On the Stability of Bipedal Walking

Mechanism and Machine Theory, 2009

The mechanical analysis of bipedal walking is a fundamental subject of research in biomechanics. Such analysis is useful to better understand the principles underlying human locomotion, as well as to improve the design and control of bipedal robotic prototypes. Modelling the dynamics of walking involves the analysis of its two phases of motion: (1) the single support phase, which represents finite motion; and (2) the impulsive motion of the impact that occurs at the end of each step (heel strike). The latter is an important event since it is the main cause of energy loss during motion and, in turn, it makes the topology of the system change. In this paper, we present a unified method to analyze the dynamics of both phases of walking. Emphasis is given to the heel strike event, for which we introduce a novel method that gives a complete decomposition of the dynamic equations and the kinetic energy of the system at topology change. As an application example, the presented approach is applied to a compass-gait biped with point feet. Based on this, the work includes a thorough analysis and discussions about the effect of the biped configuration and its inertial parameters on the dynamics and energetics of heel strike.

International Journal of Computer Applications, 2014

This paper proposes a thorough algorithm that can tune the walking parameters (hip height, distance traveled by the hip, and times of single support phase SSP and double support phase DSP) to satisfy the kinematic and dynamic constraints: singularity condition at the knee joint, zero-moment point (ZMP) constraint, and unilateral contact constraints. Two walking patterns of biped locomotion have been investigated using the proposed algorithm. The distinction of these walking patterns is that the stance foot will stay fixed during the first sub-phase of the DSP for pattern 1, while it will rotate simultaneously at beginning of the DSP for pattern 2. A seven-link biped robot is simulated with the proposed algorithm. The results show that the proposed algorithm can compensate for the deviation of the ZMP trajectory due to approximate model of the pendulum model; thus balanced motion could be generated. In addition, it is shown that keeping the stance foot fixed during the first sub-phase of the DSP is necessary to evade deviation of ZMP from its desired trajectory resulting in unbalanced motion; thus, walking pattern 1 is preferred practically.

International Journal of Intelligent Systems and Applications, 2014

This paper addresses three issues of motion planning for zero-moment point (ZMP)-based biped robots. First, three methods have been compared for smooth transition of biped locomotion from the single support phase (SSP) to the double support phase (DSP) and vice versa. All these methods depend on linear pendulum mode (LPM) to predict the trajectory of the center of gravity (COG) of the biped. It has been found that the three methods could give the same motion of the COG for the biped. The second issue is investigation of the foot trajectory with different walking patterns especially during the DSP. The characteristics of foot rotation can improve the stability performance with uniform configurations. Last, a simple algorithm has been proposed to compensate for ZMP deviations due to approximate model of the LPM. The results show that keeping the stance foot flat at beginning of the DSP is necessary for balancing the biped robot.

IEEE Transactions on Robotics, 2008

Consider a biped evolving in the sagittal plane. The unexpected rotation of the supporting foot can be avoided by controlling the zero moment point or ZMP. The objective of this study is to propose and analyze a control strategy for simultaneously regulating the position of the ZMP and the joints of the robot. If the tracking requirements were posed in the time domain, the problem would be underactuated in the sense that the number of inputs would be less than the number of outputs. To get around this issue, the proposed controller is based on a pathfollowing control strategy previously developed for dealing with the underactuation present in planar robots without actuated ankles. In particular, the control law is defined in such a way that only the kinematic evolution of the robot's state is regulated, but not its temporal evolution. The asymptotic temporal evolution of the robot is completely defined through a one degree of freedom subsystem of the closed-loop model. Since the ZMP is controlled, bipedal walking that includes a prescribed rotation of the foot about the toe can also be considered. Simple analytical conditions are deduced which guarantee the existence of a periodic motion and the convergence towards this motion.

1997

This paper presents the kinematic study of robotic biped locomotion systems. The main purpose is to determine the kinematic characteristics and the system performance during walking. For that objective, the prescribed motion of the biped is completely characterised in terms of five locomotion variables: step length, hip height, maximum hip ripple, maximum foot clearance and link lengths. In this work, we propose three methods to quantitatively measure the performance of the walking robot: locomobility measure, perturbation analysis, and lowpass frequency response. These performance measures are discussed and compared in determining the robustness and effectiveness of the resulting locomotion.

International Journal of Advanced Computer Science and Applications

The research works contained in this paper are focused on the generation of a stable walking pattern of a biped robot and the study of its dynamic equilibrium while controlling the two following criteria; the centre of gravity COG and the zero-moment point ZMP. The stability was controlled where the biped have to avoid collision with obstacle. The kinematic constraints were also taken into consideration during the walking of the biped robot. In fact, the generation of the walking patterns is composed of several stages. First, we used the Kajita method for the generation of the COG trajectory, based on the linear inverted pendulum LIPM during the simple support phase SSP and linear pendulum model LPM during double support phase DSP. After that, we used two 4 th spline function to generate the swing foot trajectory during the SSP and we used exact formulate for the foot trajectory during DSP. Finally, Newton's algorithm was performed (at the level of the inverse geometric model), in order to calculate the different joints according to the desired trajectories of the hip and the feet. Ground reaction forces were also determined from the dynamic model to satisfy the kinematic constraints on both feet of the biped. The generation of walking is done for two different speeds. To study the biped balance, ZMP generation algorithm was performed during the different walking phases and the results obtained for the two cases were compared.

Proceedings 2007 IEEE International Conference on Robotics and Automation, 2007

Consider a biped evolving in the sagittal plane. The unexpected rotation of the supporting foot can be avoided by controlling the zero moment point or ZMP. The objective of this study is to propose and analyze a control strategy for simultaneously regulating the position of the ZMP and the joints of the robot. If the tracking requirements were posed in the time domain, the problem would be underactuated in the sense that the number of inputs would be less than the number of outputs. To get around this issue, the proposed controller is based on a path-following control strategy previously developed for dealing with the underactuation present in planar robots with unactuated ankles. In particular, the control law is defined in such a way that only the kinematic evolution of the robot's state is regulated, but not its temporal evolution. The asymptotic temporal evolution of the robot is completely defined through a one degree of freedom subsystem of the closed-loop model. Simple analytical conditions, which guarantee the existence of a periodic motion and the convergence towards this motion, are deduced.

2001

A 3-dimensional computer model of sustainedbipedal walking is presented. It is intended be used as adevelopment tool for walking controllers. The directdynamic simulation has 8 segments, 19 degrees offreedom and is driven by prescribed joint moment andstiffness trajectories. Limited feedback in the form of aproportional-derivative controller provides upper bodystability and allows walking to be sustained indefinitely.The joint moment and stiffness trajectories are specifiedin coarse block segments. By changing the intensity of hipextensor activity during terminal stance the walking stridelength is modulated.

This paper describes the control of a biped robot, that uses an inverted pendulum for its balance. A control method that consists of the balance of the gaits, through the correction of the lateral and longitudinal angles of the pendulum is proposed in this work. This method p resents three phases: first t he trajectory of the foot i n movement is defined, applying the inverse kinematics to calculate the robot's internal angles, and the direct kinematics is used to ob tain the positions and o rientations of the robot's joints; then the linear and angular accelerations are obtained; l ast, the zero moment point (ZMP) is calculated as a verification parameter of the requested margin of stability. Simulation of the robot gaits to walk in horizontal, sloping plans, and up and down stairs is also made. In order to decrease the calculation time of the dynamic stability, the impact of using zero pendulum angles as starting points for the interactive process of achieving the desire...

IEEE Transactions on Robotics, 2018

From which states and with what controls can a biped avoid falling or reach a given target state? What is the most robust way to do these? So as to help with the design of walking robot controllers, and perhaps give insights into human walking, we address these questions using two simple 2-D models: the inverted pendulum (IP) and linear inverted pendulum (LIP). Each has one state variable at mid-stance, i.e., hip velocity, and two state-dependent controls at each step, i.e., push-off magnitude and step length (IP) and step time and length (LIP). Using practical targets and constraints, we compute all combinations of initial states and control actions for the next step, such that the robot can, with the best possible future controls, avoid falling for n steps or reach a target within n steps. All such combinations constitute regions in the combined space of states and controls. Farther from the boundaries of these regions, the robot tolerates larger errors and disturbances. Furthermore, for these models, and thus possibly real bipeds, usually if it is possible to avoid falling, it is possible to reach the target, and if it is possible to reach the target, it is possible to do so in two steps.