Motion Planning And Robust Control Of Two Rigid Bodies With Rolling Constraints

Dexterous manipulation and spherical mobile robot are active areas of robotic research,and both of them involve contacting when reorienting objects by in-hand manipulation or moving on the rough road.Compared with sliding contact,rolling is less reliant on exact knowledge of friction properties and energy loss for dissipation is avoided.Furthermore,nonholonomic features of system with rolling constraints are exploited for simplifying the device,reduce costs and improving system reliability.The desired contact posture is expected to achieve through motion planning and feedback control for making nonholonomic systems practical.However,the states of nonholonomic systems under rolling constraints are coupled with each other,which makes it difficult to obtain a feasible trajectory.Moreover,it is difficult to achieve real-time control for the nonlinear system under the model uncertainty and the unknown disturbances.The trajectory planning and robust control of the rolling constraint system is critical for improving the capabilities of robots interacting with the environment,and broadening the application scenario of dexterous manipulation and spherical robot.In this paper,modeling rolling contacts between two objects with no relative spinning motion is studied,and it's referred as the rolling system.A cascade motion planning algorithm for rolling system is established to obtain a valid reference trajectory based on the first-order kinematic model considering two general surfaces.Based on the motion planning results,an“offline planning,online control” strategy is adopted to establish a real-time controller.The parameterized model uncertainty and simulated disturbances from actuators and sensors are introduced to the rolling system,then a robust control method is established based on the extended Kalman filter to track the nominal trajectory.The results provide theoretical guidance for trajectory planning and robust control of rolling system existed in robotics.The main research contents are as follows:1)Cascade-form trajectory planning algorithm of rolling systemKinematic simulation platform for the rolling system is established based on the differential geometric of contacting objects.A cascade-form trajectory planning algorithm is proposed,where the optimized trajectory from two-state control cascading direct collocation is provided to the iterative linear quadratic regulator for smoothing.The two-point boundary value problem of the sphere-sphere rolling system and the ellipsoid-ellipsoid rolling system are solved to prove the applicability of the proposed algorithm to the general model.Compared with the existing methods,better trajectories are obtained by the proposed method.2)Real-time feedback controller of rolling systemThe real-time controller for the rolling system is established based on the Model Predictive Control,where the results of offline trajectory planner are used as the nominal trajectory and nominal control.The feedback control is established through the receding horizon predicting and state feedback process to stabilize the trajectory under initial perturbations.The real-time simulation results of the sphere-sphere model and ellipsoid-ellipsoid model show the high efficiency and strong robustness of the controller.Finally,the comparisons with the Sequential Action Control and the Nonlinear Model Predictive Control in terms of computing efficiency and robustness further prove the superior performance of the established controller in real-time control of rolling systems.3)Robust control of rolling system under uncertaintyThe controllability of the sphere-sphere and the ellipsoid-ellipsoid models is proved through Lie algebra,and the controllability of rolling trajectories are checked using controllability gramian.The uncertainty of model parameters and environment noise are introduced into the close-loop system,and the Extended Kalman Filter is implemented to realize the state estimation under the sensor noise and model uncertainty.The robustness ability of the robust controller under different model uncertainty ranges and external noise levels are obtained by variable controlling approach on sphere-sphere model and ellipsoid-ellipsoid model respectively.In conclusion,the trajectory planner and robust controller for pure rolling systems between two 3D objects with general surface are established in this paper.It provides efficient and feasible solution for planning and controlling of robotics with rolling constraints,such as spherical mobile robots moving control and dexterous manipulators grasping objects.