Biped robots have better mobility than conventional wheeled robots, but they tend to tip over easily. To be able to walk stably in various environments, such as on rough terrain, up and down slopes, or in regions containing obstacles, it is necessary for the robot to adapt to the ground conditions with a foot motion, and maintain its stability with a torso motion. When the ground conditions and stability constraint are satisfied, it is desirable to select a walking pattern that requires small torque and velocity of the joint actuators. We first formulate the constraints of the foot motion parameters. By varying the values of the constraint parameters, we can produce different types of foot motion to adapt to ground conditions. We then propose a method for formulating the problem of the smooth hip motion with the largest stability margin using only two parameters, and derive the hip trajectory by iterative computation. Finally, the correlation between the actuator specifications and the walking patterns is described through simulation studies, and the effectiveness of the proposed methods is confirmed by simulation examples and experimental results.

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Planning walking patterns for a biped robot

Virtual model control is a motion control framework that uses virtual components to create virtual forces generated when the virtual components interact with a robot system. An algorithm derived based on the virtual model control framework is applied to a physical planar bipedal robot. It uses a simple set of virtual components that allows the robot to walk successfully over level terrain. This paper also describes how the algorithm can be augmented for rough terrain walking based on geometric consideration. The resulting algorithm is very simple and does not require the biped to have an extensive sensory system. The robot does not know the slope gradients and transition locations in advance. The ground is detected using foot contact switches. Using the algorithm, we have successfully compelled a simulated seven-link planar biped to walk blindly up and down slopes and over rolling terrain.

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Virtual Model Control: An Intuitive Approach for Bipedal Locomotion:

A novel control method for biped locomotion on rugged terrain is introduced, assuming an ideal robot model which has massless legs. By applying constraint control to the robot body so that it moves on a particular straight line and rotates at a constant angular velocity, the dynamics of the center of mass of the body becomes completely linear. Such motion of the ideal model is called the linear inverted pendulum mode, and it is used to develop the control scheme of the biped walking on rugged terrain. Under the control method in the linear inverted pendulum mode, walking on a particular rugged ground is shown to be equivalent to walking on a level ground. It is also shown that the additional use of the ankle torque makes the proposed control scheme robust and applicable to a real biped robot with mass legs. Simulation results are presented. >

Study of dynamic biped locomotion on rugged terrain-derivation and application of the linear inverted pendulum mode

To reduce the complex walking dynamics of a biped, a particular class of trajectories of an ideal biped model where the center of gravity of the body moves horizontally and the horizontal motion of the center of gravity can be expressed by a simple linear differential equation is introduced. The authors coin the phrase 'potential energy conserving orbit' to describe this class of trajectories. Based on these properties, control laws were formulated for walk initiation, walk continuation, and walk termination. The walking motion is controlled by support leg exchange. Robust realization of the walking control is also considered. An experimental walking machine was designed as a nearly ideal biped model. To make the legs lighter, four DC motors were mounted in the body, and the legs are parallel link structures. The results of the experiment describe five steps of dynamic walking including walk initiation. >

Dynamic walking control of a biped robot along a potential energy conserving orbit

Simple locomotion algorithms provide balance for machines that run on one leg. The generalization of these one-leg algorithms for control of machines with several legs is explored. The generalization is quite simple when muitilegged systems run with gaits that use the support legs one at a time. For these gaits the one-leg algorithms can be used to control multilegged running. The concept of a virtual leg is introduced to further extend the approach to gaits that use the legs in pairs, such as the trot, the pace, and the bound. These quadruped running gaits map into gaits that use one virtual leg for support at a time, for which the one-leg algorithms can provide control. This approach was used in laboratory experiments to control a quadruped machine that runs with a trotting gait.

Running on four legs as though they were one

While biped locomotion involves very complicated dynamical processes, a good deal can be learned about stability and feedback control from an analysis of simplified mathematical models. This paper treats locomotion dynamics relative to planar motion under an assumption that leg mass can be ignored in comparison to body mass. Thus the hypothetical biped possesses one rotational degree of freedom and two translational degrees, leading to a sixth-order system of nonlinear differential equations. These equations are linearized and feedback control laws are then derived to produce the desired stable forward motion. The feedback laws proposed involve a combination of continuous and discrete concepts to produce both step length and step period control as well as control of body attitude and altitude. The applicability of the control laws to the nonlinear system in the presence of large disturbances is verified by computer simulation. Hopefully, the results presented are significant relative to control processes arising in lower extremity prostheses and orthoses as well as to the design of biped robots.

Ferdinand Gubina

Papers

On the Dynamic Stability of Biped Locomotion