- Email: [email protected]
Force Sensing to Control a Bio-Inspired Walking Robot
11th IFAC Workshop on Intelligent Manufacturing Systems The International Federation of Automatic Control May 22-24, 2013. São Paulo, Brazil
WeGT1.3
Force Sensing to Control a Bio-Inspired Walking Robot Rafael P. Bachega, Ricardo Pires and Alexandre B. Campo. Instituto Federal de São Paulo – IFSP – São Paulo, Brasil (e-mail: [email protected] [email protected] [email protected]). Abstract: This paper presents the configuration for a bio-inspired walking robot to be used as a development experimental platform in order to validate control architectures. Basing on direct exploitation of the properties of a robot’s mechanical structure, an approach for achieving force sensing is presented. During the robot’s (electronic and mechanical) developmental phase, we were able to determinate knots with increases levels of tension and compression, in order to send signals to the strain gauges and to indirectly measure contact forces between the legs and the terrain. This study allowed us to theoretically allocate a group of strain gauges on the optimal positions in the mechanical structure so that they can accomplish the dynamic control of the robot. Keywords: Biologically-inspired systems, legged robot, locomotion patterns, force sensing, dynamic control. 1. INTRODUCTION The better locomotion performance of hexapod robots in uneven floors may be obtained by use of a great number of different kinds of sensors. The signals generated by these sensors may be used to represent the real state of the robot and its interactions with the environment. The use of these signals in a closed loop control enhances the walking ability of these robots (Estremera et al., 2003). The movement of the hexapod robots is characterized by the harmonic coordination of its legs. The contact of the feet with the floor along the movement produces a reaction force pattern that determines the global stability of the robot (Kaliyamoorthy et al., 2001). By this reason the researchers are studying force control strategies based in measurement of these reaction forces. Several advantages could be obtained by this analysis, such as: damping analysis of each walking pattern, energy consumption minimization, real time analysis of impact forces while feet are on the floor, and assessment of optimal force redistribution to obtain better stability and to expand operational capabilities (Preumont et al., 1991; Marhef et al., 1998; Quinn et al., 2001; Bowling, 2007). At Quinn et al. (2001) a set of strain gauges are attached to the legs of the robotic hexapod structure to study the continuous straight gait. By studying force impact as the feet hit the floor, Bowling (2007) presents a method to analyze the dynamic performance of a hexapod robot. He analyzes how much impact of the foot on the floor is effective for one to obtain convenient movement of the robot body. In order to apply the dynamic control system, one needs to measure the forces acting upon the robot. The strain gauges consist of transducers used in many applications where environment reactions over the robot parts have to be 978-3-902823-33-5/13/$20.00 © 2013 IFAC
Fig. 1. The MYRMEX walking robot. The robot has 25.4 cm×32.5 cm footprint, measures 21.6 cm in overall height, and weighs of 3.8 kg. measured. The use of this kind of sensors provides for high sensibility, repeatability and accuracy at measurement. These transducers need signal conditioning with high-gain electronic amplifier. The main disadvantage of a strain gauge is related to its sensibility to temperature variations, which must be minimized by several methods such as those described in Gorinevsky et al. (1990) and Montes et al. (2006). Few papers describe experimental applications to develop force control systems and others propose and analyze algorithms to enhance the force redistribution at the robot legs. Some algorithms are based on linear programming or linear optimization, quadratic optimization and pseudoinverse solutions (Orin and Oh, 1981; Kumar and Waldron, 1988).
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In order to obtain the best force redistribution, one must solve - in real time - the algorithms pertaining either to the linear programming or to the quadratic programming method. This is the biggest challenge to the technique. Several papers only present simulation results of this kind by applying one of these solutions. A pseudo-inverse matrix implemented in FPGA (Field Programmable Gate Array) hardware may be used to solve the minimization problem. It is possible to quickly solve the minimization problem related to the equation that represents the sum of square forces at each foot (Wang, 2007). This paper studies several of the forces applied to the finite element model as a surrogate for the legs of a hexapod robot MYRMEX. The analyses of these forces are based in kinematic studies, and the results determine the positions of the transducers at the legs, allowing for the dynamic closed loop control of the robot (Bachega et al., 2012). There are few works that show - in detail - the procedures used to select the positions that should receive force sensors such as the strain gauges. Thus, this study tried to determine the main points where the transducers can be attached to the structure of the robot MYRMEX for optimal force redistribution. The second section of this paper shall introduce the robot structure used in this work. The third section shall describe the method used to define the positioning of the sensors and their calibration procedure. The current measurement at each servomotor is described at the end of this section. Finally, the last section shall discuss the results obtained so far and shall suggest how the results will be used to solve the problem of optimal force distribution. 2. DESCRIPTION OF THE BIO-INSPIRED WALKING ROBOT (MYRMEX) 2.1 Mechanical Assembly and Actuation The mechanical configuration of the MYRMEX robot is presented at Fig. 1. The structure has weight of 3.8 kg and each shaft at the joints is individually controlled by a servomotor using the digital signal generated by a FPGA
Xilinx Spartan3 (XC3S500E) chip and the configuration is made through the VHDL language, using the XILINX’s ISE WebPACK 13.2. The signals used to control the position of each one of the eighteen servomotors are in PWM (Pulse Width Modulation) form. The system was designed to overcome obstacles 100 mm high and its parts were built with aluminum 6061. Each leg consists of three revolute joints which are actuated by position-controlled servos. The legs structures have a revolution shaft for each degree of freedom, acting directly at the member to be moved. The servomotors (HSR-5990) used in this work don’t provide the angle information to the FPGA. Given the unavailability of information, a discrete control approach is applied, inserting frequent delays in external signal (PWM) allowing for speed control. 3. TRANSDUCER IMPLEMENTATION 3.1 Finite Element Analysis (FEA) At the cycle of locomotion, the legs movements alternate two phases: the transfer phase and the support phase. During the transfer phase, a set of legs are elevated and moved from one foothold to the next. At the other phase, the support phase, a set of legs support the weight of the structure and moves according to the march defined. At the support phase the force transducers attached to each leg have to detect the contact with the floor and estimate the force applied by the set of motors. Using the kit COSMOSWorks of the SolidWorks 2011 software it was performed a finite element analyses to define the best points to measure the forces at the links. Considering an isotropic homogeneous material subjected to a linear elastic analysis, the properties studied are the Young Modulus (E), the Poisson Coefficient (ν) and the Shear Modulus (G). To study elastic deformation characteristics of the parts, a grid were created with loads and restrictions applied according to kinematic studies. This procedure generates the points at the structure where the compression
Fig. 2. Analysis of forces in LK2: FEA to determine stresses in the normal direction.
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and tension have the higher level when the legs are at the support phase (Kaliyamoorthy et al., 2001). The Von Mises conditions of constant shearing stress intensity were analyzed at the critical parts of the structure. The FEA gave several insights about the structure design, but it is necessary to develop several essays to verify the conditions of dynamic loading. At Fig. 2 the force distribution at the link (LK2) is showed with 0.1 Nm torque and 10 N applied at the points numerically determined. The micrometric deformation is presented at the color scale. 3.2 Sensor Placement Four strain gauges were attached to each leg to validate the FEA analysis results. At these points the dimensions of the reaction forces have their greater values. At the Fig. 3 it is showed a picture of the sensor placed at the structure. 3.3 Calibration Procedure To obtain the relationship between the forces applied to each part of the link and the voltage generated at the electronic circuit an experimental procedure was performed. Setting the link, several loads were placed at the other side of it, and the voltage generated at the circuit was measured. The calibration process consists in calculating a diagonal matrix representing the relationship between the electrical voltage measured at each of the transducers on the robot’s legs and the forces measured by the reference instrument. The hexapod robot was placed at a static position and the position control actuating at the servos actuated to move the leg down in incremental steps of 2 mm. This movement was done until the voltage measured at the bridge remains constant. The signal generated at the Wheatstone bridge was amplified (Instrumentation Amplifier INA 2126) and the data was acquired using a data acquisition board with LabVIEW. The calibration procedure generated equations represented at a matrix format (1):
(1)
Fig. 3. Strain gauges at the LK2 link: Normal force measurement;
The voltage applied measured at the Wheatstone bridge was amplified eight hundred times and was acquired with the acquisition board. Fig. 4 shows the relationship between the voltage at each strain gauge circuit and the load applied at the link. The results obtained for each link were linear and the expressions presented at (1) were calibrated finding the parameters and for each link. The linear relation verified between the forces applied and the signals described above was observed when just one link was studied as well as all parts of the robot was built using the servomotors and the other links. 4. RESULTS AND SIMULATIONS
Where
are the normal forces measured at the link (LK2), are the voltage measured at the amplifier circuit attached at the link under stress, are the voltage measured at the amplifier circuit at the same bridge without the stress, is the voltage of the power supply feeding the Wheatstone Bridge. The parameters to represent the calibration constants.
978-3-902823-33-5/13/$20.00 © 2013 IFAC
The hexapod robots have several walking configurations. The postural analyses identify the structure points under higher stress. The robot legs are identified such that P1 to P3 represents the left side of the robot and P4 to P6 represent the other side. The stress analysis over the links may be done during a straight walking gait, but at this step of the work a static acquisition data with different support configurations were done.
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Fig. 4. Calibration results: (a) Voltage constant of the power supply feeding the Wheatstone bridge; (b) and (c) Linear equation between the normal forces and the voltage measured.
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Fig. 5. Experimental configurations used: (a) MYRMEX walked by utilizing a tripod gait; (b) six legs at the rigid surface; (c) tripod, with legs P2, P4 e P6 at the ground. Both picture show the robot placed at 110 mm over the floor.
The robot was positioned over a rigid surface and several static positions were used to obtain the data that will be used at the future steps of the work. The symmetry of the information generated by the strain gauges when the hexapod is positioned at tripod position (P2, P4 and P6) was used to compare with the other tripod equivalent position (P1, P3 and P5). Fig. 5 presents the hexapod placed at the ground. At the Fig. 5.b the robot sustains the body over all its legs (P1 to P6). The other picture (Fig. 5.c) shows another configuration, with only three legs sustaining the robot.
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In the first experiment (to evaluate the transducers) consisted in raising the robot 0.6 m from the ground, starting from a position where all the legs were not in contact with the ground, i.e. the frame of the robot was on the ground. The experimental procedure consist of a coordinated legs movement that elevate the hexapod frame from the ground to the static position in 3 s. After the end of this movement, the total mean force measured at the instant t = 10s was 37,71 N. This measurement is equivalent to a total mass of 3,844 kg, which represent an error of 1,5 % relative to the total weight of the robot (the total weight measured is 3,788 kg). At the second experiment it was applied an external disturb, when a total constant force of 8,34 N was added to the system at the instant t = 30s. The addiction of this force was measured and the registered value was 48,45N, representing an measurement error of 6,4%.
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Fig. 6. Dynamic experiment: the robot is placed in a static position over a horizontal plane. The servos are activated at t = 30s and the robot stay over its six feet. At the studies of the dynamics of the hexapod robot some results were obtained through the measurement of the forces measured at the links along a walking procedure. Two of these experiments are described below. At the first one, the robot was taken off from the ground, elevating the frame until no foot touch the ground. At the second one, the robot was placed over a regular horizontal plane and a tripod walk was
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executed in a fast way. At figure 7 it is possible to identify the transfer phase and the support phase along the tripod walking experiment. At each one of the figure 7 is it possible to identify, for both tripod sets (P1, P3 and P5) or (P2, P4 and P6), the support and the transference phases. Also it is possible to analyze the reaction forces at dynamic and static situations. Strain Legs 1,2 e 3.
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control problem (Jiang, 2004), but the use of the most recent advances in digital electronic design (FPGA) to solve the real time complex problems present at robotic systems represents an improvement addressing the problem. Results presented in this paper indicate that the strain-gauges can serve as specific load indicators during walking. Specifically, the strain-gauges sensors can detect the level of force and its rate of change during locomotion, providing information about force direction during stance. Using the data described at this work, an optimization algorithm based on functional analysis is being developed. The optimization will minimize the maximum value of the strain at the legs that support the robot. ACKNOWLEDGMENT
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R. P. Bachega thanks the SENAI – Roberto Simonsen, at. São Paulo - Brazil. The authors thank Texas Instruments and Xilinx, Inc. for the donation of components and development kits.
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Fig. 7. Dynamic experiments: a tripod walk in a regular horizontal plane.
5. CONCLUSIONS The measurement of the stress at each leg link by using the collected data has been successful. After this step, the gait analysis may be developed using the acquired data. After several simulations at the SolidWorks software, the strain gauges positions were defined and an experimental calibration procedure was implemented. The linear results obtained may be useful to analyze the structural configuration of the robot. Through the data collected the system algorithm may be developed. The results obtained until now represent the set of inputs of the control algorithm necessary to obtain optimal force redistribution. Several works describe this dynamic 978-3-902823-33-5/13/$20.00 © 2013 IFAC
A. Bowling, “Impact Forces and Mobility in Legged Robot Locomotion,” in IEEE Int. Conf. Advanced Intelligent Mechatronics, pp. 1-8, 4-7 September 2007. A. Preumont, P. Alexandre and D. Ghuys, “Gait Analysis and Implementation of a Six Leg Walking Machine,” in International Conference on Advanced Robotics ‘Robots in Unstructured Environments,’ Pisa, Italy, Vol. 2 (Jun. 19–22, 1991) pp. 941–945. D. Marhef, and D. Orin, “Quadratic optimization of force distribution in walking machines,” in IEEE Int. Conf. on Robotic and Automation, pp. 477–483, 16-20 May 1998. D. M. Gorinevsky, and A. Y. Schneider, “Force control in locomotion of legged vehicles over rigid and soft surfaces,” in The Int. Journal of Robotics Research vol. 9, pp 4–23, April 1990. D. Orin, and S. Oh, “Control of force distribution in robotic mechanisms containing close-kinematics chains,” in Journal Dynamic Syst. Meas. and Control, vol. 102, pp. 134–141, June 1981. H. Montes, S. Nabulsi, and M. A. Armada, “Reliable, Builtin, High-Accuracy Force Sensing for Legged Robots,” in The Int. Journal of Robotics Research, vol. 25, pp. 931– 950, September 2006. J. Estremera and P. G. Santos, “Free gaits for quadruped robots over irregular terrain” in in The Int. Journal of Robotics Research, vol. 22, pp 115–13, 2003. R. P. Bachega, R Pires and A. B. Campo, “Hardware Configuration of Hexapod Robot to Force Feedback Control Development” in IEEE. 44th Southeastern Symposium on System Theory, USA, 2012. R. D. Quinn, G. M. Nelson, and R. J. Bachmann, “Insect designs for improved robot mobility,” in Proc. 4th Int. Conf. Climbing and Walking Robots, Germany, 2001, pp. 69–76. S. Kaliyamoorthy, S. N. Zill, R. D. Quinn, R. E. Ritzmann, and J. Choi, “Finite element analysis of strains in a Blaberus cockroach leg during climbing,” in IEEE Int. Conf. on Intelligent Robots and Systems, vol. 2, pp. 833– 838, 2001. V. Kumar, and K. Waldron, “Force distribution in closed kinematics chains,” in IEEE Int. Conf. of Robotics and Automation, vol. 25, pp. 931–950, 24-29 April 1988. W. Jiang, A. Liu, and D. Howar, “Optimization of legged robot locomotion by control of foot force distribution,” in Transactions of the Institute of Measurement and Control, vol. 26, pp. 311-323, October 2004.
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Force Sensing to Control a Bio-Inspired Walking Robot Rafael P. Bachega, Ricardo Pires and Alexandre B. Campo. Instituto Federal de São Paulo – IFSP – São Paulo, Brasil (e-mail: [email protected] [email protected] [email protected]). Abstract: This paper presents the configuration for a bio-inspired walking robot to be used as a development experimental platform in order to validate control architectures. Basing on direct exploitation of the properties of a robot’s mechanical structure, an approach for achieving force sensing is presented. During the robot’s (electronic and mechanical) developmental phase, we were able to determinate knots with increases levels of tension and compression, in order to send signals to the strain gauges and to indirectly measure contact forces between the legs and the terrain. This study allowed us to theoretically allocate a group of strain gauges on the optimal positions in the mechanical structure so that they can accomplish the dynamic control of the robot. Keywords: Biologically-inspired systems, legged robot, locomotion patterns, force sensing, dynamic control. 1. INTRODUCTION The better locomotion performance of hexapod robots in uneven floors may be obtained by use of a great number of different kinds of sensors. The signals generated by these sensors may be used to represent the real state of the robot and its interactions with the environment. The use of these signals in a closed loop control enhances the walking ability of these robots (Estremera et al., 2003). The movement of the hexapod robots is characterized by the harmonic coordination of its legs. The contact of the feet with the floor along the movement produces a reaction force pattern that determines the global stability of the robot (Kaliyamoorthy et al., 2001). By this reason the researchers are studying force control strategies based in measurement of these reaction forces. Several advantages could be obtained by this analysis, such as: damping analysis of each walking pattern, energy consumption minimization, real time analysis of impact forces while feet are on the floor, and assessment of optimal force redistribution to obtain better stability and to expand operational capabilities (Preumont et al., 1991; Marhef et al., 1998; Quinn et al., 2001; Bowling, 2007). At Quinn et al. (2001) a set of strain gauges are attached to the legs of the robotic hexapod structure to study the continuous straight gait. By studying force impact as the feet hit the floor, Bowling (2007) presents a method to analyze the dynamic performance of a hexapod robot. He analyzes how much impact of the foot on the floor is effective for one to obtain convenient movement of the robot body. In order to apply the dynamic control system, one needs to measure the forces acting upon the robot. The strain gauges consist of transducers used in many applications where environment reactions over the robot parts have to be 978-3-902823-33-5/13/$20.00 © 2013 IFAC
Fig. 1. The MYRMEX walking robot. The robot has 25.4 cm×32.5 cm footprint, measures 21.6 cm in overall height, and weighs of 3.8 kg. measured. The use of this kind of sensors provides for high sensibility, repeatability and accuracy at measurement. These transducers need signal conditioning with high-gain electronic amplifier. The main disadvantage of a strain gauge is related to its sensibility to temperature variations, which must be minimized by several methods such as those described in Gorinevsky et al. (1990) and Montes et al. (2006). Few papers describe experimental applications to develop force control systems and others propose and analyze algorithms to enhance the force redistribution at the robot legs. Some algorithms are based on linear programming or linear optimization, quadratic optimization and pseudoinverse solutions (Orin and Oh, 1981; Kumar and Waldron, 1988).
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In order to obtain the best force redistribution, one must solve - in real time - the algorithms pertaining either to the linear programming or to the quadratic programming method. This is the biggest challenge to the technique. Several papers only present simulation results of this kind by applying one of these solutions. A pseudo-inverse matrix implemented in FPGA (Field Programmable Gate Array) hardware may be used to solve the minimization problem. It is possible to quickly solve the minimization problem related to the equation that represents the sum of square forces at each foot (Wang, 2007). This paper studies several of the forces applied to the finite element model as a surrogate for the legs of a hexapod robot MYRMEX. The analyses of these forces are based in kinematic studies, and the results determine the positions of the transducers at the legs, allowing for the dynamic closed loop control of the robot (Bachega et al., 2012). There are few works that show - in detail - the procedures used to select the positions that should receive force sensors such as the strain gauges. Thus, this study tried to determine the main points where the transducers can be attached to the structure of the robot MYRMEX for optimal force redistribution. The second section of this paper shall introduce the robot structure used in this work. The third section shall describe the method used to define the positioning of the sensors and their calibration procedure. The current measurement at each servomotor is described at the end of this section. Finally, the last section shall discuss the results obtained so far and shall suggest how the results will be used to solve the problem of optimal force distribution. 2. DESCRIPTION OF THE BIO-INSPIRED WALKING ROBOT (MYRMEX) 2.1 Mechanical Assembly and Actuation The mechanical configuration of the MYRMEX robot is presented at Fig. 1. The structure has weight of 3.8 kg and each shaft at the joints is individually controlled by a servomotor using the digital signal generated by a FPGA
Xilinx Spartan3 (XC3S500E) chip and the configuration is made through the VHDL language, using the XILINX’s ISE WebPACK 13.2. The signals used to control the position of each one of the eighteen servomotors are in PWM (Pulse Width Modulation) form. The system was designed to overcome obstacles 100 mm high and its parts were built with aluminum 6061. Each leg consists of three revolute joints which are actuated by position-controlled servos. The legs structures have a revolution shaft for each degree of freedom, acting directly at the member to be moved. The servomotors (HSR-5990) used in this work don’t provide the angle information to the FPGA. Given the unavailability of information, a discrete control approach is applied, inserting frequent delays in external signal (PWM) allowing for speed control. 3. TRANSDUCER IMPLEMENTATION 3.1 Finite Element Analysis (FEA) At the cycle of locomotion, the legs movements alternate two phases: the transfer phase and the support phase. During the transfer phase, a set of legs are elevated and moved from one foothold to the next. At the other phase, the support phase, a set of legs support the weight of the structure and moves according to the march defined. At the support phase the force transducers attached to each leg have to detect the contact with the floor and estimate the force applied by the set of motors. Using the kit COSMOSWorks of the SolidWorks 2011 software it was performed a finite element analyses to define the best points to measure the forces at the links. Considering an isotropic homogeneous material subjected to a linear elastic analysis, the properties studied are the Young Modulus (E), the Poisson Coefficient (ν) and the Shear Modulus (G). To study elastic deformation characteristics of the parts, a grid were created with loads and restrictions applied according to kinematic studies. This procedure generates the points at the structure where the compression
Fig. 2. Analysis of forces in LK2: FEA to determine stresses in the normal direction.
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and tension have the higher level when the legs are at the support phase (Kaliyamoorthy et al., 2001). The Von Mises conditions of constant shearing stress intensity were analyzed at the critical parts of the structure. The FEA gave several insights about the structure design, but it is necessary to develop several essays to verify the conditions of dynamic loading. At Fig. 2 the force distribution at the link (LK2) is showed with 0.1 Nm torque and 10 N applied at the points numerically determined. The micrometric deformation is presented at the color scale. 3.2 Sensor Placement Four strain gauges were attached to each leg to validate the FEA analysis results. At these points the dimensions of the reaction forces have their greater values. At the Fig. 3 it is showed a picture of the sensor placed at the structure. 3.3 Calibration Procedure To obtain the relationship between the forces applied to each part of the link and the voltage generated at the electronic circuit an experimental procedure was performed. Setting the link, several loads were placed at the other side of it, and the voltage generated at the circuit was measured. The calibration process consists in calculating a diagonal matrix representing the relationship between the electrical voltage measured at each of the transducers on the robot’s legs and the forces measured by the reference instrument. The hexapod robot was placed at a static position and the position control actuating at the servos actuated to move the leg down in incremental steps of 2 mm. This movement was done until the voltage measured at the bridge remains constant. The signal generated at the Wheatstone bridge was amplified (Instrumentation Amplifier INA 2126) and the data was acquired using a data acquisition board with LabVIEW. The calibration procedure generated equations represented at a matrix format (1):
(1)
Fig. 3. Strain gauges at the LK2 link: Normal force measurement;
The voltage applied measured at the Wheatstone bridge was amplified eight hundred times and was acquired with the acquisition board. Fig. 4 shows the relationship between the voltage at each strain gauge circuit and the load applied at the link. The results obtained for each link were linear and the expressions presented at (1) were calibrated finding the parameters and for each link. The linear relation verified between the forces applied and the signals described above was observed when just one link was studied as well as all parts of the robot was built using the servomotors and the other links. 4. RESULTS AND SIMULATIONS
Where
are the normal forces measured at the link (LK2), are the voltage measured at the amplifier circuit attached at the link under stress, are the voltage measured at the amplifier circuit at the same bridge without the stress, is the voltage of the power supply feeding the Wheatstone Bridge. The parameters to represent the calibration constants.
978-3-902823-33-5/13/$20.00 © 2013 IFAC
The hexapod robots have several walking configurations. The postural analyses identify the structure points under higher stress. The robot legs are identified such that P1 to P3 represents the left side of the robot and P4 to P6 represent the other side. The stress analysis over the links may be done during a straight walking gait, but at this step of the work a static acquisition data with different support configurations were done.
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Fig. 4. Calibration results: (a) Voltage constant of the power supply feeding the Wheatstone bridge; (b) and (c) Linear equation between the normal forces and the voltage measured.
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Fig. 5. Experimental configurations used: (a) MYRMEX walked by utilizing a tripod gait; (b) six legs at the rigid surface; (c) tripod, with legs P2, P4 e P6 at the ground. Both picture show the robot placed at 110 mm over the floor.
The robot was positioned over a rigid surface and several static positions were used to obtain the data that will be used at the future steps of the work. The symmetry of the information generated by the strain gauges when the hexapod is positioned at tripod position (P2, P4 and P6) was used to compare with the other tripod equivalent position (P1, P3 and P5). Fig. 5 presents the hexapod placed at the ground. At the Fig. 5.b the robot sustains the body over all its legs (P1 to P6). The other picture (Fig. 5.c) shows another configuration, with only three legs sustaining the robot.
978-3-902823-33-5/13/$20.00 © 2013 IFAC
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In the first experiment (to evaluate the transducers) consisted in raising the robot 0.6 m from the ground, starting from a position where all the legs were not in contact with the ground, i.e. the frame of the robot was on the ground. The experimental procedure consist of a coordinated legs movement that elevate the hexapod frame from the ground to the static position in 3 s. After the end of this movement, the total mean force measured at the instant t = 10s was 37,71 N. This measurement is equivalent to a total mass of 3,844 kg, which represent an error of 1,5 % relative to the total weight of the robot (the total weight measured is 3,788 kg). At the second experiment it was applied an external disturb, when a total constant force of 8,34 N was added to the system at the instant t = 30s. The addiction of this force was measured and the registered value was 48,45N, representing an measurement error of 6,4%.
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Fig. 6. Dynamic experiment: the robot is placed in a static position over a horizontal plane. The servos are activated at t = 30s and the robot stay over its six feet. At the studies of the dynamics of the hexapod robot some results were obtained through the measurement of the forces measured at the links along a walking procedure. Two of these experiments are described below. At the first one, the robot was taken off from the ground, elevating the frame until no foot touch the ground. At the second one, the robot was placed over a regular horizontal plane and a tripod walk was
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executed in a fast way. At figure 7 it is possible to identify the transfer phase and the support phase along the tripod walking experiment. At each one of the figure 7 is it possible to identify, for both tripod sets (P1, P3 and P5) or (P2, P4 and P6), the support and the transference phases. Also it is possible to analyze the reaction forces at dynamic and static situations. Strain Legs 1,2 e 3.
1 P1 P2 P3
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control problem (Jiang, 2004), but the use of the most recent advances in digital electronic design (FPGA) to solve the real time complex problems present at robotic systems represents an improvement addressing the problem. Results presented in this paper indicate that the strain-gauges can serve as specific load indicators during walking. Specifically, the strain-gauges sensors can detect the level of force and its rate of change during locomotion, providing information about force direction during stance. Using the data described at this work, an optimization algorithm based on functional analysis is being developed. The optimization will minimize the maximum value of the strain at the legs that support the robot. ACKNOWLEDGMENT
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R. P. Bachega thanks the SENAI – Roberto Simonsen, at. São Paulo - Brazil. The authors thank Texas Instruments and Xilinx, Inc. for the donation of components and development kits.
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5. CONCLUSIONS The measurement of the stress at each leg link by using the collected data has been successful. After this step, the gait analysis may be developed using the acquired data. After several simulations at the SolidWorks software, the strain gauges positions were defined and an experimental calibration procedure was implemented. The linear results obtained may be useful to analyze the structural configuration of the robot. Through the data collected the system algorithm may be developed. The results obtained until now represent the set of inputs of the control algorithm necessary to obtain optimal force redistribution. Several works describe this dynamic 978-3-902823-33-5/13/$20.00 © 2013 IFAC
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