Sliding mode control is often used for systems with parametric uncertainties due to its desirable robustness and stability, but this approach carries undesirable chattering. Similarly, joint elasticity is a common phenomenon induced by transmission systems in robots, but it presents additional complexity in robot dynamics that could lead to robot vibrations or even instability. Coupling these two phenomena presents further compounded challenges, particularly when faced with the human interface's added uncertainties. Here, a stable voltage-based adaptive fuzzy strategy to sliding mode control is proposed for an elastic joint robot arm that uses a human's upper limb electromyogram (EMG) signals to direct its movement. The concurrent use of EMG with the elastic joint arm provides a suitable framework for human-robot interaction. EMG signals represent human's ‘intention’ on motion, i.e., they move between 50–100 ms before the mechanical motion begins. Hence this strategy potentially builds better synchronization between the robot and human intention. Furthermore, the adaptive fuzzy strategy eliminates the system chattering while also providing robustness against parametric uncertainties and time delay. Lyapunov analysis also shows bounded-input bounded-output stability of the closed-loop system. Finally, the proposed approach is experimentally implemented in the Sport Science Research Institute. Comparisons with a competing strategy, as well as a torque mode controller, shows that the proposed approach leads to a computationally faster and more accurate controller.

It is increasingly clear that robots will fulfill a growing number and range of duties in modern life. Human-robot interaction and its various applications have hence received considerable attention in the past several years. However, the complexity of sensing processes and dynamics of biological systems, coupled with nonlinearities of robot dynamics, have considerably challenged every successful experimental development. In particular, there is a fundamental shortage of study in developing a system of sensors to conveniently map human desires and intentions to the robot's actions.

Recent studies differ considerably in their approach to human-robot interaction. For example, a robust nonlinear scheme is introduced in [

An essential aspect of our interface relies on the fact that the EMG signals can be recorded for almost everyone, even those with limb amputations since EMG can be recorded merely by placing the surface electrodes on the participant's skin. While the EMG signals and arm motions are related in a very complex and highly nonlinear manner [

The above works assume robot rigidity. They also often ignore the dynamics of the employed electrical actuators and expect a power transmission system coupled with the electrical motors, by which high torques can be generated at relatively low speeds. This is while joint elasticities are a common phenomenon induced by transmission system deformations. This is particularly unreasonable for the small size and subtle movements in applications such as telesurgery. However, with elastic joint robots, the link angle no longer follows the actuator angle, hence doubling the robot's degrees of freedom (states) compared to the number of control actions. Thus, joint elasticity presents additional complexity and nonlinearity through its input-output coupling and, as indicated in [

Much research has addressed elastic joint robots’ modeling and control. For instance, an efficient finite element formulation is introduced for robot modeling [

Here we use a voltage control strategy that is free from robot dynamics [

In contrast with [

The above qualities have already been confirmed for sliding-based designs in several reports such as [

The proposed control strategy is also compared with the control strategy [

The remainder of this paper is organized as follows. The proposed control architecture, robot modeling, theoretical analysis of stability, and results from experimental implementation at the Sports Science Research Institute are discussed in Section 2. Section 3 offers conclusions and further discussions on future works.

Here, we describe the training and real-time laboratory procedures to control the proposed elastic joint robot arm using surface EMG. We consider the upper limb muscles to focus on the future utility of the approach in telesurgery. In the primary stage, the participant is advised to move his/her arm in random patterns. During this movement, a Cortex motion capture system records the arm movement trajectory, while the EMG electrodes record the activities of four muscles from the shoulder and elbow. The processed signals are then used to train an Artificial Neural Network (ANN) model that estimates arm movement trajectory in a real-time operation using only the EMG recordings. Upon the completion of the training phase, the real-time operation phase begins. In this phase, the participant controls the robot by using the AFSMC, directly by moving his or her hand.

Four EMG channels are employed as principle input signals to assess the participant's arm movement trajectory, with each channel corresponding to one muscle, as depicted in

Several tests are performed to study the signal quality of each muscle. The device employed to record the EMG signal from muscles is ME6000 (BIOMATION Co., Almonte, Ontario, Canada,

The experiment was conducted using four male subjects, 25 to 30 years of age, who had never used EMG-controlled devices. During the training phase, the users were instructed to move their elbow and shoulder to random positions (with 2 degrees-of-freedom planar movements) 50 times to cover a wide range of the arm workspace. Hence, our training data consists of 160 instances, and the testing data set has 40 instances with the same number of inputs and outputs.

The desired robot trajectories are prepared using the estimated paths from processed EMG signals. The raw EMG signals are first normalized. Subsequently, the following three steps are performed. The first step is filtering the raw EMG signals by a 5th order notch filter to remove the 50 Hz power supply noise. The second step is to rectify the EMG signals, and the third step is calculating the signals’ Online Moving Average (OMA). The processed signal is written as,

Selecting the number of neurons in the hidden layer is still challenging since many hidden neurons may deteriorate the network performance and complicate the training process. Also, a large number of network variables require a large amount of memory. Networks with too few neurons in the hidden layer are also unable to properly adjust weights and biases during the training process, leading to overfitting and excessively complicating the training process. Here, the performance criteria for different ANN architectures are analyzed to determine the appropriate number of neurons. According to [

The relationship between EMG channels and the participant trajectory is modeled as,

An integrated state-space model is introduced here using the robot kinematics and dynamics, including those of the actuator. By employing a linear torsional spring to represent the joint elasticity, the mechanical dynamics of the robot are illustrated as,

where _{m} ∈ ^{n} and ^{n} are vectors of motor angles and joint angles, respectively. Hence, this framework has 2_{m}]. Also, ^{n} is the vector of gravitational forces, and ^{n×n} are diagonal matrices representing motor inertia, motor damping, and reduction gear coefficients, respectively.

Control of elastic joint robots is generally tricky since they are highly nonlinear, computationally costly, vigorously coupled, with double the size of the state space, i.e., 2

where ^{n} is the motor voltages vector, _{a} ∈ ^{n} is the motor currents vector, and _{a}, _{a}, _{b} ∈ ^{n×n} are diagonal matrices representing the coefficients for armature resistance, armature inductance, and back-emf constant, respectively. The vector of torques

A decentralized controller based on voltage strategy is proposed here for the real-time operation phase. Using

The system

To design a novel sliding mode control law, the sliding surface should be defined as,

In _{d} and

To obtain the proposed sliding mode control law, a positive definite function Λ is defined as,

For

where

where

However, the effect of

By multiplying both sides of

It is well known that classical sliding mode control carries undesirable chattering due to the constant value of

We develop here a decentralized fuzzy controller using two variables, namely _{1} and _{2}, as inputs to the controller, which are defined as,

The motor voltage

Three membership functions, _{1} and _{2}; therefore, control input space is covered by nine fuzzy rules. These rules are proposed in the form of Mamdani type, as,

where _{l}, _{l}, and _{l} are fuzzy membership functions for variables _{1}, _{2} and _{1} and

The membership functions for _{2} are similar to those of _{1}.

The membership functions for the output _{l} . To determine _{l} is a fuzzy basis, which is a positive value expressed as,

for _{1}…_{9}] ^{T}, and

Applying the fuzzy control

where ^{T}ψ(_{1}, _{2}) to approximate the following function, according to the universal approximation theorem of fuzzy systems, that is,

where ɛ is the approximation error. Also, _{1} and _{2} are positive gains that are selected as control design parameters.

To derive the adaptation law, the tracking system is formed from

where

Here, a positive definite function

then,

where _{2} denotes the second column of the matrix

If the adaptive law is given by,

So we have,

The tracking error is reduced if

One can imply _{min}(^{2} < ^{T}_{max}(^{2} where _{min}(_{max}(

In the following section, stability analysis for the closed-loop control system

_{d} should be smooth enough in the sense that _{d} and its derivatives, up to necessary orders, are available and are all uniformly bounded [

_{max}.

It can be said that the value of _{i}(0) is bounded. Therefore the value of _{i} converge to a negligible value, and the matrix

Based on the Routh-Hurwitz criterion, the system in

Moreover, since in Assumption 1, it is assumed that the desired trajectory _{d} and its derivatives _{d} −

_{a} and

_{a} and

_{a} and _{m} is bounded.

_{a} and _{m} in

Since ^{2}_{m}_{a} + _{m} is bounded. ▪

In conclusion, as the above theorems indicate, all system states are bounded. Thus, it is concluded that the proposed controller guarantees BIBO stability.

The experimental results are reported here in two phases. The first phase is about training an ANN to discover a mapping between EMG signals and the hand motion and the second phase is about the applying the proposed adaptive controller in a real-time operation. The Mean Squared Error (MSE) is used as a performance index for the ANN and

Joint | Shoulder | Elbow |
---|---|---|

[ |
0.198 | 0.186 |

Proposed method MSE | 0.183 | 0.171 |

The EMG signals provide information on the user's intention to move before the motion occurs; therefore, the trajectory is estimated before the participant moves his/her hand. This prediction should create added robustness in applications with communication delay, such as in telesurgery. To study this, we consider a uniform probability distribution function by using MATLAB (rand) function as a random time delay between 0–80 ms in this communication system. The proposed control law

DC motor | ||||||||

500 | 0.02 | 1.6 | 1 | 0.26 | 0.001 | 0.0002 | 40 | |

Controller | _{shoulder} |
|||||||

10 | 40 | 600 | 400 | 1 | 1 | 2 | 1 |

Some statistical results, such as the maximum error of each joint and MSE, are used as a performance index to evaluate the proposed method. Since the random time delay is used in communication channels, the experiment is run ten times, and

Controller | Proposed controller | [Souzanchi-K et al.] controller | [Panagiotis & Kyriakopoulos] controller |
---|---|---|---|

|_{error}| Joint 1 |
7.047 ± 0.692 | 40.56 ± 0.712 | 22.28 ± 0.611 |

|_{error}| Joint 2 |
8.244 ± 0.384 | 23.14 ± 0.525 | 23.15 ± 0.431 |

MSE | 21.43 ± 1.23 | 518.5 ± 12.21 | 313.2 ± 10.57 |

This paper presents a stable adaptive fuzzy strategy to sliding mode control based on the voltage control strategy for an elastic joint robot arm that uses human upper limb EMG signals. The proposed approach is robust against time delay in data transformation channels due to the use of EMG signals and robust against parametric uncertainty and eliminates the system chattering due to an adaptive fuzzy strategy. The Lyapunov analysis proves that the proposed control design guarantees BIBO stability.

For future studies, we hope to study the robustness of the proposed strategy to larger delays in teleoperation application. Also we hope to study isotonic exercises, in addition to the current isokinetic exercise signals. Furthermore, the current experimental work is performed in a 2-D space due to the available measurement hardware. As a next step, we hope to extend our results in 3-D space.

The authors would like to express their gratitude to the Sport Science Research Institute of Iran for providing the facilities to implement the experimental tests in this study.

Parameters | _{1} |
|||||||

0.5 | 0.35 | 0.7 | 0.7 | 0.35 | 0.35 | 0.081 | 0.057 |