Immersion And Invariance-based Controller For An Uncertain Robot With Full-state Constraints

In the past few decades,more and more scholars pay attention to the control problem of robotic systems.Nowadays,robots are used in various fields.However,the inaccuracy of the acquired information will be not accurate because their position and speed are easily disturbed by the outside world,which results in the limitation of the robot's action.Moreover,due to the influence of the external environment and its physical limitations,the state will be subject to certain constraints.At this stage,there are many solutions for unconstrained state.However,there is little attention and research on the problem with constraints.Therefore,based on the existing methods,this paper proposes an immersed and invariant manifold(I&I)to solve the problem of robot controller design with full constraints.The immersed and invariant manifolds are used to render the control object into the manifold surface by selecting the appropriate mapping,so that the image of the target system is bounded within the manifold surface.But in this paper,we need find the manifold surface through the constraint conditions and estimate the unknown variables through immersion and invariant manifolds,so that the robot system reaches a steady state under the constraint conditions.Sometimes,it is difficult to find the manifold surface,so we can consider itfrom the target system,because the basic principle is to immerse the high order original system into the low order target system.The condition is that the target system is stable and controllable.Therefore,it is necessary to select the objective function which is stable and satisfies the constraints.However,it is found that not all robot systems can directly control the design of the system by finding the objective function when the I&I method is used to control the robot.So in the third part of this paper,we introduce the barrier Lyapunov function(BLF),which is a new method based on the original barrier function to solve the problem with constraints.Also,BLF can be directly used to solve the full constraint state of the robot system when designing the function.However,some of the states are not measurable in the design process,so we need to combine the I&I method with BLF to estimate the parts of which can not be measured,so that the controller is valid.