Modeling, Simulation and VHDL Controller Design for an Underground Roof Support as Two Robotic Arms

Transcription

1 Modeling, Simulation and VHDL Controller Design for an Underground Roof Support as Two Robotic Arms Emil Pop, and Monica Leba Abstract In this paper, an underground roof support considered as two robotic arms is first analyzed. Based on Denavit-Hartenberg formalism, the cinematic direct and inverse models were developed and simulated. Based on the simulation results was designed an embedded software controller and implemented in VLSI solution using VHDL language. This solution is a good faster alternative versus microcontroller design. the translation beam (TB) and C 4 that is the hydraulic cylinder for the peak beam (PB). The elements of the second arm are: the main floor beam (MFB), C 5 that is the hydraulic cylinder for the stepping beam (SB) and the conveyor machine (CM). The link between the two arms is made through the shield mechanism (SM). F Keywords controller, robot, underground roof support, VHDL. I. INTRODUCTION IRST, the underground roof support will be considered and analyzed in order to transform it in a two arms robot. []. Then, using the Denavit-Hartenberg (D-H) formalism the movement homogeneous matrix is determined. Based on this matrix, the cinematic direct and inverse models are determined. A. eneral view For the underground works like tunnel or minerals exploitations, there is used special machinery. This machinery may be designed to sustain the roof of works, protect the personal and other equipments and continue to move in underground to accomplish its task. Today the underground roof support has hydraulic drives with different degrees of mobility. The most complex one have five degrees of mobility, four on the roof and one on the base. In fig. is presented an underground roof support (URS) as real view and its schematic. [7] The support has two arms, one on the roof with four joints (two of these are prismatic and two are rotation) and one on the floor with only one prismatic joint. For each arm the characteristic point is placed on the terminal element. The two characteristic points are called RCP (Roof Characteristic Point) and FCP (Floor Characteristic Point). The elements of the first arm are: C that is the main hydraulic cylinder, C that is the hydraulic cylinder for the main roof beam (MRB), C 3 that is the hydraulic cylinder for Manuscript received August 9,. E.Pop is with the University of Petrosani, Romania ( emilpop@upet.ro, emilpop@yahoo.com). M.Leba is with the University of Petrosani, Romania (corresponding author to provide phone: ; monicaleba@upet.ro, monicaleba@yahoo.com). Fig. Five grades of mobility underground support: a) Real view; b) Schematic representation 597

2 This underground roof support operates in seven sequences as follows: Initial position, when the CM is in the face of working, having the peak beam (PB) folded and the MRB fixed on the roof. This is the initial state S. The URS is fixed to the roof by the cylinder C. This is the state S. The mining combine cut a strip from the face of working in front of the URS and the PB is set to horizontal position by the cylinder C 4. This is the state S. The SB pushes the CM in the face of working by the cylinder C 3. This is the state S3. The URS is outstretched from the roof by the main cylinder C. This is the state S4. The URS is moved near the CM by the cylinder C 5. This is the state S5. The PB is folded by the cylinder C 4. This is the state S6. Each sequence defines a state starting from the initial state S to the final state S6, after which it is continued with S. So, the state S is an initial stop state. B. Underground Roof Support as Five rades of Mobility Robot The underground roof support is represented as a TTRTR robot with five degrees of mobility, three of these are prismatic (T) and two are rotations (R). The schematic diagram of this robot together with the appropriate systems of coordinates for applying the D-H method is presented in fig.. [5] The equations of the robot are: T,4 cos( θ + θ) = sin( θ + θ) sin( θ + θ ) cos( θ + θ ) for the upper arm and: c cos( θ + θ ) + ( L + l) cos θ c sin( θ + θ ) ( + ) sin θ H h L l T =, U + V + u () for the lower arm. [] We will use the following notations: Y T lower arm translation on y Y upper arm translation and rotation on y Z upper arm translation and rotation on z () Fig. Five grades of mobility two arms underground robot: a) URS upper arm; b) Upper arm D-H table; c) URS lower arm; d) Lower arm D-H table; There are obtained the direct cinematic model equations: Y Y Z T = U + V + u = c cos( θ + θ ) + ( L + l) cos θ (3) = c sin( θ + θ ) + ( L + l) sin θ + H + h These equations are very important for URS analyzing, testing and controller design. In order to control the URS it is necessary to determine the extremity position of the two robot arms. Based on equations (3) of the direct cinematic model, there is determined the inverse cinematic model, using the following data: the geometrical and technological dimensions of the URS: H, L, U, V, c, h, l, u; the RCP and FPC coordinates: Y, Z, Y T. The cinematic inverse model consists of the equations:. The peak rotation angle: θ π Y + [ Z ( H + h)] c ( L l) = arccos ; θ [,] (4) c ( L + l) 598

3 . The intermediary angle ϕ : Y [( c + B) A ][ Y + A ( c B) ] ϕ = arctg, Y + A c + B where A = Z ( H + h) B = L + l (5) 3. The roof beam rotation angle: A θ = arcsin ϕ; θ [ π /, π / ] Y + A (6) 4. The horizontal translation: u = YT U V (7) II. MATLAB-SIMULINK MODELIN AND SIMULATION In this section there will be modeled, simulated and tested the major performances of the URS, using the direct and inverse models determined above. Next are presented the MatLab-Simulink models and simulation results for practical cases. Using the equations of the inverse model (4) - (7), there is designed the Simulink model from fig.3.a. In fig.3.b are shown the simulation results for the case of URS outstretched position. [8] III. VHDL CONTROLLER DESIN The controller must generate appropriate signals to control the joints based on each joint sensors. [6] It is necessary to design the control sequences using the Moore state machine. A. State Machine Design The controller has five inputs and four outputs as presented in fig.4.a. The five outputs are the following: the clock (clk), start/stop (on_off), PB sensor (sz_lev), sensor for conveyor and support pull (sz_con) and sensor for roof support (sz_sup). The four outputs are: support control (sup), conveyor and support move (con), PB move (lev) and regime move/stop (run). The states s..s6 depend on the output signals as shown in fig.4.b. [4] The transitions between the states will be done according to fig.4.c, depending on the input signals. Fig.3 URS controller simulation: a) Simulation model; b) Simulation result 599

4 Fig.4 State machine: a) controller block diagram; b) truth table; c) state transition diagram Fig.5. Algorithm block diagram Fig.6. VHDL design program 6

5 Fig.8. VHDL simulation waveforms B. VHDL Controller Algorithm The controller is implemented according to the algorithm presented in fig.5 and was written based on fig.4. The VHDL program that implements the algorithm from fig.5 is presented in fig.6. [] C. VHDL Controller Modeling and Simulation In fig.7 there is presented the VHDL test bench and in fig.8 the waveform simulation results for the URS controller. The results are as expected and this is important for the design of the real controller as a VHDL solution. [3] IV. CONCLUSION In order to design a controller for an URS machine it is considered as a two arms robot, in this paper. This two armed robot is analyzed using the Denavit- Hartenberg formalism and are determined the direct and inverse cinematic models. These models are validated using MatLab-Simulink environment. This solution uses rigorous mathematic models allowing the implementation of complex control algorithms. Based on the simulation results there was designed the URS controller as a VLSI solution using VHDL hardware description language. REFERENCES Fig.7. VHDL simulation test bench [] Leba, M., Pop, E., Vamvu, P., Corina C. and Covaciu, C. (9). Modeling and Simulation for Cinematic and Dynamic Regime of an Industrial Articulated Robot. Proceedings of the 8th WSEAS International Conference on CIRCUITS, SYSTEMS, ELECTRONICS, CONTROL & SINAL PROCESSIN, Puerto de la Cruz, Spain, ISBN , ISSN 79 57, pp [] Perry, D. (). VHDL programming by examples. Mcraw Hill, USA. [3] Petroni, V. (4). Circuit design with VHDL. MIT Press, Cambridge, Massachusetts, USA. [4] Pop, E. (983). Automatizari in industria miniera, Editura Didactica si Pedagogica, Bucharest, Romania. 6

6 [5] Pop E. and Leba M. (9). Digital Controller Design Based on Logic Neural Networks. In Proceeding of IFAC Workshop DESDES 9, andia, Spain, pp [6] Pop, E., Leba, M. and Pop, M. (7). Sisteme de conducere a robotilor. Structura, modelarea, simularea si conducerea robotilor ficsi si mobili, Editura Didactica si Pedagogica, Bucharest, Romania. [7] Pop, E., Leba, M., Sirb, V., and Badea, A. (8). Modeling, simulation and control for an underground roof support as two robotic arms. In: IEEE International Conference on Automation, Quality and Testing, Robotics (AQTR 8), Cluj Napoca, Romania, pp. 5-8, ISBN: , BIF. [8] Pop, E., Pop, M. and Leba, M. (). Simulation of optimal control for mining drilling robot, Proceedings of the 7th International Mining Congress and Exhibition of Turkey (IMCET ), Ankara, Turkey, pp , BS9X. 6