robust control Lyapunov function (IRCLF) constraint to ensure the system stability with minimal control effort while using the estimates of the unknown dynamics. The proposed IRCLF scheme automatically compensate for acceleration estimation errors, unmodeled dynamics, and disturbances without the knowledge of their bounds a priori. The uniform ultimate boundedness of all system signals is proven using the Lyapunov stability argument and Barbalat's lemma. The performance of the proposed QP‐AIR‐CLF control framework is validated on two different underactuated systems: a foot‐leg model on a deformable ground, and an overhead crane system. Simulation results show the benefits of the proposed controller over the baseline QP‐RCLF and an adaptive QP‐RCLF in terms of the control optimality, tracking accuracy, dynamic estimation performance, and robustness to disturbances.

Robust adaptive control Lyapunov‐barrier function for non‐collocated control and safety of underactuated robotic systems

AbstractQuadratic program‐based control Lyapunov‐control barrier function (QP‐CLBF) is a recently developed control scheme that balances stability and safety in an optimal fashion. However, direct application of such controllers to uncertain nonlinear systems with model uncertainties and disturbances could potentially degrade the performance of closed‐loop systems and violate/restrict safety‐critical constraints. This article presents a novel robust QP‐based adaptive approach for non‐collocated control of a class of underactuated robotic systems with a semi‐strict‐feedback form through which exponential disturbance‐to‐error (eDE) stability of all system solutions is ensured. We begin by developing a backstepping design technique based on which a neural network‐based adaptive control is designed to approximate unknown nonlinear functions. To compensate for uncanceled uncertainties, including modeling approximation error, chained error effects between coordinates, and disturbances, virtual inputs are designed whose gains are evolved by projection‐based adaptation mechanisms. To construct a three‐term control law, including feedforward, adaptive, and optimal terms, a QP optimization problem is synthesized to compute a family of optimal stabilizing signals while encoding time‐varying robust CLF (TVRCLF) and CBF (TVRCBF), and control bounds as constraints. In contrast with existing QP‐CLBF, our control technique with the proposed TVRCLF and TVRCBF significantly improves control objectives and strictly guarantees safety by automatically compensating for unknown uncertainties without the need for knowing their bounds a priori. The eDE stability of all system errors is proven using Lyapunov stability arguments for both collocated and non‐collocated coordinates. Simulations and comparisons to a baseline QP‐CLBF‐based feedback linearization (QP‐CLBF/FL) on a single‐link flexible‐joint robot verify the benefits of the proposed control approach.

Linear controllability of two multi-link robotic systems with multiple unactuated joints

We deal with the linear controllability of two underactuated multi-link robotic systems in this paper. First, for a general n-link inverted pendulum mounted on a cart in a vertical plane, we prove that it is linearly controllable around the equilibrium point with the cart in a desired position and each link of the pendulum in the upright position regardless of its physical parameters, if and only if the cart is actuated. Second, for an n-link underactuated planar robot with its first joint mounted on a fixed base in a horizontal plane, we prove that it is linearly controllable around the trajectory where each link of the robot stretches straight out and rotates with a constant angular velocity, if and only if its first joint is actuated, regardless of its physical parameters and regardless of the actuation or underactuation of its rest joints. We illustrate the above results via a quintuple pendulum–cart system and a four-link planar gymnastic robot in literature. We give new insights into the linear controllability around an equilibrium point or a trajectory of underactuated robotic planar systems with multiple unactuated joints.

Event-Triggered Consensus Control for Networked Underactuated Robotic Systems.

In this article, the consensus of networked underactuated robotic systems subject to fixed and switched communication networks is discussed by developing some novel event-triggered control algorithms, which can synchronously guarantee the convergence of the active states, the boundedness of the velocities of passive actuators, and the exclusion of Zeno behaviors. In the cases of fixed networks, the sufficient criteria are established for the presented distributed event-triggered mechanisms with and without using neighbors' velocities, in order to achieve a better tradeoff between the communication load and system performance. Besides, in the situation of switched networks, the sufficient criterion is established by assuming that the union of the network has a spanning tree. A distributed sampled-data rule is constructed to decide when to update its own and neighbors' estimated positions, and thus further reduces the unnecessary control cost. Finally, by further extending the main results to three other sampled-data control algorithms, several examples with performance comparisons are provided to validate the efficiency and advantages of the theoretical results.

Design of rotary inverted pendulum swinging-up and stabilizing

The mechanical design of inverted pendulum systems may be very diverse. This study makes use of mathematics to explain the expanded unstable Rotary planer inverted pendulum arrangement (Rotary -inverted system). Pin connections are used in planer-inverted pendulums to attach the pendulum to the rotating- Rotary actuation base. This design of a Rotary -inverted pendulum is explored in the development of underactuated robotic systems because it best simulates the balance of a broomstick in the hand by treating the elbow and shoulder as revolute joints. It is necessary to utilize the Lagrangian equation of motion when creating the dynamical equation for the Rotary -inverted pendulum. MATLAB Simulink is used to simulate a nonlinear computational model of the system so as to test the accuracy of the mathematical model.

Fast Terminal Sliding Control of Underactuated Robotic Systems Based on Disturbance Observer with Experimental Validation

In this study, a novel fast terminal sliding mode control technique based on the disturbance observer is recommended for the stabilization of underactuated robotic systems. The finite time disturbance observer is employed to estimate the exterior disturbances of the system and develop the finite time control law. The proposed controller can regulate the state trajectories of the underactuated systems to the origin within a finite time in the existence of external disturbances. The stability analysis of the proposed control scheme is verified via the Lyapunov stabilization theory. The designed control law is enough to drive a switching surface achieving the fast terminal sliding mode against severe model nonlinearities with large parametric uncertainties and external disturbances. Illustrative simulation results and experimental validations on a cart-inverted pendulum system are provided to display the success and efficacy of the offered method.

A physically motivated control algorithm for an autonomous underwater vehicle

An Autonomous Underwater Vehicle (AUV) is an underactuated mobile robotic system. This paper is focused on the control of an AUV, which is an interesting problem in robotics. In engineering applications, achieving a precise mathematical model for a given system is not realistic due to the existence of many unknown and unpredictable phenomena in real systems. Therefore, less reliant algorithms on the system mathematical equations are certainly preferable. To this end, first, the mathematical model of the AUV is presented. Then, the desired signals for the control algorithm are produced. After that, a nonlinear PID-based kinematic control is proposed to solve the trajectory tracking problem for the AUV. Subsequently, a Lyapunov-based dynamic control is designed for system actuator torques. In contrast to many existing solutions, control formulation does not require any model transformation or approximation and it is formulated in the original configuration space of the system. The proposed control law is simple, with an explainable mechanism and straightforward tuning, and it leads to the non-oscillatory robot motions in the Cartesian space.

Nonlinear Control System Design of an Underactuated Robot Based on Operator Theory and Isomorphism Scheme

The number of actuators of an underactuated robot is less than its degree of freedom. In other words, underactuated robots can be designed with fewer actuators than fully actuated ones. Although an underactuated robot is more complex than a fully actuated robot, it has many advantages, such as energy, material, and space saving. Therefore, it has high research value in both control theory and practical applications. Swing-up is a mechanism with two links, which mimics a gymnast performing a horizontal bar movement. Over the past few decades, many sufficiently robust control techniques have been developed for a fully actuated robot but almost none of them can be directly applicable to an underactuated robot system. The reason is that such control techniques require certain assumptions that are valid only for fully actuated robot systems but not for underactuated ones. In this paper, a control system design method for underactuated robots based on operator theory and an isomorphism scheme is first proposed. Bezout identity is designed using isomorphism. The effectiveness of the design method is confirmed by simulation. The simulation results show that the performances, such as robust stability and response time, of an underactuated robot control system are improved.

Direct Policy Optimization Using Deterministic Sampling and Collocation

We present an approach for approximately solving discrete-time stochastic optimal-control problems by combining direct trajectory optimization, deterministic sampling, and policy optimization. Our feedback motion-planning algorithm uses a quasi-Newton method to simultaneously optimize a reference trajectory, a set of deterministically chosen sample trajectories, and a parameterized policy. We demonstrate that this approach exactly recovers LQR policies in the case of linear dynamics, quadratic objective, and Gaussian disturbances. We also demonstrate the algorithm on several nonlinear, underactuated robotic systems to highlight its performance and ability to handle control limits, safely avoid obstacles, and generate robust plans in the presence of unmodeled dynamics.

Gained switching-based fuzzy sliding mode control for a discrete-time underactuated robotic system with uncertainties

This study proposes a gained switching-based discrete-time sliding mode control method to address the chattering issue in disturbed discrete-time systems, which suffer from various unknown uncertainties. Through the new structure of the designed reaching law, the proposed method can effectively increase the convergence speed while guaranteeing chattering-free control. The performance of controlling underactuated robotic systems can be further improved by the adoption of fuzzy logic to perform adaptive online hyper-parameter tuning. In addition, an underactuated robotic system with uncertainties is studied to validate the effectiveness of the proposed reaching law. Results reveal the dynamic performance and robustness of the proposed reaching law in the studied system and prove the proposed method’s superiority over other state-of-the-art methods.

Stabilization of a Class of Nonlinear Underactuated Robotic Systems through Nonsingular Fast Terminal Sliding Mode Control

To facilitate the stabilization of nonlinear underactuated robotic systems under perturbation, a novel nonsingular fast terminal sliding mode control method is proposed. Based on the system transformation into an integrator chain, the combination of twisting-like algorithm and a nonsingular fast terminal sliding mode control technique is employed to achieve the stabilization of the studied systems, which can drive the robot states (joint positions and velocities) to the desired region and then maintain the system at the equilibrium point in finite time. The robustness of the proposed method is validated by the Lyapunov direct method. Finally, numerical simulation results further demonstrate that the proposed method has better performance on the convergent speed of the system state (robot joint positions and velocities) than state-of-the-art methods, especially for the underactuated joints.