feat: make the constraints regularization coefficients configurable with angular frequency instead of explicit ERP

8 files changed, 131 insertions, 63 deletions

diff --git a/src/dynamics/integration_parameters.rs b/src/dynamics/integration_parameters.rs
index c662128..2d580e2 100644
--- a/src/dynamics/integration_parameters.rs
+++ b/src/dynamics/integration_parameters.rs
@@ -1,4 +1,5 @@
 use crate::math::Real;
+use na::RealField;
 use std::num::NonZeroUsize;
 
 // TODO: enabling the block solver in 3d introduces a lot of jitters in
@@ -9,9 +10,9 @@ pub(crate) static BLOCK_SOLVER_ENABLED: bool = cfg!(feature = "dim2");
 #[derive(Copy, Clone, Debug)]
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
 pub struct IntegrationParameters {
-    /// The timestep length (default: `1.0 / 60.0`)
+    /// The timestep length (default: `1.0 / 60.0`).
     pub dt: Real,
-    /// Minimum timestep size when using CCD with multiple substeps (default `1.0 / 60.0 / 100.0`)
+    /// Minimum timestep size when using CCD with multiple substeps (default: `1.0 / 60.0 / 100.0`).
     ///
     /// When CCD with multiple substeps is enabled, the timestep is subdivided
     /// into smaller pieces. This timestep subdivision won't generate timestep
@@ -23,20 +24,24 @@ pub struct IntegrationParameters {
     /// to numerical instabilities.
     pub min_ccd_dt: Real,
 
-    /// 0-1: multiplier for how much of the constraint violation (e.g. contact penetration)
-    /// will be compensated for during the velocity solve.
-    /// (default `0.1`).
-    pub erp: Real,
-    /// 0-1: the damping ratio used by the springs for Baumgarte constraints stabilization.
-    /// Lower values make the constraints more compliant (more "springy", allowing more visible penetrations
-    /// before stabilization).
-    /// (default `20.0`).
-    pub damping_ratio: Real,
+    /// > 0: the damping ratio used by the springs for contact constraint stabilization.
+    /// Lower values make the constraints more compliant (more "springy", allowing more visible
+    /// penetrations before stabilization).
+    /// (default `5.0`).
+    pub contact_damping_ratio: Real,
 
-    /// 0-1: multiplier for how much of the joint violation
-    /// will be compensated for during the velocity solve.
-    /// (default `1.0`).
-    pub joint_erp: Real,
+    /// > 0: the natural frequency used by the springs for contact constraint regularization.
+    /// Increasing this value will make it so that penetrations get fixed more quickly at the
+    /// expense of potential jitter effects due to overshooting. In order to make the simulation
+    /// look stiffer, it is recommended to increase the [`Self::damping_ratio`] instead of this
+    /// value.
+    /// (default: `30.0`).
+    pub contact_natural_frequency: Real,
+
+    /// > 0: the natural frequency used by the springs for joint constraint regularization.
+    /// Increasing this value will make it so that penetrations get fixed more quickly.
+    /// (default: `1.0e6`).
+    pub joint_natural_frequency: Real,
 
     /// The fraction of critical damping applied to the joint for constraints regularization.
     /// (default `1.0`).
@@ -45,7 +50,8 @@ pub struct IntegrationParameters {
     /// The coefficient in `[0, 1]` applied to warmstart impulses, i.e., impulses that are used as the
     /// initial solution (instead of 0) at the next simulation step.
     ///
-    /// This should generally be set to 1. Can be set to 0 if using a large [`Self::erp`] value.
+    /// This should generally be set to 1.
+    ///
     /// (default `1.0`).
     pub warmstart_coefficient: Real,
 
@@ -53,7 +59,7 @@ pub struct IntegrationParameters {
     ///
     /// This value is used internally to estimate some length-based tolerance. In particular, the
     /// values [`IntegrationParameters::allowed_linear_error`],
-    /// [`IntegrationParameters::max_penetration_correction`],
+    /// [`IntegrationParameters::max_corrective_velocity`],
     /// [`IntegrationParameters::prediction_distance`], [`RigidBodyActivation::linear_threshold`]
     /// are scaled by this value implicitly.
     ///
@@ -71,7 +77,7 @@ pub struct IntegrationParameters {
     /// Maximum amount of penetration the solver will attempt to resolve in one timestep.
     ///
     /// This value is implicitly scaled by [`IntegrationParameters::length_unit`].
-    pub normalized_max_penetration_correction: Real,
+    pub normalized_max_corrective_velocity: Real,
     /// The maximal distance separating two objects that will generate predictive contacts (default: `0.002m`).
     ///
     /// This value is implicitly scaled by [`IntegrationParameters::length_unit`].
@@ -123,20 +129,53 @@ impl IntegrationParameters {
         }
     }
 
-    /// The ERP coefficient, multiplied by the inverse timestep length.
+    /// The contact’s spring angular frequency for constraints regularization.
+    pub fn angular_frequency(&self) -> Real {
+        self.contact_natural_frequency * Real::two_pi()
+    }
+
+    /// The [`Self::erp`] coefficient, multiplied by the inverse timestep length.
     pub fn erp_inv_dt(&self) -> Real {
-        self.erp * self.inv_dt()
+        let ang_freq = self.angular_frequency();
+        ang_freq / (self.dt * ang_freq + 2.0 * self.contact_damping_ratio)
+    }
+
+    /// The effective Error Reduction Parameter applied for calculating regularization forces
+    /// on contacts.
+    ///
+    /// This parameter is computed automatically from [`Self::natural_frequency`],
+    /// [`Self::damping_ratio`] and the substep length.
+    pub fn erp(&self) -> Real {
+        self.dt * self.erp_inv_dt()
+    }
+
+    /// The joint’s spring angular frequency for constraint regularization.
+    pub fn joint_angular_frequency(&self) -> Real {
+        self.joint_natural_frequency * Real::two_pi()
     }
 
-    /// The joint ERP coefficient, multiplied by the inverse timestep length.
+    /// The [`Self::joint_erp`] coefficient, multiplied by the inverse timestep length.
     pub fn joint_erp_inv_dt(&self) -> Real {
-        self.joint_erp * self.inv_dt()
+        let ang_freq = self.joint_angular_frequency();
+        ang_freq / (self.dt * ang_freq + 2.0 * self.joint_damping_ratio)
     }
 
-    /// The CFM factor to be used in the constraints resolution.
+    /// The effective Error Reduction Parameter applied for calculating regularization forces
+    /// on joints.
+    ///
+    /// This parameter is computed automatically from [`Self::joint_natural_frequency`],
+    /// [`Self::joint_damping_ratio`] and the substep length.
+    pub fn joint_erp(&self) -> Real {
+        self.dt * self.joint_erp_inv_dt()
+    }
+
+    /// The CFM factor to be used in the constraint resolution.
+    ///
+    /// This parameter is computed automatically from [`Self::natural_frequency`],
+    /// [`Self::damping_ratio`] and the substep length.
     pub fn cfm_factor(&self) -> Real {
         // Compute CFM assuming a critically damped spring multiplied by the damping ratio.
-        let inv_erp_minus_one = 1.0 / self.erp - 1.0;
+        let inv_erp_minus_one = 1.0 / self.erp() - 1.0;
 
         // let stiffness = 4.0 * damping_ratio * damping_ratio * projected_mass
         //     / (dt * dt * inv_erp_minus_one * inv_erp_minus_one);
@@ -145,7 +184,10 @@ impl IntegrationParameters {
         // let cfm = 1.0 / (dt * dt * stiffness + dt * damping);
         // NOTE: This simplifies to cfm = cfm_coeff / projected_mass:
         let cfm_coeff = inv_erp_minus_one * inv_erp_minus_one
-            / ((1.0 + inv_erp_minus_one) * 4.0 * self.damping_ratio * self.damping_ratio);
+            / ((1.0 + inv_erp_minus_one)
+                * 4.0
+                * self.contact_damping_ratio
+                * self.contact_damping_ratio);
 
         // Furthermore, we use this coefficient inside of the impulse resolution.
         // Surprisingly, several simplifications happen there.
@@ -166,11 +208,14 @@ impl IntegrationParameters {
         1.0 / (1.0 + cfm_coeff)
     }
 
-    /// The CFM (constraints force mixing) coefficient applied to all joints for constraints regularization
+    /// The CFM (constraints force mixing) coefficient applied to all joints for constraints regularization.
+    ///
+    /// This parameter is computed automatically from [`Self::joint_natural_frequency`],
+    /// [`Self::joint_damping_ratio`] and the substep length.
     pub fn joint_cfm_coeff(&self) -> Real {
         // Compute CFM assuming a critically damped spring multiplied by the damping ratio.
         // The logic is similar to `Self::cfm_factor`.
-        let inv_erp_minus_one = 1.0 / self.joint_erp - 1.0;
+        let inv_erp_minus_one = 1.0 / self.joint_erp() - 1.0;
         inv_erp_minus_one * inv_erp_minus_one
             / ((1.0 + inv_erp_minus_one)
                 * 4.0
@@ -186,11 +231,11 @@ impl IntegrationParameters {
 
     /// Maximum amount of penetration the solver will attempt to resolve in one timestep.
     ///
-    /// This is equal to [`Self::normalized_max_penetration_correction`] multiplied by
+    /// This is equal to [`Self::normalized_max_corrective_velocity`] multiplied by
     /// [`Self::length_unit`].
-    pub fn max_penetration_correction(&self) -> Real {
-        if self.normalized_max_penetration_correction != Real::MAX {
-            self.normalized_max_penetration_correction * self.length_unit
+    pub fn max_corrective_velocity(&self) -> Real {
+        if self.normalized_max_corrective_velocity != Real::MAX {
+            self.normalized_max_corrective_velocity * self.length_unit
         } else {
             Real::MAX
         }
@@ -210,9 +255,9 @@ impl IntegrationParameters {
         Self {
             dt: 1.0 / 60.0,
             min_ccd_dt: 1.0 / 60.0 / 100.0,
-            erp: 0.1,
-            damping_ratio: 20.0,
-            joint_erp: 1.0,
+            contact_natural_frequency: 30.0,
+            contact_damping_ratio: 5.0,
+            joint_natural_frequency: 1.0e6,
             joint_damping_ratio: 1.0,
             warmstart_coefficient: 1.0,
             num_internal_pgs_iterations: 1,
@@ -226,7 +271,7 @@ impl IntegrationParameters {
             // tons of islands, reducing SIMD parallelism opportunities.
             min_island_size: 128,
             normalized_allowed_linear_error: 0.001,
-            normalized_max_penetration_correction: Real::MAX,
+            normalized_max_corrective_velocity: 10.0,
             normalized_prediction_distance: 0.002,
             max_ccd_substeps: 1,
             length_unit: 1.0,
@@ -240,8 +285,7 @@ impl IntegrationParameters {
     /// warmstarting proves to be undesirable for your use-case.
     pub fn tgs_soft_without_warmstart() -> Self {
         Self {
-            erp: 0.6,
-            damping_ratio: 1.0,
+            contact_damping_ratio: 0.25,
             warmstart_coefficient: 0.0,
             num_additional_friction_iterations: 4,
             ..Self::tgs_soft()
@@ -253,12 +297,9 @@ impl IntegrationParameters {
     /// This exists mainly for testing and comparison purpose.
     pub fn pgs_legacy() -> Self {
         Self {
-            erp: 0.8,
-            damping_ratio: 0.25,
-            warmstart_coefficient: 0.0,
-            num_additional_friction_iterations: 4,
             num_solver_iterations: NonZeroUsize::new(1).unwrap(),
-            ..Self::tgs_soft()
+            num_internal_pgs_iterations: 4,
+            ..Self::tgs_soft_without_warmstart()
         }
     }
 }
diff --git a/src/dynamics/solver/contact_constraint/one_body_constraint.rs b/src/dynamics/solver/contact_constraint/one_body_constraint.rs
index 1243d11..cf9fe67 100644
--- a/src/dynamics/solver/contact_constraint/one_body_constraint.rs
+++ b/src/dynamics/solver/contact_constraint/one_body_constraint.rs
@@ -333,7 +333,8 @@ impl OneBodyConstraintBuilder {
             }
         }
 
-        constraint.cfm_factor = if is_fast_contact { 1.0 } else { cfm_factor };
+        constraint.cfm_factor = cfm_factor;
+        // constraint.cfm_factor = if is_fast_contact { 1.0 } else { cfm_factor };
     }
 }
 
diff --git a/src/dynamics/solver/contact_constraint/one_body_constraint_simd.rs b/src/dynamics/solver/contact_constraint/one_body_constraint_simd.rs
index 5710bc4..131702c 100644
--- a/src/dynamics/solver/contact_constraint/one_body_constraint_simd.rs
+++ b/src/dynamics/solver/contact_constraint/one_body_constraint_simd.rs
@@ -330,7 +330,8 @@ impl SimdOneBodyConstraintBuilder {
             }
         }
 
-        constraint.cfm_factor = SimdReal::splat(1.0).select(is_fast_contact, cfm_factor);
+        constraint.cfm_factor = cfm_factor;
+        // constraint.cfm_factor = SimdReal::splat(1.0).select(is_fast_contact, cfm_factor);
     }
 }
 
diff --git a/src/dynamics/solver/contact_constraint/two_body_constraint.rs b/src/dynamics/solver/contact_constraint/two_body_constraint.rs
index 1511d4f..e98305a 100644
--- a/src/dynamics/solver/contact_constraint/two_body_constraint.rs
+++ b/src/dynamics/solver/contact_constraint/two_body_constraint.rs
@@ -432,7 +432,8 @@ impl TwoBodyConstraintBuilder {
             }
         }
 
-        constraint.cfm_factor = if is_fast_contact { 1.0 } else { cfm_factor };
+        constraint.cfm_factor = cfm_factor;
+        // constraint.cfm_factor = if is_fast_contact { 1.0 } else { cfm_factor };
     }
 }
 
diff --git a/src/dynamics/solver/contact_constraint/two_body_constraint_simd.rs b/src/dynamics/solver/contact_constraint/two_body_constraint_simd.rs
index 4c4ef52..4af0d10 100644
--- a/src/dynamics/solver/contact_constraint/two_body_constraint_simd.rs
+++ b/src/dynamics/solver/contact_constraint/two_body_constraint_simd.rs
@@ -317,7 +317,8 @@ impl TwoBodyConstraintBuilderSimd {
             }
         }
 
-        constraint.cfm_factor = SimdReal::splat(1.0).select(is_fast_contact, cfm_factor);
+        constraint.cfm_factor = cfm_factor;
+        // constraint.cfm_factor = SimdReal::splat(1.0).select(is_fast_contact, cfm_factor);
     }
 }
 
diff --git a/src/dynamics/solver/island_solver.rs b/src/dynamics/solver/island_solver.rs
index 159bfa7..718542b 100644
--- a/src/dynamics/solver/island_solver.rs
+++ b/src/dynamics/solver/island_solver.rs
@@ -47,8 +47,6 @@ impl IslandSolver {
 
         let mut params = *base_params;
         params.dt /= num_solver_iterations as Real;
-        params.damping_ratio /= num_solver_iterations as Real;
-        // params.joint_damping_ratio /= num_solver_iterations as Real;
 
         /*
          *
diff --git a/src/dynamics/solver/velocity_solver.rs b/src/dynamics/solver/velocity_solver.rs
index 9d5c279..a4e03b2 100644
--- a/src/dynamics/solver/velocity_solver.rs
+++ b/src/dynamics/solver/velocity_solver.rs
@@ -205,17 +205,19 @@ impl VelocitySolver {
             /*
              * Resolution without bias.
              */
-            for _ in 0..params.num_internal_stabilization_iterations {
-                joint_constraints
-                    .solve_wo_bias(&mut self.solver_vels, &mut self.generic_solver_vels);
-                contact_constraints.solve_restitution_wo_bias(
-                    &mut self.solver_vels,
-                    &mut self.generic_solver_vels,
-                );
-            }
+            if params.num_internal_stabilization_iterations > 0 {
+                for _ in 0..params.num_internal_stabilization_iterations {
+                    joint_constraints
+                        .solve_wo_bias(&mut self.solver_vels, &mut self.generic_solver_vels);
+                    contact_constraints.solve_restitution_wo_bias(
+                        &mut self.solver_vels,
+                        &mut self.generic_solver_vels,
+                    );
+                }
 
-            contact_constraints
-                .solve_friction(&mut self.solver_vels, &mut self.generic_solver_vels);
+                contact_constraints
+                    .solve_friction(&mut self.solver_vels, &mut self.generic_solver_vels);
+            }
         }
     }
 
diff --git a/src_testbed/ui.rs b/src_testbed/ui.rs
index 7f3bdac..491e15c 100644
--- a/src_testbed/ui.rs
+++ b/src_testbed/ui.rs
@@ -162,7 +162,7 @@ pub fn update_ui(
             ui.add(
                 Slider::new(
                     &mut integration_parameters.num_internal_stabilization_iterations,
-                    1..=100,
+                    0..=100,
                 )
                 .text("max internal stabilization iters."),
             );
@@ -170,12 +170,35 @@ pub fn update_ui(
                 Slider::new(&mut integration_parameters.warmstart_coefficient, 0.0..=1.0)
                     .text("warmstart coefficient"),
             );
-            ui.add(Slider::new(&mut integration_parameters.erp, 0.0..=1.0).text("erp"));
+
+            let mut substep_params = *integration_parameters;
+            substep_params.dt /= substep_params.num_solver_iterations.get() as f32;
+            let curr_erp =  substep_params.erp();
+            let curr_cfm_factor = substep_params.cfm_factor();
+            ui.add(
+                Slider::new(
+                    &mut integration_parameters.contact_natural_frequency,
+                    0.0..=120.0,
+                )
+                .text(format!("contacts Hz (erp = {:.3})", curr_erp)),
+            );
             ui.add(
-                Slider::new(&mut integration_parameters.damping_ratio, 0.0..=20.0)
-                    .text("damping ratio"),
+                Slider::new(
+                    &mut integration_parameters.contact_damping_ratio,
+                    0.0..=20.0,
+                )
+                .text(format!(
+                    "damping ratio (cfm-factor = {:.3})",
+                    curr_cfm_factor
+                )),
+            );
+            ui.add(
+                Slider::new(
+                    &mut integration_parameters.joint_natural_frequency,
+                    0.0..=1200000.0,
+                )
+                .text("joint erp"),
             );
-            ui.add(Slider::new(&mut integration_parameters.joint_erp, 0.0..=1.0).text("joint erp"));
             ui.add(
                 Slider::new(&mut integration_parameters.joint_damping_ratio, 0.0..=20.0)
                     .text("joint damping ratio"),