Refactor RelaxedRigidContacts to improve kinematic constraint handlin…

…g and adding Baumgarte terms

src/jaxsim/rbda/contacts/relaxed_rigid.py

@@ -349,14 +349,14 @@ def compute_contact_forces(
             W_R_F1 = W_H_F1[:3, :3]
             W_R_F2 = W_H_F2[:3, :3]
 
-            J_WF1 = js.frame.jacobian(model=model, data=data, frame_index=F1_idx)[:3, :]
-            J_WF2 = js.frame.jacobian(model=model, data=data, frame_index=F2_idx)[:3, :]
+            J_WF1 = js.frame.jacobian(model=model, data=data, frame_index=F1_idx)
+            J_WF2 = js.frame.jacobian(model=model, data=data, frame_index=F2_idx)
             J̇_WF1 = js.frame.jacobian_derivative(
                 model=model, data=data, frame_index=F1_idx
-            )[:3, :]
+            )
             J̇_WF2 = js.frame.jacobian_derivative(
                 model=model, data=data, frame_index=F2_idx
-            )[:3, :]
+            )
 
             # Add the kinematic constraint terms to the Jacobians
             Jl_WC = jnp.vstack([Jl_WC, J_WF1 - J_WF2])
@@ -373,26 +373,26 @@ def compute_contact_forces(
         # jax.debug.print("a_ref.shape: \n{}", a_ref.shape)
         # jax.debug.print("R.shape: \n{}", R.shape)
 
-        num_zeros_kin_constr = J_WF1.shape[0]
+        dim_kin_constr = J_WF1.shape[0]
 
         # Compute Baumgarte stabilization terms for the kinematic constraints
 
-        # K_P = 0  # 1e1
-        # K_D = 0  # 2 * jnp.sqrt(K_P)
-        # vel_error = (J_WF1 - J_WF2) @ BW_ν
-        # position_error = 0 * (W_p_F1 - W_p_F2)
-        # # R_error = W_R_F1.T @ W_R_F2
-        # R_error = W_R_F2.T @ W_R_F1
-        # orientation_error = jaxsim.math.rotation.Rotation.log_SO3(R_error)
-        # baumgarte_term = (
-        #     K_P * jnp.hstack([position_error, orientation_error]) + K_D * vel_error
-        # )
-
-        R_ext = jnp.pad(
-            R, ((0, num_zeros_kin_constr), (0, num_zeros_kin_constr)), mode="constant"
+        K_P = 100  # 1e1
+        K_D = 2 * jnp.sqrt(K_P)
+        K_D = jnp.diag(jnp.array([K_D, K_D, K_D, K_D, K_D, K_D]))
+        vel_error = (J_WF1 - J_WF2) @ BW_ν
+        position_error = W_p_F1 - W_p_F2
+        R_error = W_R_F2.T @ W_R_F1
+        orientation_error = jaxsim.math.rotation.Rotation.log_vee(R_error)
+        baumgarte_term = (
+            K_P * jnp.hstack([position_error, orientation_error]) + K_D @ vel_error
         )
-        # a_ref_ext = jnp.hstack([a_ref, -baumgarte_term])
-        a_ref_ext = jnp.hstack([a_ref, jnp.zeros((3,))])
+
+        # baumgarte_term = K_P * position_error + K_D * vel_error
+
+        R_ext = jnp.pad(R, ((0, dim_kin_constr), (0, dim_kin_constr)), mode="constant")
+        a_ref_ext = jnp.hstack([a_ref, -baumgarte_term])
+        # a_ref_ext = jnp.hstack([a_ref, jnp.zeros((3,))])
 
         # Compute the Delassus matrix and the free mixed linear acceleration of
         # the collidable points.
@@ -492,7 +492,7 @@ def continuing_criterion(carry: OptimizationCarry) -> jtp.Bool:
         init_params = jnp.hstack([
             init_params,
             jnp.zeros(
-                3,
+                dim_kin_constr,
             ),
         ])
 
@@ -514,15 +514,10 @@ def continuing_criterion(carry: OptimizationCarry) -> jtp.Bool:
         )
 
         # Extract the last 6 values from the solution
-        kin_constr_force_mixed_linear = solution[-3:]
-        jax.debug.print("f_loop_mixed: \n{}", kin_constr_force_mixed_linear)
+        kin_constr_force_mixed_F1 = solution[-dim_kin_constr:]
+        # jax.debug.print("f_loop_mixed: \n{}", kin_constr_force_mixed_linear)
 
-        kin_constr_force_mixed_F1 = (
-            jnp.zeros(6).at[0:3].set(kin_constr_force_mixed_linear)
-        )
-        kin_constr_force_mixed_F2 = (
-            jnp.zeros(6).at[0:3].set(-kin_constr_force_mixed_linear)
-        )
+        kin_constr_force_mixed_F2 = -kin_constr_force_mixed_F1
 
         # Transform the wrench in inertial representation
         kin_constr_force_inertial_F1 = (
@@ -546,7 +541,7 @@ def continuing_criterion(carry: OptimizationCarry) -> jtp.Bool:
         jax.debug.print("f_loop_inertial_F2: \n{}", kin_constr_force_inertial_F2)
 
         # Reshape the optimized solution to be a matrix of 3D contact forces.
-        CW_fl_C = solution[0:-3].reshape(-1, 3)
+        CW_fl_C = solution[0:-dim_kin_constr].reshape(-1, 3)
 
         # Convert the contact forces from mixed to inertial-fixed representation.
         W_f_C = jax.vmap(