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A review on Cubli and non linear control strategy

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The paper depicts the reviews on evolution of a cube shaped device called the Cubli, which has the ability to leap up, create equilibrium on different angles and edges. The study is focussed upon the control techniques when there is a sudden brake on high angular velocity rotation of reaction wheels, which are seated on the surface of Cubli, allowing the Cubli to leap up, first to its edge, and then to its corner without any extrinsic control. As the cubli obtains a balancing position, Model predictive control was implemented for overall effective controlling by analyzing future state.
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      
A Review on Cubli and Non Linear
Control Strategy
Rupam Singh), Vijay Kumar Tayal2 and Hemandar Pal Singh3

 
 
 paper depicts the reviews on evolution of
a cube shaped device called the Cubli, which has the ability
to leap up, create equilibrium on dierent angles and edges.
The study is focussed upon the control techniques when there
is a sudden brake on high angular velocity rotation of
reaction wheels, which are seated on the surface of Cubli,
allowing the Cubli to leap up, rst to its edge, and then to its
corner without any extrinsic control. As the cubli obtains a
balancing position, Model predictive control was
implemented for overall eective controlling by analyzing
future state.
    

 
        
        
        
       

         
     
       

   
        
          
      
       
          
        

       
        
        
       
       

          
       
      
       

  
          
      
  
         
      
    
     
      
    
        
 
  

      
        
      
        
      
   

      
      
       
  
       
      

        
     
      
       
        
    
    
       
      


      
       
      
         
       
       
     
        
     
       
       
     
  
     
   
       
      
        

         
      
      
      
   
       
      
      
       
        
     
    
     
      
        
     
 
     
        
       

     
      
     
       

       
    
     
          
       


 

      
       
        
         
        
      
        
        
        
  
       
     
       
     

      
      
        
    
       

       
      
        
       
       
       
        
         
        
         
        
       
      
         
        

      
      

 
    

 

          
       
     

 
         
      
    
        
        
      

     
        

 
       
         
       
       
        

        
 
  
        
 
         
          
       
     
    

      

          
 
         
      
      
       


       
       

       
       
        
 
      
        


      
      
     
    
     
    
    
     


      
        
     
     
     
    
    
  
 

      
     
   
    
   
   
  
 


     
     
     
     
   
   
   
   


       

      
    
et      
      
   
 

      
et       
     
    
 


      
et       
      
   
   
  
       
et        
     
    
    
    
 

       
et    
 
 

 
      
    
       
        
       
       
      
         
       
       
      
        
      
       
      
 

     
      
 
  
      
  

 
  
  


        
       
 
      
      
       

        
   
         
 
          
       

         
      

          
       

      
  
      

     
      
   
      
        

       
         
        
       

         
   
 
        
       

        
      
      

       
    
       
 
        
     

         
        
 
        
     
    
       

        
    

        
     
     

     
   
     


      
     

 
      
         
     

    
     
      
 
       
     
       
       
 
      
         
       
 
     
      
   
       
      
      
  
   
 
  
 
 
        
    
   
        
       
        
    

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The status of using many, distributed optimization-based controllers for feedback control of large-scale, dynamic processes is presented and evaluated. We show that modeling the interactions between subsystems and exchanging trajectory information among subsystem model predictive controllers (MPCs) is insufficient to provide even closed-loop stability. The cause of this closed-loop instability is competition between the local agents. We next discuss the cooperative distributed MPC framework, in which the objective functions of the local MPCs are modified to achieve systemwide control objectives. This approach provides guaranteed nominal stability and performance properties, but at the cost of a high degree of communication between the local controllers. We next discuss the issue of taking advantage of the structure of the connections between the subsystems to reduce the required communication. The paper concludes by briefly presenting seven fcurrent and unsolved research challenges.
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In this paper a three-dimensional self-balancing cube is introduced. For stabilization and swing-up, reaction wheels are placed within the cube along with the actuation, electronics and sensors. This allows the cube to swing up from a rest position and to balance around the unstable steady-state positions. We first conducted a design assessment to review different design approaches. For the most promising design, we then formulated a parameter optimization to calculate the most suitable dimensions for the cube and the inertia elements. These results were then used in the mechanical design stage to obtain the optimal design parameters for the cube in an iterative process. In addition to this mechatronic design, we also focused on the control of swing-up and the stabilization of the cube. We considered a proportional control law using virtual springs with feed-forward control. The performance of the proposed control was first evaluated in simulations and then extensively tested on the real system.
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We present an algorithm that probabilistically covers a bounded region of the state space of a nonlinear system with a sparse tree of feedback stabilized trajectories leading to a goal state. The generated tree serves as a lookup table control policy to get any reachable initial condition within that region to the goal. The approach combines motion planning with reasoning about the set of states around a trajectory for which the feedback policy of the trajectory is able to stabilize the system. The key idea is to use a random sample from the bounded region for both motion planning and approximation of the stabilizable sets by falsification; this keeps the number of samples and simulations needed to generate covering policies reasonably low. We simulate the nonlinear system to falsify the stabilizable sets, which allows enforcing input and state constraints. Compared to the algebraic verification using sums of squares optimization in our previous work, the simulation-based approximation of the stabilizable set is less exact, but considerably easier to implement and can be applied to a broader range of nonlinear systems. We show simulation results obtained with model systems and study the performance and robustness of the generated policies.
Conference Paper
This paper presents control and learning algorithms for a reaction wheel-based 3-D inverted pendulum. The inverted pendulum system has two main features: the ability to balance on its edge or corner and to jump from lying flat to its corner by suddenly braking its reaction wheels. Algorithms that address both features are presented. For balancing, a backstepping-based controller providing global stability (almost everywhere) is derived, together with a simple tuning method based on the analysis of the resulting closed-loop system. For jump-up, a computationally efficient gradient-based learning algorithm is provided, which is shown experimentally to converge to the correct angular velocities enabling a successful jump-up. Moreover, a controller based on feedback linearization is derived and used to track an ideal trajectory during jump-up, increasing robustness and reliability.
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This paper summarizes the mechanical and control design concepts of an inverted or unstable pendulum where stabilization is achieved by a moment exchange generated by a controlled symmetric rotation of a rotational inertia attached to the pendulum. The proposed design of the pendulum has a fixed bottom rotation or point of support as opposed to the usual vertically or horizontally moving point of support to stabilize the pendulum, allowing for small form factor desktop design of an inverted pendulum experiment. The symmetry of the rotational inertia allows for stabilization of the pendulum without the need to control the position of the mass attached to the pendulum. The paper reviews the design considerations, dynamic modeling, system identification and control design strategy to stabilize the pendulum.
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In decentralized control of multivariable systems, the system is decomposed into a number of subsystems and individual controllers are designed for each subsystem. Advantages of such decomposition include reduced modelling requirements and ease of implementation. However, a potential disadvantage is a reduction in achievable control performance due to restricted controller structure. In this paper we consider performance limitations from non-minimum phase transmission zeros in decentralized control. In particular, we derive conditions on when closing the loop around one subsystem moves transmission zeros of other subsystems across the imaginary axis. Such zero crossings may occur regardless of the existence of non-minimum phase behavior in the open-loop system, and may, therefore, represent performance limitations specific to the use of decentralized controllers.
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In order to deal with the computational burden of optimal control, it is common practice to reduce the degrees of freedom by fixing the input or its derivatives to be constant over several time-steps. This policy is referred to as "move blocking". This paper will address two issues. First, a survey of various move blocking strategies is presented and the shortcomings of these blocking policies, such as the lack of stability and constraint satisfaction guarantees, will be illustrated. Second, a novel move blocking scheme, "Moving Window Blocking" (MWB), will be presented. In MWB, the blocking strategy is time-dependent such that the scheme yields stability and feasibility guarantees for the closed-loop system. Finally, the results of a large case-study are presented that illustrate the advantages and drawbacks of the various control strategies discussed in this paper.