Complete Low-Cost Implementation of a Teleoperated Control System for a Humanoid Robot

2.1. Resistive Sensors and Accelerometers

Figure 1(a) shows the developed teleoperator suit. The Arduino Fio microcontroller installed on the suit provides 8 analog inputs that are used to capture data from the sensors. Due to this limitation in the number of channels of the ADC, only 8 sensors can be installed on the teleoperator suit and priority is given to the legs. Figure 1(b) depicts the degrees of freedom (DoF) at each joint of the legs. The thigh points have two DoFs while each knee joint has only one. The sensors in these joints measure different angles: a1 and a6 the knees flexion, a2 and a5 the legs rise up and a3 and a4 the legs opening.

Concerning the accelerometers in the bracelets, they have 3 degrees of freedom, although only the measurement of the shoulder angular movement with respect to frontal horizontal axis is considered, i.e., movement parallel to sagittal plane, flexion/extension of arms with respect to shoulder.

Liu et al. [1] proposed a suit with a higher number of accelerometers and gyroscopes on the joints allowing more variables in the model to characterize yaw, roll and pitch variations. However, higher computational resources are required, which also means more power consumption. Our approach is a specific implementation for a fast 8 bit microprocessor that needs only a 3.3 volts battery.

2.2. Data Wireless Transmission

The digital outputs from the ADC are transmitted to a receiver integrated on the humanoid robot employing a wireless XBee module [17] attached to the Arduino Fio board. Considering that a low bandwith is needed for the radio communication channel between the teleoperator suit and the robot, ZigBee technology [16] has been chosen. Its low power requirements, low latency and low cost offers a reliable serial communication between the two devices at distances around 10 meters.

Given the linear response of the sensors and assuming Gaussian noise of very low amplitude, the relationship between sensors voltages and the angle of inclination of every joint can be easily and robustly computed. The output data from the ADC embedded on the Arduino Fio board has a resolution of 10 bits, which are reduced to 8 bits for saving reasons and mapped to the angle variation range of the servo motors: 0° – 179°. Thus, providing enough resolution to get steps of 1° in order to control them.

On the other hand, we propose a binary codification of the angle values, such that a byte encodes each angle (0° – 179°). Then, the resultant data frame for the 8 sensors has a size of 9 bytes (1 of them representing the frame header). Considering a serial communication channel of 57,600 bauds, the data frame transmission takes 1.56 ms.

3.1. Robot Servo Motors

The humanoid robot movements are performed by a set of 12 actuators (see Figure 2) managed by an Arduino Fio microcontroller [15]. The servo control signal is a PWM (Pulse-Width Modulation), as shown in Figure 3, where there are three examples for 0°, 90° and 180°.

Each servo motor starts in a known position and is internally regulated by a PID (Proportional-Integral-Derivative) controller with resistive feedback. On the other hand, the states of the servos are unknown and cannot be used for the stability control. However, the whole robot state can be estimated measuring the initial positions and the angular increments.

3.2. Balance Feedback and Kalman Filtering

Replicating the person movements on the humanoid robot requires a balance control. The microcontroller actuates on the robot servo motors according to the measurements of the sensors in the suit. The direct execution of commands that include knee flexion, causes a loss of robot's stability and its consequent fall. Thus, a global balance control is needed.

The balance feedback depicted in Figure 4 is done through the measurement provided by an accelerometer located in the robot's back. The state vector of the sensor contains 3-axes orientations (see Figure 2) called Euler angles [18]. However, in this work the needed axes are the X axis for the stability control in the frontal plane and the Y axis for a simple sagittal plane control of the robot balance. From these linear axes, their corresponding inclination angles are calculated using trigonometrical basic reasoning.

The balance control system is based on a Takagi-Sugeno fuzzy controller [19], which is sensitive to noisy inputs. Due to this, it is necessary to filter the sensor signal to improve the response of the controller. For this task, a Kalman filter [14] is employed, which is commonly used in related works to directly estimate the orientation [18] or correct small misalignments in accelerometers.

The X axis data includes a high Gaussian noise that must be lessened to obtain a reliable measurement of the inclination angle (θ) and the angular velocity (ω) in the frontal plane of the robot. This is achieved applying a Kalman filter, as it is shown in Figure 4. On the other hand, the measurement from the Y axis (γ) has a low noise and it does not require any filtering step. Then, a simpler control is used in the sagittal plane consisting on a fixed maximum inclination angle limiter. If γ is higher than this bound (empirically adjusted to 30°) some constant corrections are made on servo motors a and h (see Figure 2).

According to Kalman's formulation [14], the Q and R noise covariance matrices parameters are adjusted empirically [20]. It must be noted that the measurements from the accelerometer are slightly smoothed by an integrated hardware filter. Nevertheless, in order to achieve superior filter performance, Kalman method is applied. Figure 5 shows a series of plots of a sensor measurement from the accelerometer in the back of the robot and its filtered version for different Q and R values. As it can be seen, in Figure 5(a) there is an overfitting and in Figure 5(c) there is too much filtering and low tracking. Then, after these experiments, the selected values in Figure 5(b) for R and Q are 0.5 and 0.03, respectively. It is a trade-off between filter response delay, the level of signal smoothness and the tracking performance. Besides, these values account for the global system reponse. They allow to adjust the control delay with the mechanical delay, thus the execution of movements is smooth and correct.

Regarding to the deterministic matrices of the system, the following values are defined: A = 1; B = 0 and C = 1. A is the updating matrix depending on the previous state, B is the updating matrix depending on the input state and C relates the state with the measurement.

The Kalman filter initialization is set to x₀ = θu₀ and P₀ = Q, where x₀ is the initial state, θu₀ is the initial unfiltered inclination angle and P₀ is the initial error covariance matrix.

Considering the previous defined matrices and the initial conditions, the Kalman implementation featured for the robot can be summarized in the formulas below, where x′ is the state prediction, x̂ is the state update and the filtered θ is considered as the Kalman output x̂_k+1:

3.3. Fuzzy Control of the Robot Balance

The robot balance control is performed by a fuzzy algorithm based on Takagi-Sugeno methodology [19]. This controller presents a low time response because of the definition of a set of simple functions that require low processing resources. Hence, it is a suitable method for real time purposes [21].

Fuzzy sets of input, output and the set of rules are defined based on prior knowledge of system behavior. More specifically, the two inputs for our fuzzy system correspond to the filtered frontal plane inclination angle (x = θ) and the angular velocity (ω) computed with Equation (7). The output of the fuzzy controller represents an angular compensation (ϕ) to keep robot balance.

As it can be observed, the subsets for the linguistic variable θ are all triangular due to real time implementation. The subsets of ω have two trapezoidal memberships and a triangular central one, which is also a very common format [12]. The letters on top of the input subsets stand for L = Left, CL = Center Left, C = Center, CR = Center Right, R = Right, Ne = Negative, ZZ = Zero and Po = Positive.

This work proposes a zero order Takagi-Sugeno model, which is a kind of Mandami Fuzzy control where the consequent of the rule is a singleton function. Thus, the output function is a constant characterized by a set of Dirac deltas in the fuzzyfier. The range of the output fuzzy set is from −10° to 10° as depicted in Figure 6(c), where NB = Negative B, N = Negative, Z = Zero, P = Positive, PB = Positive B.

According to a singleton model, the rules are built upon Equation (8). Besides, it is a completeness system because the number of rules (i) is 15 which results from all the possible combinations of the input linguistic variables. In our approach, the rules have been established in an experimental way. However, some authors apply Genetic Algorithms or other heuristics for tuning the rules and membership functions [22].

The conjunctive operator AND that connects fuzzy input variables has been set to MIN (r_x = min(θ,ω)) because it is usually employed for practical cases, while the PROD is used in stability studies [23]. Additionally, for the aggregation of N equal consequents a MAX$(u_{R,{\delta }_k}=max[V_{i-1}^N{r}_i\to Y_{\delta k}])$ is selected. Assuming the following definitions x ₁ ≔ θ, x ₂ ≔ ω and y ≔ ϕ, the 15 rules are enumerated below:

Let us define the following set of variables on Equations (9–13) represented by the notation u_R,δk and corresponding to the singleton consequents PB, P, Z, N and NB.

Then, the result from fuzzy control in order to compensate the servo motors is given by Equation (14).

Finally, this angular correction is applied to different servo motors depending on the right or left knee flexion in order to achieve the goal of keeping robot's stability This function is carried out by the SIMO (Single Input Multiple Output) module in Figure 4. Besides, Table 1 collects the joints compensations to be applied on the servo motors (check Figure 2 to locate each servo on the robot). The servo motors i and j correspond to the ankles of the robot and they are set to the same angle as the corresponding knee in order to have coherent angles in the segment that links them. The constant values (c*) on the table have been empirically determined.

3.4. Fuzzy Control Simulation

This system has been previously analyzed using XFuzzy tools resulting in the control surface of Figure 7(a). The surface shows the relation between fuzzy input variables θ and ω and the output ϕ, which can vary from 10° to −10°, being 10° when the θ fuzzy input is −90°. For this case, the other input variable (ω) can be at its maximum or minimum values. This indicates that the control system is correcting the error as much as possible. Furthermore, it can be observed the desired system behavior: when the angle and angular velocity variables are negative, the fuzzy algorithm returns a positive output to compensate and keep the robot balance and vice versa.

Figure 7(b) depicts the transition line in the states space allowing an early error detection at the moment of rules design. Additionally, it can be observed the distribution of consequents of the rules along the states space.

Moreover, Figure 8(a) presents a plot of the inputs and output signals in a simulation exercise of angular correction. The robot is stabilized around the angle of 0° and an angular velocity of 0 °/s, through the application of a mild angular correction (−10°, 10°). The trajectory along the linguistic variables during this simulation is depicted on Figure 8(b). The starting point is randomly set on R12 (58′5°, 25 °/s) and the goal is on R8 (0°, 0 °/s). There is a clear oscillation until reaching the stability vector in the center of R8. Several additional simulations have been done configuring different points of the states space and the results were similar. Then, these experiments validate the successful correction performed by the proposed fuzzy control algorithm.