A Back-stepping Based Trajectory Tracking Controller for a Non-chained Nonholonomic Spherical Robot

A spherical mobile robot, BHQ-1, designed for environment exploration, was briefly introduced. The dynamic model of BHQ-1 was established with a simplified Boltzmann-Hamel equation. From the dynamic model the expressions of the input moments of two motors to drive the robot are deduced when the robot moves along straight trajectory and circular trajectory separately. Simulation result of the robot to track a complex trajectory and experiments of the robot to avoid an obstacle show the trajectory planning method is effective.

Dynamic Trajectory Planning of a Spherical Mobile Robot

This paper deals with the dynamics and motion control of a spherical robot designed for reconnaissance and unstructured hostile environment exploration. The robot in this paper has three DOFs and two inputs, of which the nature is a nonlinear and underactuated system with nonholonomic dynamic constraints. The improved construction of two pendulums offers novel motion principle of spherical robot, which is moving simultaneously actuated by both eccentric moment and inertial moment generated by the two pendulums. Meanwhile the mobility is enhanced when the robot behaves dynamically. The emphasis is placed on the linear motion and turning in place motion control. The dynamic model of linear motion is formulated on the basis of Lagrange equation, and a smooth trajectory planning method is proposed for linear motion. A feedback controller is constructed to ensure the accurate trajectory planning. Turning in place motion is an indispensable element of omni directional locomotion which can enhance the mobility of spherical robots. The dynamic model of turning in place motion is derived on the theory of moment of momentum, and a stick-slip principle is analyzed. The two motion control methods are validated by both simulations and prototype experiments.

Dynamics and motion control of a two pendulums driven spherical robot

This study deals with mathematical modelling and motion control of a pendulum-driven spherical robot (PDSR) moving on an inclined plane. Firstly, the model of a PDSR on an inclined plane is developed using a Lagrangian formulation. Afterwards, a PID controller is tuned to stabilise the robot on the inclined plane. A heuristic fuzzy controller and a PID controller are also designed to move the robot upward or downward the inclined plane and approach the target point. A switched control, i.e. a combination of the designed controllers, is finally suggested to control the motion of the robot on the inclined plane. Simulations are conducted to investigate and compare the performance of the proposed controllers. Experiments are also conducted for different cases to validate the simulations and also evaluate the control strategies via image processing.

https://ietresearch.onlinelibrary.wiley.com/doi/epdf/10.1049/iet-cta.2016.0964

Modelling and control of a non-holonomic pendulum-driven spherical robot moving on an inclined plane: simulation and experimental results

Spherical robot is a special kind of nonholonomic system that cannot be converted to chained form, which means most of the well-known control methodologies are not suitable for this system. For the trajectory tracking of BHQ-1, a spherical robot designed by our lab, a two-state trajectory tracking controller is proposed in this paper. First, the kinematic model of the robot is built using screw theory and exponential method and the controllability is proved based on the differential geometric control theory. Then to solve the two-state trajectory tracking problem of BHQ-1, a shunting model of neurodynamics and Lyapunov's direct method are combined to design a two-state trajectory tracking controller, of which the Lyapunov stability is validated. Finally, typical simulation examples, such as tracking linear, circular, and sinusoidal trajectories, are introduced to verify the effectiveness of the proposed controller. In this paper the proposed method can also be applied to the control of other spherical robots.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0263574711000518

Two-state trajectory tracking control of a spherical robot using neurodynamics

A new spherical mobile robot BHQ-1 is designed. The spherical robot is driven by two internally mounted motors that induce the ball to move straight and turn around on a flat surface. A dynamic model of the robot is developed with Lagrange method and factors affecting the driving torque of two motors are analyzed. The relationship between the turning radius of the robot and the length of two links is discussed in order to optimize its mechanism design. Simulation and experimental results demonstrate the good controllability and motion performance of BHQ-1.

Mechanism design and motion analysis of a spherical mobile robot

: Meshing backlash mainly determines the transmission accuracy of harmonic drive, which is an important index in design. In this paper, a design method of short tooth involute profile is proposed, which relies on positive modification to enhance the strength of dedendum. By intercepting part of tooth profile, the meshing interference of addendum can be effectively avoided. Based on the dimensions of over pins of circular spline and flexspline, a calculation method of tooth thickness deviation is proposed, and the positive and negative of tooth thickness deviation are defined. Involute functions need not be calculated by this method, which simplifies the solution process. By discretizing the teeth profile points of circular spline and flexspline, a calculation method of time-varying backlash is proposed, the variation of backlash in the process of meshing in and out is analyzed, and the influence law of tooth thickness deviation on backlash is studied. On this basis, an algorithm of adjusting the radial deformation to compensate the backlash is proposed. The results show that the excessive backlash in the meshing area can be reduced by increasing the radial deformation. when meshing interference occurs, the interference free meshing can be realized by decreasing the radial deformation.

Qiang

Papers

Mechanism design and motion analysis of a spherical mobile robot

Calculation of tooth thickness errors and its in�uence on meshing backlash of harmonic drive