Combined control with sliding mode and Partial feedback linearization for a spatial ridable ballbot

•Ballbot dynamics divided into two sub-dynamics are modeled as nonlinear differential equations.•A controller combining PFL and SMC is proposed to balance and transfer of the ballbot.•The system state quickly reaches the target sliding mode surface using the proposed control.•The combined control has better control performance than other controllers and has solid robustness. A ridable ballbot, a personal robot, is an underactuated system. The four state variables of the ball motion and body motion are controlled by two input signals acting on the ball. Euler–Lagrange equation is applied to obtain the dynamic model of the ridable ballbot. On the basis of this dynamic model, a nonlinear controller is analyzed and designed to control balancing and transferring of the robot. The nonlinear control scheme is proposed based on the combination of two control design techniques: (i) partial feedback linearization, which is designed to maintain the body in the upright position; and (ii) sliding mode control, which provides robust control in ball motion on the floor against model imprecision, uncertainty of system parameters and friction, and external disturbances. These two control mechanisms are successfully merged into a combined controller. Numerical and experimental results indicate the effectiveness of the combined controller and proposed a dynamic model. The control algorithm asymptotically stabilizes all system responses.