Motion Control of a Bipedal Walking Robot

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1 Motion Control of a Bipedal Walking Robot Lai Wei Ying, Tang Howe Hing, Mohamed bin Hussein Faculty of Mechanical Engineering Universiti Teknologi Malaysia, UTM Skudai, Johor, Malaysia. Wylai2@live.my Abstract: - This paper investigates the performance of different control schemes applied on a 5-link biped robot by simulation studies. The primary controller are implemented with a conventional Proportional Derivative (PD) controller and Computed Torque controller, later enhanced with Active Force Control (AFC). The mathematical modeling and motion control for a bipedal walking robot in this paper consisted of five links, which includes torso, two thighs and two legs. The joints connecting these links are assumed to be friction free and driven by independent servo motors. Reference trajectory for each joint are plotted and designed to produce a five steps gait on horizontal plane with constraint to sagittal plane. Kinematic and dynamic modelling are derived for motion controller to achieve dynamic walking. An animation of bipedal walking robot is simulated using MATLAB Simulink to visualize the bipedal locomotion. By default, proportional and derivative (PD) and computed torque control schemes are implemented into the dynamic model of the five degree of freedom bipedal robot for motion control. The control scheme is further implemented with Active Force Control strategy. The performance of the control schemes are evaluated to determine the control system that can produce optimum performance. It is found that AFC integration on the default controller resulted a robust and stable control system. Key-Words: - biped robot, active force control, neural network, computed torque. 1 Introduction Research in the area of robotics embarks in the 20 th century and had created various types of robots, some of them play an important part in today s industry. These robots perform jobs that are physically demanding, monotonous or even hazardous to human beings. Moreover, they also increase the work rate and quality of products in factories, and thus fulfilling the industrial essential requirements of speed and accuracy. Today, robots are found in almost all modern assembly production lines. Even though various types of robots had been developed and implemented in factories, many of these robots has the limitation of having small and fixed movement patterns, which limits their potential to interact with the surroundings. As a result, robots are rarely in contact with humans, despite many years of research study for a robot that can interact with various changing environments, for examples hexapod, insect robots and others (Jan Helbo, 2007). Research on this field is still at an early stage. One of these research areas compounding robot development using bipedal locomotion, for instances, walking on two legs. Bipedal locomotion study seems to be the solution to this problem, as these robots could function and perform tasks in human environment without adjusting the surroundings of them. Therefore, study and investigation on bipedal robot and bipedal locomotion is essential to the development of the robotic industry. As the balancing of dynamic walking of biped robot is more complicated than only consider static balance, a control system able to compensate the disturbance effects is required. 2 Prior Research Work Early experiment on biped robot locomotion stressed on static balance walking. Through solving kinematic equations, static balance walking is easily achievable, but it actually constraints the biped structure and inefficient. Dynamic walking pattern is more ISBN:

2 sophisticated than static balance walking, but dynamic walking is able to produce walking gait with higher walking speed, better efficiency and more versatile at the same time (Kun et al., 1996). Both static and dynamic balance walking of biped robot are studiedd by Kun and Miller, using foot force sensing (Kun et al., 1996). Designed with neural network learning system, their biped robot is able to learn the balancing front to back disturbances and side to side disturbances. model, the ground in contact with the leg is considered to be highh friction to prevent slipping at the foot end. Gravity effect is utilized to propel the leg forward. Motion of biped robot illustrated at Figure 1 can be described using the angles θ i (i = 1, 2,, 5 ) based on the Lagrange dynamic model at single support phase (SSP). The Lagrange dynamic model is derived as : Then, an autonomous biped system using reactive force control on the foothold and the force distribution system was proposed by Fujimoto and Kawamura (Fujimoto et al., 1998). The physical constraints of the contact force on the foothold are precisely considered. Their work was further enhanced by using variable structure control on a five link biped robot by Lum et al. (Lum et al.., 1999). AFC Strategy with neural network control and iterative learning control had been implemented on robot arm by Mailah.(Mailah, 1998). In overview, a good biped robot walking control algorithm should has the features as followed (Hewit et al.,1981): 1. It does not require excessive computing time relative to the walking cycle, 2. It does not require excessive memory, 3. It does not require an accurate dynamic model 4. It will be impervious to parameters variations and external disturbances. In this paper, PD based computed torque control method is implemented for biped walking control in conjunctionn with AFC control strategy. The performance of each control scheme is evaluated Link Biped Robot In this paper, biped dynamic model is derived according to the five DOF biped robot shown in Figure 1. To derive the dynamic Figure 1: Biped Robot in Single Support Phase (SSP) Where θ = [θ 1 θ 2 θ 3 θ 4 θ 5 ] T is the joint angle vector, D(θ) is positive-definite inertia matrix, h is column vector with Coriolis and centripetal torques, G(θ) as gravity vector and T θ as generalized torque. Only four out of the five degree of freedom can be controlled directly by the four driving torques as there is only four independent motors for joints. The angle θ 1, located at the contact point with the ground is controlled indirectly using the gravitational effect. The existence of ISBN:

3 this degree of freedom whichh cannot be controlled directly is one of the most important characteristics of the locomotion of our biped robot. In order to facilitate the control procedure, is transformed into: 2.2 Control From starting step to steady walking step on horizontal plane, the reference joint trajectory, or reference signals are put into cycles, which one cycle will take 0.5 seconds to accomplish one stride. The reference joint trajectories are plotted in Figure 2 with, Figure 3: Block Diagram of PD Based Computed Torque Control Scheme The generalized torque is represented by, Active Force Control (AFC) AFC control is a control system which calculates error between ideal and actual force vectors to make adjustment to the actuation system. It has fast decoupling property and versatile in different loading conditions. The block diagram is as followed. Figure 2: Reference Trajectory of starting step to steady walking PD Based Computed Torque Control Computed torque control is a method which uses feedback linearization technique, using a control law similar to the biped robot dynamic model. Figure 3 illustrated the structure and block diagram of the PD based computed torque control scheme. Figure 4: Block Diagram of PD Based Computed Torque Control Scheme with AFC integration (Source: L.C. Kwek, 2003) Motion equation for the biped robot becomes Where T is taken as applied torque, Q as disturbance torque, IN(q) as mass moment of inertia and q as the robot joint angle. ISBN:

4 To decouple the actual disturbance torque, Q for the applied torque, estimated torque Q is obtained as followed, 3.1 Simulation Setup The parameters used in the simulations are as followed, Parameters of the small size biped robot Link Link Mass, Length, Location Moment No. m L (m) of centre of (kg) of mass, Inertia, d (m) (kgm) Torso X 10-2 Thigh 2, X 10-2 Leg 1, X 10-2 Table 1: Parameters of the five link biped robot 3.2 Simulation Result The simulation results visualizing the five steps walking gait of the five dof biped robot on a horizontal plane are shown in this section. Using MATLAB, information of tracking error and joint angle can be presented in graph form. The following graph illustrated data collected for PD based Computed Torque control scheme (PDCT) and PD based Computed Torque control scheme integrated with Active Force Control (PDCTAFC), ISBN:

5 Table 2: Average Tracking Error of each joint at 2.5 sec sampling time The performance of different control schemes is evaluated by comparing average tracking error produced by all four joints during simulation, as shown in Table 2. Judging from the results obtained in Figure 5, controller with AFC integration perform better than the controller without AFC integration as AFC minimise the average tracking error possible. It is observed that AFC integration demonstrated a highly accurate controller, as having smaller average tracking error as shown in Table 2. Disturbance test also conducted on both PDCT and PDCTAFC controllers, but since PDCT controller produce substantial amount of tracking error due to its requirement to have proper setting and configuration in order to work, the resulted tracking error influence the whole walking gait simulation, thus the value of average tracking error for PDCT controller under disturbance test is not shown here. Also, from graphs in Figure 6, it is observed that AFC controller is robust under disturbances. Figure 5: Graph of Tracking Error for Joints versus time using PDCT and PDCTAFC control scheme Average Tracking Error (rad) Joint PDCT PDCTAFC PDCTAFC with disturbance ISBN:

6 Figure 6: Graph of Tracking Error for Joints versus time using PDCTAFC without disturbance test and PDCTAFC with disturbance test. ISBN:

7 Figure 7: Graph of Tracking Error for Joints versus time using PDCT and PDCTAFC at 1.25 sec sampling time. Average Tracking Error (rad) Joint PDCT PDCTAFC Table 3: Average Tracking Error of each joint at 1.25 sec sampling time As for Figure 7, the simulation is running at walking speed faster than previous test, which completed five steps in 1.25 seconds. In these study, PDCT significantly having larger average tracking error compared to PDCTAFC controller, with the largest error at rad. PDCTAFC controller shown its accuracy by having rad tracking error at joint 3. Thus, it could be observed that AFC have the advantage of being robust even at faster walking pace, covering up the weakness of ISBN:

8 solely having PD based computed torque controller. 4 Conclusion The simulation study of the biped robot walking on a horizontal plane has been developed successfully. Descriptions on the kinematic model, dynamic model, and studies on the walking gait of this robot have been carried out. Thus, the objective of this project is achieved. Among many other control schemes existed for biped walking, Proportional and Derivative (PD) based computed torque control scheme and Active Force Control (AFC) Integration are chosen for the setup of this project. Simulation studies are carried out to visualize the performance of control scheme used for bipedal walking robot. With different system parameters applied(disturbances, walking speed), PD based computed torque controller is proved to be superior when integrated with AFC. Comparing PD based computed torque control scheme and PD based computed torque control scheme with AFC integration, both using same biped robot parameter and optimized system parameters, PD based computed torque control scheme with AFC integration is proved to be a better control scheme as it is more accurate, response faster, and robust in dealing with disturbances. [5] Fujimoto. Y. And Kawamura. A. (1998), Simulation of an autonomous biped walking robot including environmental force interaction. IEEE Robotics Automat. Mag [6] Hewit. J. R. And Burdess. J. S. (1981), Fast dynamic decoupled control for robotics using active force control. Mechanism Machine Theory 16(5), [7] Lum, H. K., Zribi. M. And Soh, Y. C. (1999), Planning and control of a biped robot, Internat. J. Engrg. Sci. 37, [8] Kun. A. And Miller. W. T. (1996), Adaptive dynamic balance of a biped robot using neural networks. Proc. Of IEEE Internat. Conf. On Robotics and Automation, References: [1] Jan. Helbo (2007), Modelling and Control of a Biped Robot, Aalborg University, 1-28 [2] Hu. J. Pratt, and Pratt G.(1998), Adaptive dynamic control of a biped walking robot with radial basis function neural networks. Proc of IEEE/RSJ Internat. Conf on Intelligent Robots and Systems, [3] L.C. Kwek et. al.(2003), Application of Active Force Control and Iterative Learning in a 5- linnk Biped Robot. [4] Mailah, M (1998), Intelligent Active Force Control of a Rigid Robot Arm using Neural Network and Iterative Learning Algorithms, Ph.D. dissertation, University of Dundee, Dundee, ISBN:

ZMP Trajectory Generation for Reduced Trunk Motions of Biped Robots

ZMP Trajectory Generation for Reduced Trunk Motions of Biped Robots Jong H. Park School of Mechanical Engineering Hanyang University Seoul, 33-79, Korea email:jong.park@ieee.org Yong K. Rhee School of