Table 1 Four-WMR parameter notations.
From: A novel fixed-time prescribed performance sliding mode control for uncertain wheeled mobile robots
Symbol | Parameters’ name |
|---|---|
\(O_G-XY\) | Global Cartesian coordinate system |
\(O_B-xy\) | Body-fixed coordinate system |
\(O_B\) | Center of mass (CoM) |
T | Tracking point |
u | Longitudinal velocity at CoM |
v | Lateral velocity at CoM |
r | Yaw rate |
\(\theta\) | Heading angle |
\(u_l\) | Longitudinal velocity at left wheel |
\(u_r\) | Longitudinal velocity at right wheel |
\(\omega _l\) | Angular velocity at left wheel |
\(\omega _r\) | Angular velocity at right wheel |
\(v^s\) | Wheel skidding |
\(u_l^s\) | Slipping at left wheel |
\(u_r^s\) | Slipping at right wheel |
b | Gap from wheel center to geometrical center line |
d | Gap from wheel center line to CoM \(O_B\) |
l | Position of tracking point T |
R | Wheel’s radius |
\(P_x\) | External disturbances along x-axis |
\(P_y\) | External disturbances along y-axis |
\(M_d\) | Moment at CoM |
\(F_l-\left\{ F_{xl}, F_{yl}\right\}\) | Friction forces on driving left wheel |
\(F_r-\left\{ F_{xr}, F_{yr}\right\}\) | Friction forces on driving right wheel |
