Field programmable gate array–based servo control integrated chip for a six-axis articulated robot manipulator

Abstract

The objective of this article is to build a field programmable gate array–based six-axis servo control integrated chip which can integrate the function of a motion trajectory planning and the function of six position/speed/current servo controllers into one integrated chip. In the work, first, a mathematical modeling of a robot manipulator with the actuator using permanent magnet synchronous motor is derived. Second, the proportional controller in the position loop, a proportional–integral controller in the speed loop and a vector controller in the current loop for each axis are applied. Third, a system on a programmable chip) technology which comprises an Altera field programmable gate array chip and an embedded soft-core Nios-II processor is considered to develop the proposed servo control integrated chip. However, in the servo control integrated chip, it has two modules. The first module is an embedded soft-core Nios-II processor which is used to generate the motion trajectory planning by software. The second module presents a six-axis servo controller intellectual property by hardware which is applied to execute six position/speed/current controllers. Therefore, the function of a motion trajectory command and the function of six position/speed/current servo controllers for a six-axis robot manipulator can be integrated into one field programmable gate array. Finally, to verify the effectiveness and correctness of the proposed field programmable gate array–based servo control integrated chip, a six-axis robot manipulator is applied and some experimental results are demonstrated.

Keywords

Servo control integrated chip robot manipulator field programmable gate arrays system on a programmable chip

Introduction

The traditional automatic machine usually utilizes one central controller for the motion trajectory planning and multiple microprocessors for multi-axis servo motor drive system to establish a multi-axis motion controller. However, there appear some drawbacks, such as large volume, easily affected by noise, high cost, inflexibility, and so on. Therefore, the integration of a multi-axis servo and motion controller into one chip then applying to XYZ table, computed numerically controlled (CNC) machine or robotic system, and so on for reducing the system volume and increasing the system performance and motion stability have become a popular research topic in literature.^1–7 To solve this problem, field programmable gate array (FPGA)^8–11 provides the best solution among those high-end commercial microprocessors due to its fast computational power, parallel processing ability, field programmable characteristics, and system on a programmable chip (SoPC) environment which can perform hardware–software co-design task. The fast computational capability and the parallel processing characteristics make it possible to integrate six-axis servo controllers and motion trajectory planning for an articulated robot manipulator into one FPGA.

In the realization of the proposed work, SoPC technology is established to develop a six-axis servo control integrated chip (IC), and is shown in Figure 1. It includes a six-servo controller intellectual property (IP) and one Nios-II processor in an FPGA. Each servo controller IP in Figure 1(b) performs the function of position/speed/current controller for each permanent magnet synchronous motor (PMSM) drive, and Nios-II processor executes the function of the motion trajectory planning. In position/speed/current controller IP, the vector control is adopted in the current loop, proportional (P) controller is used in the position loop, and proportional–integral (PI) controller is applied in the speed loop for each PMSM drive. Therefore, a six-axis servo controller for a six-axis articulated robot manipulator can be integrated into one FPGA. Our previous study¹² focuses on the FPGA-based IC design for a five-axis robot manipulator with direct current (DC) motor drive. In this study, we upgraded it to a six-axis robot manipulator with PMSM drive. However, the mathematical modeling is re-derived to make it suitable for the PMSM drive in the robot manipulator system. Moreover, the architecture and very high speed IC hardware description language (VHDL) design in the servo control IC is re-designed as the servo controller in PMSM is more complicated than DC motor.

Figure 1.

(a) FPGA-based servo control system for a six-axis articulated robot manipulator. (b) The ith axis servo controller.

System description and controller design of the robot manipulator

Mathematical model of a robot manipulator with the actuator using PMSM

The dynamic equation of an n-link manipulator is given by¹³

M (θ) \overset{\cdot\cdot}{θ} + V_{m} (θ, \overset{\cdot}{θ}) \overset{\cdot}{θ} + F (\overset{\cdot}{θ}) + G (θ) = τ

(1)

where $M (θ)$ denotes the inertial matrix, $V_{m} (θ, \overset{\cdot}{θ})$ denotes the Coriolis/centripetal vector, $G (θ)$ denotes the gravity vector, and $F (θ^{.})$ denotes the friction vector. The terms $θ$ , $\overset{\cdot}{θ}$ , $\overset{\cdot\cdot}{θ}$ , and $τ$ represent the n-vector of the position, the velocity, the acceleration, and the generalized forces, respectively, and are set to $R^{n}$ .

The typical dynamic model of the ith axis PMSM drive system for the robot manipulator is described, in two-axis d–q synchronous rotating reference frame, as follows

{\overset{\cdot}{i}}_{d_{i}} = - \frac{r_{s_{i}}}{L_{d_{i}}} i_{d_{i}} + ω_{e_{i}} \frac{L_{q_{i}}}{L_{d_{i}}} i_{q_{i}} + \frac{1}{L_{d_{i}}} v_{d_{i}}

(2)

{\overset{\cdot}{i}}_{q_{i}} = - ω_{e_{i}} \frac{L_{d_{i}}}{L_{q_{i}}} i_{d_{i}} - \frac{r_{s_{i}}}{L_{q_{i}}} i_{q_{i}} - ω_{e_{i}} \frac{λ_{f_{i}}}{L_{q_{i}}} + \frac{1}{L_{q_{i}}} v_{q_{i}}

(3)

where $v_{d_{i}}$ , $v_{q_{i}}$ are the d- and q-axis voltages; $i_{d_{i}}$ , $i_{q_{i}}$ are the d- and q-axis currents; $r_{s_{i}}$ is the phase winding resistance; $L_{d_{i}}$ , $L_{q_{i}}$ are the d- and q-axis inductance; $ω_{e_{i}}$ is the rotating speed of magnet flux; and $λ_{f_{i}}$ is the permanent magnet flux linkage.

If the vector control approach is applied in the current loop control of PMSM drive in which the $i_{d_{i}}$ is controlled to 0, the PMSM will be decoupled and controlling a PMSM will be similar to controlling a DC motor. Therefore, after decoupling, the torque of PMSM can be written as follows

τ_{M_{i}} = \frac{3 P}{4} λ_{f_{i}} i_{q_{i}} \underline{\underline{Δ}} K_{M_{i}} i_{q_{i}}

(4)

with

K_{M_{i}} = \frac{3 P}{4} λ_{f_{i}}

(5)

where $τ_{M_{i}}$ is the motor torque and P is pole pairs. Thus, considering the mechanical load, the overall dynamic equation of the ith axis PMSM drive system for the robot manipulator is obtained by

J_{M_{i}} {\overset{\cdot\cdot}{θ}}_{M_{i}} + B_{M_{i}} {\overset{\cdot}{θ}}_{M_{i}} = τ_{M_{i}} - τ_{L_{i}}

(6)

Terms $J_{M_{i}}$ , $B_{M_{i}}$ , $τ_{M_{i}}$ , and $τ_{L_{i}}$ denote the inertial, viscous, and generated torque of the PMSM, and the load torque to the ith axis of the robot manipulator, respectively. Consider a friction $F_{M_{i}}$ added to each arm link and the load torque $τ_{L_{i}}$ replaced by an external load torque through a gear ratio $r_{i}$ , giving

τ_{L_{i}} = r_{i} τ_{i}

(7)

Then, equations (4)–(7) can be arranged and simplified by the following equation

J_{M_{i}} {\overset{\cdot\cdot}{θ}}_{M_{i}} + B_{M_{i}} {\overset{\cdot}{θ}}_{M_{i}} + F_{M_{i}} + r_{i} τ_{i} = K_{M_{i}} i_{q_{i}}

(8)

Therefore, the dynamics of the PMSM that drive the arm links are given by the n decoupled equations

J_{M} {\overset{\cdot\cdot}{θ}}_{M} + B {\overset{\cdot}{θ}}_{M} + F_{M} + R τ = K_{M} i_{q}

(9)

with

\begin{array}{l} θ_{M} = v e c {θ_{M_{i}}}, J_{M} = d i a g {J_{M_{i}}}, \\ B = d i a g {B_{M_{i}}}, R = d i a g {r_{i}}, \\ K_{M} = d i a g {K_{M_{i}}}, i_{q} = v c e (i_{q_{i}}), \\ τ = v e c (τ_{i}), F_{M} = v e c (F_{M_{i}}) \end{array}

(10)

The dynamic equations including the robot manipulator and PMSM can be obtained by combining equations (1) and (9). The gear ratio of the coupling from the motor i to arm link i is given by $r_{i}$ , which is defined as

θ_{i} = r_{i} θ_{M_{i}} or θ = R θ_{M}

(11)

Hence, substituting equation (11) into equation (9), then into equation (1), yields

\begin{array}{l} (J_{M} + R^{2} M (θ)) \overset{\cdot\cdot}{θ} + (B + R^{2} V_{m} (θ, \dot{θ})) \dot{θ} \\ + R F_{M} (\dot{θ}) + R^{2} F (\dot{θ}) + R^{2} G (θ) = R K_{M} i_{q} \end{array}

(12)

The gear ratio $r_{i}$ of a commercial robot manipulator is frequently small (1/50 ∼ 1/200) to increase the torque value. Therefore, the formula can be simplified. From equation (12), the dynamic equation combining the motor and the arm link is expressed as

J_{M_{i}} {\overset{\cdot\cdot}{θ}}_{i} + B_{i} {\overset{\cdot}{θ}}_{i} + r_{i} F_{M_{i}} = r_{i} K_{M_{i}} i_{q_{i}} - r_{i}^{2} d_{i}

(13)

where

d_{i} = \sum_{j \neq i} m_{ij} {\overset{\cdot\cdot}{θ}}_{j} + \sum_{j, k} V_{jki} {\overset{\cdot}{θ}}_{j} {\overset{\cdot}{θ}}_{k} + F_{i} + G_{i}

(14)

Since the gear ratio $r_{i}$ is small in a commercial robot manipulator, the $r_{i}^{2}$ term in equation (14) can be ignored, and equation (13) can be simplified as

J_{M_{i}} {\overset{\cdot\cdot}{θ}}_{i} + B_{i} {\overset{\cdot}{θ}}_{i} + r_{i} F_{M_{i}} = r_{i} K_{M_{i}} i_{q_{i}}

(15)

Substituting equations (10) and (11) into equation (15) yields

J_{M_{i}} {\overset{\cdot\cdot}{θ}}_{M_{i}} + B_{M_{i}} {\overset{\cdot}{θ}}_{M_{i}} + F_{M_{i}} = K_{M_{i}} i_{q_{i}}

(16)

Finally, if the gear ratio is small, the overall system of the robot manipulator and PMSM will become a linearized and decoupled system as in equation (16). Under the above description, the servo controllers at each axis of the robot manipulator can be independently designed and it is robust with the external load. Therefore, the control block diagram combining arm link, PMSM, the position loop P controller and the speed loop PI controller in i-axis robot manipulator can be represented as in Figure 2. If it includes the motion trajectory planning, the servo and motion controllers for a six-axis robot manipulator can be represented as in Figure 3. Furthermore, in Figure 3, the digital PI controllers in the speed loop are formulated as follows

u_{p} (n) = K_{vp} e_{v} (n)

(17)

u_{i} (n) = u_{i} (n - 1) + K_{vi} e_{v} (n - 1)

(18)

\begin{array}{l} u (n) = u_{p} (n) + u_{i} (n) = u_{i} (n - 1) \\ + K_{v p} e_{v} (n) + K_{v i} e_{v} (n - 1) \end{array}

(19)

where $u_{p}$ , $u_{i}$ , $u$ are the outputs of P controller, integral (I) controller, and PI controller, respectively; $K_{vp}$ , $K_{vi}$ are the gains of the P controller and I controller, respectively. Furthermore, $e_{v} (n)$ is the error between the speed command and the measured speed.

Figure 2.

The block diagram of a servo controller with PMSM in the i-axis robot manipulator.

Figure 3.

The block diagram of motion and servo controller with PMSM for a six-axis robot manipulator.

In the stability analysis of the overall six-axis robot control system, as the servo controllers at each axis of the robot manipulator can be decoupled and independently designed, we only need to analyze the stability of each axis in the robot manipulator. Therefore, for the i-axis robot manipulator, the block diagram of a servo controller is shown in Figure 2 and its overall transfer function is presented as follows

\begin{array}{l} \frac{θ_{i} (s)}{θ_{i}^{*} (s)} \\ = \frac{K_{p} K_{M_{i}} (K_{v p} s + K_{v i})}{J_{M_{i}} s^{3} + (B_{M_{i}} + K_{M_{i}} K_{v p}) s^{2} + (K_{M_{i}} K_{v i} + K_{p} K_{M_{i}} K_{v p}) s + K_{p} K_{M_{i}} K_{v i}} \end{array}

(20)

For the purpose of analyzing the stability, a Routh table is first built up and listed in Table 1. Then, using the Routh–Hurwitz criterion, the stable condition in Table 1 is to make kk large than 0, as follows

kk = \frac{- | \begin{matrix} J_{M_{i}} & K_{M_{i}} K_{vi} + K_{p} K_{M_{i}} K_{vp} \\ B_{M_{i}} + K_{M_{i}} K_{vp} & K_{p} K_{M_{i}} K_{vi} \end{matrix} |}{B_{M_{i}} + K_{M_{i}} K_{vp}} > 0

(21)

\begin{array}{l} B_{M_{i}} K_{v i} + K_{M_{i}} K_{v p} K_{v i} + B_{M_{i}} K_{p} K_{v p} \\ + K_{p} K_{M_{i}} K_{v p}^{2} - J_{M_{i}} K_{p} K_{v i} > 0 \end{array}

(22)

Table 1.

Routh Table.

s³	J_Mi	K_MiK_vi + K_pK_MiK_vp
s²	B_Mi + K_MiK_vp	K_pK_MiK_vi
s¹	kk	0
s⁰	Kp K_Mi Kvi

Equation (22) provides the stability condition for each axis of the robot manipulator.

Point-to-point motion trajectory

The point-to-point (PTP) trajectory is considered to evaluate the motion performance in PMSM. For the purpose of smoothing the move of the PMSM at the start and stop condition, the motion trajectory is designed with the trapezoidal velocity profile and its equation is shown as follows

s (t) = {\begin{matrix} \frac{1}{2} A t^{2} + s_{0} 0 \leq t \leq t_{a} \\ v_{m} (t - t_{a}) + s (t_{a}) t_{a} \leq t \leq t_{d} \\ - \frac{1}{2} A {(t - t_{d})}^{2} + v_{m} (t - t_{d}) + s (t_{d}) t_{d} \leq t \leq t_{s} \end{matrix}

(23)

where 0 < t < t_a is at the acceleration region, t_a < t < t_d is at the constant velocity region, and t_d < t < t_s is at the deceleration region. S represents the position command; A is the acceleration/deceleration value; s₀ is the initial position; v_m is the maximum velocity; t_a, t_d, and t_s represent the end time of the acceleration region, the start time of the deceleration region, and the end time of the trapezoidal motion, respectively.

The design of an FPGA-based six-axis servo control IC

The internal architecture of the proposed FPGA-based six-axis servo control IC is shown in Figure 4. There are a Nios-II processor and six servo control modules inside. Each servo control module includes one circuit of position P and speed PI controller, one circuit of current controller and coordinate transformation (CCCT), one space vector pulse width modulation (SVPWM), one analog-to-digital converter (ADC) interface, and one absolute encoder interface circuit. The FPGA herein uses Cyclone IV-EP4CE115, which is the product of Altera cooperation. There are 114,480 logic elements (LEs), 3,981,312 random access memory (RAM) bits, and 150 embedded multipliers in the Cyclone IV. Also, a Nios-II processor is embedded into FPGA to establish a SoPC environment. The Nios-II processor is utilized to perform a PTP motion trajectory computation. The code in Nios-II processor is developed with C language. The main program establishes the initial parameters setting, the motion command setting, and so on, and the interrupt service routine (ISR) executes the motion trajectory and the position command generation. All circuits in Figure 4 are realized by hardware in FPGA, and the circuit behavior is described in VHDL. The sampling frequencies (interval) in position, speed, and current control loops are designed as 2 kHz (0.5 ms), 2 kHz (0.5 ms), and 16 kHz (0.0625 ms), respectively. The operating clock of the designed FPGA controller is 50 MHz, and the frequency divider generates another 12.5 MHz clock to supply all module circuits in Figure 3. A finite state machine (FSM) method is employed to model the algorithms of the position P and speed PI controller, the CCCT, and the SVPWM, which utilizes one adder, one multiplier, a look-up table, comparators, registers to carry out the overall computation.

Figure 4.

FPGA-based multi-axis servo control IC for a six-axis robot manipulator.

Each internal circuit of CCCT shown in Figure 4 performs the function of two PI controllers, table look-up for sin/cos function and the coordinate transformation for Clark, Park, inverse Park, modified inverse Clarke. The CCCT circuit designed using by FSM is shown in Figure 5, and it manipulates 24 steps machine to carry out the overall computation. The data type is 12-bit length with a Q11 format and 2’s complement operation. In Figure 5, steps s₀–s₁ are for the look-up sin/cos table; steps s₂–s₅ and s₅–s₈ are for the transformation of Clarke and Park, respectively; steps s₉–s₁₄ are for the computation of d-axis and q-axis PI controller; and steps s₁₅–s₁₉ and s₂₀–s₂₃ represent the transformation of the inverse Park and the modified inverse Clarke, respectively. The operation of each step in FPGA can be completed within 40 ns (25 MHz clock); therefore, whole 24 steps need 0.96 µs operation time. Furthermore, the position P controller and speed loop PI controller designed using by FSM are shown in Figure 6, and they manipulate seven steps machine to carry out the overall computation. In Figure 6, steps s₀–s₁ execute the position loop P controller; steps s₂–s₆ present the speed loop PI controller. K_p, K_vp, and K_vi are the P controller gain of position loop, P and I controller gains of speed loop, respectively. The data type adopts 2’s complement operation. Furthermore, the 32-bit with Q24 is applied in the position loop controller and 16-bit length with Q15 is used in the speed loop controller. In Figure 6, total seven steps need 0.28 µs operation time.

Figure 5.

Designed CCCT circuit using FSM.

Figure 6.

Designed position loop P controller and speed loop PI controller using FSM.

Finally, the FPGA utility of the proposed six-axis servo control IC for a six-axis robot manipulator in Figure 4 is evaluated, and the result is listed in Table 2. It shows that the overall circuits of the proposed six-axis servo control IC include a Nios-II embedded processor IP (5,114 LEs and 75,136 RAM bits) and a six-axis servo control IP (37,506 LEs and 299,520 RAM bits), which uses 37.22% of the LEs resources and 9.41% of the RAM resources of a Cyclone IV-EP4CE115.

Table 2.

FPGA utility of the proposed six-axis servo control IC.

IP	Module circuit	Logic elements (LEs)	Memory(bits)
Nios-II Embedded Processor IP		5114	75,136
The six-axis servo control IP	Position P controller and speed PI controller	1192*6	0
	Current controller and coordinate transformation (CCCT)	1252*6	49,920*6
	SVPWM generation	1766*6	0
	ADC interface circuit	647*6	0
	Absolute encoder interface circuit	1394*6	0
Total		42,620	374,656

FPGA: field programmable gate array; IC: integrated chip; IP: intellectual property; SVPWM: space vector pulse width modulation; ADC: analog-to-digital converter.

Experimental system and results

The overall experimental system shown in Figure 7 includes an FPGA control board, three sets (it can be extended to six sets) of voltage source intelligent power modules (IPM)-based inverter, and a robot manipulator which is driven by six PMSMs. The power, rating, voltage, current, and rating speed of PMSM in J1- and J2-axis are 400W, 92V, 1.6A, and 3000 r/min; for J3-axis, the power is 200 W; for J4-axis, the power is 100 W; and for J5- and J6-axis, the power is 50 W. An absolute encoder with 131,072 pulses per cycle is attached on the PMSM to measure the rotor position and rotor speed. A harmonic drive is attached to the PMSM for reducing the mechanical running speed and increasing torque. The reduction ratio in J1, J2, J3, J4, J5, and J6 are 1:120, 1:120, 1:120, 1:162, 1:121.5, and 1:50, respectively. Inside IPM, there are six sets of insulated-gate bipolar transistor (IGBT)-type power transistors with an emitter of the rated voltage of 600 V, collector DC current rating of 20 A, and a short time (1 ms) rated current of 40 A. The Photo coupler IC adopts TLP250, whose output has push-pull amplifier functions. The FPGA uses Cyclone IV-EP4CE115, which is the kernel of this system. There are 114,480 LEs, 3,981,312 RAM bits, and 150 embedded multipliers in the Cyclone IV. Furthermore, a Nios-II processor can be embedded into FPGA to establish a SoPC environment.

Figure 7.

Experimental system.

To evaluate the performance of the proposed six-axis servo control IC, a step position response for individual axis motion and a PTP trajectory for two-axis simultaneous motion are tested. In the former test, the step signal with 2/3 Hz square wave and within 2.22°–7.2° magnitude is sent to each axis as a position command which will generate the individual arm motion. The parameters of PI controller in the current loop are manually tuned to the requirement through which the measured current in q-axis can quickly and smoothly track the command current in q-axis and the measured current in d-axis can be controlled to zero. In addition, the parameters of PI controller in the speed and position loop are tuned, which requires not only to match the stability condition in (22) but also to reach the required performance of the position step response with near zero steady-state error, fast response with a short rising time, and a little overshoot within 10%. Herein, the PI controller gains are chosen by kp = 2.75, ki = 0 in position loop; kp = 0.91, ki = 0.005 in speed loop; and kp = 0.39, ki = 0.009 in current loop, respectively. A payload with 5 kg is considered to mount on the tip of the sixth axis of the robot manipulator. This is to evaluate the response performance of the proposed system under the effect of the external load. In the experiment, the step position and current responses at the J1–J6 axis of the robot manipulator with and without 5 kg payload are tested and its results are shown in Figure 8. The rising time and overshoot are presented by 0.267 s, 8.27% (0 kg payload) and 0.281 s, 8.81% (5 kg payload) at J1-axis; 0.276 s, 9.39% (0 kg payload) and 0.282 s, 9.74% (5 kg payload) at J2-axis; 0.245 s, 6.13% (0 kg payload) and 0.258 s, 6.07% (5 kg payload) at J3-axis; 0.194 s, 3.27% (0 kg payload) and 0.2 s, 3.58% (5 kg payload) at J4-axis; 0.185 s, 2.9% (0 kg payload) and 0.206 s, 3.07% (5 kg payload) at J5-axis; 0.197 s, 2.18% (0 kg payload) and 0.21 s, 3.05% (5 kg payload) at J6-axis. In addition, the steady-state errors are all near zero. In Figure 8, it is apparent that the step position responses for the heavy-weight axis in the J1–J3 axis are slower than the light-weight axis in the J4–J6 axis. Also, the step position appears to provide very similar responses both with and without 5 kg payload for all axes. However, it still presents a little slow motion in the case of 5 kg payload. Further inspecting Figure 8, the i_d current in all axes can be controlled near to zero, which reveals the success of the vector control. It also shows that the condition with 5 kg payload needs the larger i_q current than 0 kg payload, especially in the J2-, J3-, and J5- axis. To investigate the effect of parameter variations in viscous B, and inertial J on the dynamic response of the PMSM drive system, the step position responses for the J1–J3 axis with and without payload are redrawn in Figure 9. The J1-axis and J2-axis in robot manipulator use same PMSM (400 W) and same harmonic drive with reduction ratio being 1:120, but bear distinct mechanical structure with different B and J values. However, in Figure 9, the step position still shows a very similar response in J1-axis, J2-axis, and J3-axis. Therefore, from the experiments in Figures 8 and 9, it is demonstrated that the proposed controller system is robust in the effect of the external payload and the parameter variations in B and J. Finally, the experiments of the PTP motion with trapezoid trajectory by two-axis simultaneous motion in J1−J2 axis, J3–J4 axis, and J5–J6 axis are revealed in Figures 10 –12. The maximum position move, maximum speed, and acceleration are designed with 60°, 20.2°/s, and 370°/s² at J1−J3 axis; 44.4°, 15.1°/s, and 370°/s² at J4-axis; 59.2°, 20.2°/s, and 370°/s² at J5-axis; and 144°, 49.1°/s, and 370°/s² at J6-axis. Figures 10(a)–12(a) and Figures 10(b)–12(b) are presented in two different postures at different position commands. Meanwhile, Figures 10(c) and (d)–12(c) and (d) display the position/speed command, the position/speed tracking response, and the position/speed tracking error. From Figures 10 –12, it can be seen that the tracking of the position/speed response at each axis of robot manipulator can follow up the position/speed command under PTP motion trajectory very well, which demonstrates that our proposed FPGA-based six-axis servo control IC for a six-axis articulated robot manipulator is effective and correct.

Figure 8.

Step position and current responses at at (a) J1 axis, (b) J2 axis, (c) J3 axis, (d) J4 axis, (e) J5 axis, and (f) J6 axis of the robot manipulator with and without 5 kg payload.

Figure 9.

Step position at J1–J3 axis of the robot manipulator with a payload of (a) 0 kg and (b) 5 kg.

Figure 10.

Simultaneous J1–J2 axis PTP motion response of the robot manipulator at (a) posture one, (b) posture two, and the position/speed response for, (c) J1 axis, and (d) J2 axis.

Figure 11.

Simultaneous J3–J4 axis PTP motion response of the robot manipulator at (a) posture one, (b) posture two, and the position/speed response for, (c) J3 axis, and (d) J4 axis.

Figure 12.

Simultaneous J5–J6 axis PTP motion response of the robot manipulator at (a) posture one, (b) posture two, and the position/speed response for, (c) J5 axis, and (d) J6 axis.

Conclusion

The FPGA-based six-axis servo control IC for a vertical-type six-axis articulated robot manipulator has been successfully demonstrated in this article. The mathematical modeling of a robot manipulator with PMSM has been derived. It shows that for a commercial robot, as the harmonic drive (with a small gear ratio value) is applied for speed reduction and increasing torque, the overall robot manipulator system becomes linearized and decoupled after the vector control is used in the current loop of each PMSM drive. Under this design, the servo controllers at each axis of the robot manipulator can be independently designed and it is robust with the external load. In the realization, the functionalities required to build a six-axis servo controller and motion trajectory planning can be integrated into one FPGA chip by a hardware–software co-design task. The execution time of some key modules, such as CCCT and PI controller, need only 0.96 and 0.28 µs. The parallel processing in Nios-II processor and six servo controller modules as well as the powerful computation ability enhance the performance of the motion and servo control in robot manipulator. Furthermore, the FPGA resource usage of the overall circuits of the proposed six-axis servo control IC uses 42,620 LEs and 374,656 RAM bits. Finally, some experimental results by position step response and PTP motion trajectory tracking have revealed that the proposed FPGA-based six-axis servo control IC for an articulated robot manipulator is effective and correct.

Footnotes

Academic Editor: Stephen D Prior

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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