Development of a New Hydraulic Ankle for HYDROïD Humanoid Robot

Abstract

For humanoid robots, design of the ankle mechanism is still open research problem since high torque is required while compact structures have to be maintained. This paper investigates an enhanced design of 3 degree-of-freedom hydraulic hybrid ankle mechanism. The design is based on (US9327785) Alfayad et al. (2011). Using a hybrid kinematic structure with hydraulic actuation, allows us to reach a slender humanoid ankle shape while enabling the high torque performances required for stable walking. Performances analysis of the first version ankle mechanism designed for HYDROïD humanoid robot showed some limits mainly induced by seal friction and pistons misalignment. In this paper, the influence of the friction parameters is explored. A virtual model is developed to evaluate the performances of a new flexion/extension and adduction/abduction pistons arrangement. Then, a control algorithm is simulated and implemented, as an example, to the flexion/extension motion of the new ankle mechanism. Finally, an experimental validation for the performances of the new proposed hydraulic ankle is conducted using the built hardware prototype, the results show significant improvement.

Nomenclature

𝜃 :

Angle of rotation [degree]

Q _{l e a k a g e} :

Internal leakage flow rate [l/min]

α :

Angle of piston misalignment with respect to cylinder center line [degrees]

ΔP:

Difference in pressure across the servo valve [bar]

d :

Piston diameter in [m]

ρ :

Density of the hydraulic oil [kg/m³]

c :

Radial clearance [m]

ν :

Kinematic viscosity [m²/s]

c _f :

Coefficient of viscous friction [N.s/mm]

μ _f :

Coefficient of static friction [−]

β :

Bulk modulus of hydraulic oil [GPa]

$v_{p_{i}}$ :

Velocity of the piston i[mm/s]

v _f :

Velocity of the piston during the transition phase [mm/s]

S _p :

cross-sectional area of the hydraulic piston [m²]

F _s :

Friction force of static friction [N]

$F_{f_{i}}$ :

Total friction force which operates against the direction of piston i movements. [N]

$\tau ^{max}_{y}$ :

Maximum required torque in the sagittal plane [N.m]

$\tau ^{max}_{x}$ :

Maximum required torque in the frontal plane [N.m]

τ _y :

Flexion/Extenstion torque [N.m]

τ _x :

Eversion/Inversion torque [N.m]

α :

Rotating angle between the two hydraulic pistons couples around the roll axis [degree]

X _d :

Desired angles of rotation for the ankle [degree]

X _m :

Measured angles of rotation for the ankle [degree]

L(i):

The stroke of the hydraulic piston [mm]

SC(i):

The outer diameter of the hydraulic pistons [mm]

E(i):

Piston connecting point with cables [−]

AN(i):

Air pressure outlet point from the piston [−]

F _{l o a d} :

Weight of the load applied on the foot [N]

m _{l o a d} :

Mass of the load applied on the foot [kg]

m _{f o o t} :

Mass of the foot [kg]

x _{r o t a t i o n} :

Distance between the frontal end point of the foot with the point of rotation of the foot [m]

T _{r o t a t i o n} :

Rotation torque of the foot in the frontal plane [N.m]

g :

Gravitational constant [m/s²]

𝜃 _x :

Angle of rotation in the frontal plane [degree]

𝜃 _y :

Angle of rotation in the sagittal plane [degree]

𝜃 _z :

Angle of rotation in the vertical plane [degree]

𝜃 _{t o e} :

Angle of rotation of the toe of the ankle [degree]

I :

Servo valve current [A]

K :

Static flow gain constant $[\frac {m^{3}/s}{A}]$

T :

Time constant of first order equation [s]

x _v :

Displacement of the servo valve spool [mm]