Examples of jinngine.physics.solver.Solver

jinngine.physics.solver.Solver
Solver for a non-linear complimentarity problem (NCP).
The contact force problem generated by Jinngine is ultimately a non-linear complementarity problem. In fact, when disregarding the coupling between friction forces and normal forces, the problem becomes a mixed linear complimentarity problem, or MLCP for short. The MLCP is on the form
Given the matrix A, the vector b, and the solution limit vectors l and u, Find x, such that
w = A x + b
where
if x_i=u_i then w_i<=0
if x_i in (l_i,u_i) then w_i = 0
if x_i=l_i then w_i>=0
A is the matrix J M^(-1) J^T which describes constraint relations, and b is the vector of desired change in velocities.
This problem class can model normal-component contact forces and various joint types. The reason why this becomes a NCP when contact friction is introduced, is that we allow u and l to depend on the magnitude of some x_i vales, namely the x_i's that represent normal contact forces, so
l_i = -|mu * x_j| and u_i = |mu*x_j|
where i is the index of a friction constraint, j is the index of the normal force, and mu is the friction coefficient. constraint to which the friction constraint is coupled. This coupling is done to model an approximation to Coulomb's law of friction.

   */
  public void testConjugateGradients1() {
    
    double epsilon = 1e-7;
    
    Solver s = new ConjugateGradients();
    
    Body b1 = new Body("default");
    Body b2 = new Body("default");
    
    Solver.NCPConstraint c1 = new NCPConstraint();
    Vector3 va =new Vector3(1,0,0);
    Vector3 vb =new Vector3(-1,0,0);
    Vector3 z = new Vector3(0,0,0);
    c1.assign(b1,b2,
        va,z,vb,z,
        va,z,vb,z,
        -Double.POSITIVE_INFINITY,Double.POSITIVE_INFINITY,null,1, 0);
    
    //This is the system
    //
    // [ 1 0 0  0 0 0  -1 0 0  0 0 0] [1 0 0  0 0 0  -1 0 0  0 0 0 ]^T x + 1= 0  =>
    // 2 x + 1 = 0  
    //
    // with the solution x = -1/2 
    
    //list of bodies and constraints
    List<Body> bodies = new ArrayList<Body>();
    List<NCPConstraint> constraints = new ArrayList<NCPConstraint>();
    bodies.add(b1); bodies.add(b2); constraints.add(c1);


    //run the solver
    s.solve(constraints, bodies, 0.0);
    
    System.out.println("cg test="+c1.lambda);
    
    //expect solution 1/2
    assertTrue( Math.abs(-0.5 - c1.lambda) < epsilon );

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   */
  public void testConjugateGradients2() {
    
    double epsilon = 1e-7;
    
    Solver s = new ConjugateGradients();
    Body b1 = new Body("default");
    Body b2 = new Body("default");
    
    Solver.NCPConstraint c1 = new NCPConstraint();
    Solver.NCPConstraint c2 = new NCPConstraint();


    Vector3 va =new Vector3(1,0,0);
    Vector3 vb =new Vector3(-1,0,0);
    Vector3 z = new Vector3(0,0,0);
    c1.assign(b1,b2,
        va,z,vb,z,
        va,z,vb,z,
        0,0,null,1, 0);
    c2.assign(b1,b2,
        va,z,vb,z,
        va,z,vb,z,
        0,0,null,1, 0);


    
    //This is the system
    //
    // [ 1 0 0  0 0 0  -1 0 0  0 0 0] [1 0 0  0 0 0  -1 0 0  0 0 0 ]^T x + 1 = 0  
    // [ 1 0 0  0 0 0  -1 0 0  0 0 0] [1 0 0  0 0 0  -1 0 0  0 0 0 ]           =>
    //
    // 2  2 x1 + 1 = 0  
    // 2  2 x2 + 1 = 0
    //
    // with a least squares solution solution x1 = -1/4 and x2 = -1/4 
    
    //list of bodies and constraints
    List<Body> bodies = new ArrayList<Body>();
    List<NCPConstraint> constraints = new ArrayList<NCPConstraint>();
    bodies.add(b1); bodies.add(b2); constraints.add(c1); constraints.add(c2);


    //run the solver
    s.solve(constraints, bodies, 0.0);
    
    System.out.println("("+c1.lambda+","+c2.lambda+")");
    
    //expect solution (1/4,1/4)
    assertTrue( Math.abs(-0.25 - c1.lambda) < epsilon );

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Related Classes of jinngine.physics.solver.Solver

jinngine.test.unit.ConjugateGradientTest

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