Fig 1.
Self-balancing robot (SBR) in parking position.
Fig 2.
Free body diagram of the self-balancing robot platform (a) left wheel (b) right wheel (c) chassis.
Fig 3.
Torque diagram about the z-axis (a) vertical reaction forces between wheels and chassis (b) horizontal reaction forces between wheels and chassis, (c) control torques from left and right wheel.
Fig 4.
Torque diagram of the horizontal reaction forces between wheels and chassis about the y-axis.
Fig 5.
Force vector diagram of the horizontal reaction forces between wheels & chassis, and the disturbance force at the COG of the robot.
Fig 6.
Force vector diagram of the vertical reaction forces between wheels and chassis, FCθ, Mg acting at the COG.
Fig 7.
Force vector diagram of the components of FCθ.
Fig 8.
Force vector diagram representing the components of L for the distance traveled along the x-axis.
Fig 9.
Force vector diagram representing the components of L for the distance traveled along the y-axis.
Fig 10.
Force vector diagram of the chassis representing the yaw angle δ.
Fig 11.
Free body diagram of the rider and its contribution to the value of L.
Fig 12.
Schematic diagram of a direct current motor.
Fig 13.
Flowchart for the extended Kalman filter algorithm.
Fig 14.
Block diagram representation of the proposed algorithm for EKF based SMC.
Fig 15.
Flow chart for the proposed SBR’s stability control algorithm.
Fig 16.
EKF based estimation for the upper limit of (a) rider’s mass, (b) rider’s length.
Fig 17.
EKF rider’s estimation for lower limit (a) mass (b) length.
Fig 18.
A comparison of system response for case 1: (a) Pitch angle, (b) Yaw angle, (c) Distance, (d) Velocity.
Fig 19.
A comparison of system response for case 2: (a) Pitch angle, (b) Yaw angle, (c) Distance, (d) Velocity.
Table 1.
Maximum difference between the states of ESMC and SMC for Case 2.
Fig 20.
A comparison of system response for case 3: (a) Pitch angle, (b) Yaw angle, (c) Distance, (d) Velocity.
Table 2.
Maximum difference between the states of ESMC and SMC for Case 3.
Fig 21.
A comparison of system response for case 4: (a) Pitch angle, (b) Yaw angle, (c) Distance, (d) Velocity.
Fig 22.
Comparison of the control effort generated by the controllers to stabilize the pitch angle.
Table 3.
Maximum difference between the states of ESMC and SMC for Case 4.
Fig 23.
A comparison of system response for case 5: (a) Pitch angle, (b) Yaw angle, (c) Distance, (d) Velocity.
Table 4.
Maximum difference between the states of ESMC and SMC for Case 5.
Fig 24.
A comparison of system response for case 6: (a) Pitch angle, (b) Yaw angle, (c) Distance, (d) Velocity.
Fig 25.
Comparison of the control effort generated by the controllers to stabilize the pitch angle.
Table 5.
Maximum difference between the states of ESMC and SMC for Case 6.
Fig 26.
A comparison of system response for case 7: (a) Pitch angle, (b) Yaw angle, (c) Distance, (d) Velocity.
Fig 27.
Comparison of the control effort generated by the controllers to stabilize the pitch angle.
Fig 28.
Changes in L and Jr resulting from an incremental 10% increase in Lr and Mr from their nominal values of 1.8 meters and 80 kg, respectively.
Fig 29.
The sensitivity of pitch angle resulting from a similar increase in the values of Lr and Mr.
Table 6.
Maximum difference between the states of ESMC and SMC for Case 7.
Table 7.
Comparison of the proposed ESMC technique with the earlier work reported in the literature.