Oscillator-controlled Bipedal Walk with Pneumatic Actuators

The development of an oscillator controller for a bipedal robot with antagonistic pairs of pneumatic actuators is reported. Periodic motions of the legs switch between the swinging and supporting stages based on the phase of the oscillators. The oscillators receive touch sensor signals at the end of the legs as feedback when the leg touches the ground and compose a steady limit cycle of the total periodic dynamics of bipedal locomotion. The effectiveness and performance of the proposed controller were evaluated with numerical simulations and experiments with the hardware. Introduction Locomotion is an important function of mobility. Human bipedal locomotion is especially mobile and adaptable to variations in the environment. There has been a lot of research on bipedal robots driven by DC rotary actuators with local position feedback controls. However, most of them consume a lot of energy and their knees are always bent because they are based on high-gain position control of the joints with inverse kinematics for given trajectories of the legs. This type of robot cannot utilize its own dynamics for good energy efficiency or adaptive adjustment of physical properties of the body mechanism during locomotion. Furthermore, DC rotary actuators have serious difficulties in maintaining their power-weight ratios, which limits the functions of the robots' mobility. Leg motions in bipedal locomotion have two essential stages. One is the swinging stage and the other is the supporting stage. In the swinging stage, the actuator forces are relaxed; the joints become less stiff and more passive. In the supporting stage, stiffness of the joints increases due to forces generated by the antagonistic pair of actuators. By controlling and tuning the stiffness of the joints through the balanced adjustment of the generated force of such a pair of actuators, the robot is expected to become more adaptive to variations in the environment and in the surface of the ground. Hosoda et al. built a 3D bipedal robot driven by antagonistic pairs of McKibben actuators. This robot has a well-balanced design and body mechanism with a simple timing controller for switching between the leg motion stages and was able to walk stably and steadily. But the control parameters, such as the time period for each stage, are determined based on trial and error. This article reports the development of an oscillator controller for bipedal robots with antagonistic pairs of pneumatic actuators. In the proposed controller, nonlinear oscillators are assigned to each joint. Periodic motions of the legs are switched between the swinging and supporting stages based on the phase of the oscillators. Oscillators contain network architecture, interact mutually with each other, and receive touch sensor signals as feedback signals at the end of the legs when the leg touches the ground. At the moment the leg makes contact, the oscillator phase is reset, and the swinging stage is forced to change to the supporting stage. These dynamic interactions make possible mutual entrainments between oscillators and create a steady limit cycle of the total periodic dynamics of bipedal locomotion. The effectiveness and performance of the proposed controller for the bipedal robot were investigated through numerical simulations and experiments with the hardware. Model Figure 1 is a schematic model of a planar bipedal robot. The robot has two legs, composed of two links, and a main body. The contact model at the end of the leg assumes one point of support. The motion of the robot is restricted to the sagittal plane, i.e. it is assumed to be in 2D motion. The supporting and swinging legs are numbered 1 and 2, respectively. The position vector from the origin of the inertial coordinate to the center of mass (C.M.) of the main body is defined as r0 = (r0x, r0y)T. Figure 1. Schematic model of a bipedal robot The rotational angle of the main body and each link of the legs are defined as shown in Figure 1. The state variable is defined as follows: z = [r0x, r0y ,θ0, θ1(1), θ2(1), θ1(2), θ2(2) ]T Equations of motion for state variable z are derived as: M d2z/dt2 + H = G + T + E λ where M, H, G, and E are inertia matrix, nonlinear term, gravity term, and Jacobian matrix, respectively. λ is the reaction force at the contact point of the supporting leg. Vector T is composed of the input torques at the rotational joints of the legs Tj(), i=1,2,j=1,2, which are generated by the antagonistic pairs of pneumatic actuators. T = [0 0 0 T1(1) T2(1) T1(2) T2(2) ]T Control Scheme Figure 2 shows the control scheme of the proposed system. The controller has a nonlinear oscillator network with individual oscillators assigned to joints. The antagonistic pairs of pneumatic actuators are driven by timing signals as functions of the oscillator phases. The contact sensor signals are feedback for the oscillator network. These dynamic interactions cause the entrainment and generate a stable limit cycle for locomotion. With the oscillator phase defined as φm(k) (k,m=1,2), the oscillator network can be expressed in the following equations; Oscillator network