Joan Batlle, Enric Hospital, Jeroni Salellas and Marc Carreras Institut d Informàtica i Aplicacions Universitat de Girona Avda. Lluis Santaló s/n 173 Girona tel: 34.972.41.84.74 email: jbatlle, ehospit, jsalell, marcc@eia.udg.es DEVELOPMENT OF A BIPED ROBOT Abstract: In this paper we present the work done on the construction and control of a biped robot. In our research we have developed two robot prototypes, the first prototype was made using a flexible polyamide with three degrees of freedom in each leg, but with the movement of the ankle joint not controlled, in the second one we have improved several features of the first prototype, like the material used, more controlled joints and location and movement of the counterweight. This paper is structured in three sections, the first section explains the mechanical structure of the robot. The second section shows the control and the power system of the second prototype and finally, the last section explains the software application used to control the biped robot. 1 Introduction In recent years the study of the biped robots has increased due to the large numbers of applications that we can use them, for example modern control theory (Pratt et al., 1997), the study of mechanisms (Yi, 1997) (Vukobratoic et al., 199), or medical applications (Jalics, 1997). The main problem of the biped robots is that they are very difficult to control because they are unstable systems and Multi-Input and Multi-Output (they take a lot of information of the environment and drive a great number of actuators) (Pratt et al., 1997). The performance of these kind of robots is usually measured in terms of biological similitude, efficiency, smoothness of movements, maximum step speed and robustness in rough superficies. We have developed two biped robots. Both, have three degrees of freedom on each leg and a counterweight. On each prototype, we have used a different material, actuators and position and trajectory of the counterweight. 2 Mechanical structure The first prototype, shown in figure 1, was made using a flexible polyamide, and it has two legs joint to a rectangular platform placed on the top. Each leg has three degrees of freedom as shown in figure 2.
Figure 1 Figure 2 In the low part you can find the foot degree of freedom, that belong to the ankle joint. This movement is not controlled. When the foot contacts against the floor, it adapts its position automatically, and we only use springs to keep the foot in a centred position when it s on the air. Further, there is a support in the forward of the foot that doesn t allow to fall down. The next degree of freedom is the knee joint, allowing to bend the leg. The third degree of freedom is the hip joint, and it allows moving all the links of the leg. These last two movements are controlled by a DC motors with reductions that allow a linear displacement. The top platform that joins the legs has another actuator what we use to move a counterweight side to side. This actuator is composed by a DC motor too and its reductions. When we move the counterweight to one side we change the robot s global centre gravity position. For each degree of freedom we use a variable resistor, which value shows us its position. With the information of the sensors we can build the robot s position versus the floor. As a security system, the actuators have a switch that stops the movements when it arrives to an edge. The mechanical structure has been designed to walk like a human, by means of a sequence of reference positions, as show the fig. 3. This sequence allows the robot to advance on the movement without falling down. The top of the figure shows the required positions of the counterweight, in order that the projection of the centre of gravity cross the foot s base. To do a step, the robot only must raise the free leg, advance and descent it. Figure 3
Once we have tested the mechanical structure and detected the design problems, we have built the last prototype. The first important change is the material used to build the robot, it has been aluminium, a light, robust and easy mechanise material. The figure shows a table with the length and weight of each part. DIMENSIONS WEIGHT NUMBER (one leg) TOTAL WEIGHT FOOT 24 x 13 mm 685 gr. 1 685 gr. FEMUR 4 mm 745 gr. 1 745 gr. TIBIA 4 mm 7 gr. 1 7 gr. LINEAR MOTOR 15 254 mm 82 gr. 3 246 gr. TOTAL WEIGHT (one leg) 459 gr. The DC actuators used are another important change. Which, faster than the first, allow a linear velocity of.5 m/s. Each of the legs has three degrees of freedom like the first prototype, except that the ankle joints aren t free but it disposes of two new actuators to move them. The new biped robot is shown in fig. 4, such as one of the DC actuators used. Figure 4 θ 1 θ 3 Figure 5 θ 2 Next we explain how we have compute the movement range for each joint. These movement ranges depend of the actuator positions. To compute them we have used trigonometric equations we have done with small programs in MATLAB. The movement ranges calculated for each joint are represented in fig. 5 as θ 1, θ 2 and θ 3. Hip joint: -35º < θ 1 < +6º Knee joint: -85º < θ 2 < +25º Ankle joint: +55º < θ 3 < +125º
But one the most important changes of this second prototype is the position of the counterweight to keep the robot s equilibrium. In the first version the counterweight was placed on the top platform and moved side to side to change the global centre of gravity. In this second version the counterweight is composed by one axis with a weight in its edge, that turns 36º and is placed on the top platform, too. With one actuator we can turn the weight to any point over an imaginary circle placed on the robot. The fig. 6 shows a general scheme of the biped robot (legs and counterweight). With this new location of the counterweight we achieve new movements for the robot. One of this movements could be, for example, to climb small steps. Figure 6 3 Control system By now, the last prototype is not autonomous. All the control and power circuits and interfaces are external, so the control signals are sent to the robot across the link cable. Three parts as shows fig. 7 of the blocs diagram basically compose the control and power system of the prototype. The first part is formed by the PC which enclose the data acquisition card. This card allows to catch the variable resistors actuators values (Position Signals), which give us the joints position and in accord with the read values and the movement we want to do, it allows us to send the 1 bits Control Word to the FPGA card we do the control with. PC Control Word FPGA Card PWM Signals Power Card ROBOT Position Signals Power Signals Figure 7
Now we show the bits that form the Control Word: RESET: System reset bit. DECODE: Bit to enable to decode, for validate the new inputs. ADR, ADR1, ADR2: Address Bits to select the actuators (It allow us to control since 8 motors). DATA: Date Bit that provides the direction to turn. DATA1, DATA2, DATA3, DATA4: Date Bits that provides the PWMs level, or velocity, for the select motor (since 16 different levels). The FPGA card composes the second part. The two main functions of this card are: to isolate optically the signals of the control word sent by the PC, and with the control word to generate the PWM s signals need to control the motors. The generation of the PWMs is made with a Xilinx FPGA. Each moment we connect this FPGA card to supply, we do the download of the logic circuit of this PWMs. Now the FPGA is configured. The third part of the control system is the power card. This card receives the PWMs of the FPGA card and with electronic drivers, it actives the corresponding actuator with a movement speed proportional to input. The activation of the motors is made with MOSFETs. Due to the big consumption of these motors, each motor has a full or H bridge of MOSFETs. 4 Control software The control program has been carried out with the LabWindows/CVI software and it seeks to control the robot in a simple and intuitive way, besides visualising its position in each moment. We can control the robot in a manual way or in an automatic way by means of two of the panels of the application. From the manual control panel we can indicate the speed and the sense in that we want to move the motor. From the automatic control panel certain parameters can be altered so that the robot can walk in an autonomous way. In this prototype we control the motors don't arrive at the edge with the application. When the value of some variable resistor is outside of some present limits, we stopped the motor. We can also make it by means of one of this panel buttons and with a General STOP button in case of emergency, when it is necessary to stop all the motors at the same time. The fig. 8 shows the main window of the program and the window of manual control of the motors. Figure 8
With this application we can also visualise the robot's state, whether with the panel where we have the graphs for each one of the articulations or with the panel where the robot's movement is simulated, and they are shown in fig. 9. Figure 9 To visualise the robot's state and to calculate each one of the points of the articulations we have used the cinematic direct problem (Snyder, 1985) from the angles and the real lengths of the robot's links. We consider the robot's lateral view (plane XY) and the rotations that take place in the axis Z and the translations in the axis X. The transformation womb that we have used for each one of the articulations is this: x' cosθ y' sinθ = z' 1 sinθ cosθ 1 1 1 1 1 l x y z 1 1 Where: x, y, z are the origin point co-ordinates x', y', z ' are the destination point co-ordinates θ is the angle we want to rotate l is the length of the link 5 Conclusions and future work When we made the first prototype the main goal was to achieve that the robot walks. This first target was reach but the positions of trajectory are not completely stable and the speed of the movement was very slow (3 seconds for one step of 2 cm). With the last prototype we have used a new material and new lineal actuators, so the robot can walk faster (1 seconds for one step). And the position, structure and trajectories of the counterweight allow to the robot to do a wide range of movements. 6 References JALICS L., HEMAMI H., ZENG Y.F. 1997. Pattern Generation using Coupled Oscillators for Robotic and Biorobotic adaptive periodic movement. Proceedings ICRA. pp 179-184. PRATT J., DILWORTH P., PRATT G. 1997. Virtual Model Control of Bipedal Walking Robot. Proceedings ICRA. pp 193-198. SNYDER E.WESLEY. 1985. Industrial Robots: Computer Interfacing and Control. Ed. Prentice-Hall
VUKOBRATOIC M., BOROVAC B., SURLA D., STOKIC D. 199. Biped Locomotion: Dynamics, Stability, Control and Application. Springer-Verlag. YI K.Y. 1997. Locomotion of a Biped Robot with complian ankle joints.. Proceedings ICRA. pp 199-24.