Implement multibody joints and the new solver

2022-01-02 14:47:40 +01:00
parent b45d4b5ac2
commit f74b8401ad
182 changed files with 9871 additions and 12645 deletions
--- a/src/dynamics/solver/joint_constraint/joint_velocity_constraint_builder.rs
+++ b/src/dynamics/solver/joint_constraint/joint_velocity_constraint_builder.rs
@@ -0,0 +1,699 @@
+use crate::dynamics::solver::joint_constraint::joint_velocity_constraint::{
+    JointVelocityConstraint, JointVelocityGroundConstraint, WritebackId,
+};
+use crate::dynamics::solver::joint_constraint::SolverBody;
+use crate::dynamics::solver::MotorParameters;
+use crate::dynamics::{IntegrationParameters, JointIndex};
+use crate::math::{Isometry, Matrix, Point, Real, Rotation, Vector, ANG_DIM, DIM};
+use crate::utils::{IndexMut2, WCrossMatrix, WDot, WQuat, WReal};
+use na::SMatrix;
+use simba::simd::SimdRealField;
+
+#[derive(Debug, Copy, Clone)]
+pub struct JointVelocityConstraintBuilder<N: SimdRealField> {
+    pub basis: Matrix<N>,
+    pub cmat1_basis: SMatrix<N, ANG_DIM, DIM>,
+    pub cmat2_basis: SMatrix<N, ANG_DIM, DIM>,
+    pub ang_basis: SMatrix<N, ANG_DIM, ANG_DIM>,
+    pub lin_err: Vector<N>,
+    pub ang_err: Rotation<N>,
+}
+
+impl<N: WReal> JointVelocityConstraintBuilder<N> {
+    pub fn new(
+        frame1: &Isometry<N>,
+        frame2: &Isometry<N>,
+        world_com1: &Point<N>,
+        world_com2: &Point<N>,
+        locked_lin_axes: u8,
+    ) -> Self {
+        let mut frame1 = *frame1;
+        let basis = frame1.rotation.to_rotation_matrix().into_inner();
+        let lin_err = frame2.translation.vector - frame1.translation.vector;
+
+        // Adjust the point of application of the force for the first body,
+        // by snapping free axes to the second frame’s center (to account for
+        // the allowed relative movement).
+        {
+            let mut new_center1 = frame2.translation.vector; // First, assume all dofs are free.
+
+            // Then snap the locked ones.
+            for i in 0..DIM {
+                if locked_lin_axes & (1 << i) != 0 {
+                    let axis = basis.column(i);
+                    new_center1 -= axis * lin_err.dot(&axis);
+                }
+            }
+            frame1.translation.vector = new_center1;
+        }
+
+        let r1 = frame1.translation.vector - world_com1.coords;
+        let r2 = frame2.translation.vector - world_com2.coords;
+
+        let cmat1 = r1.gcross_matrix();
+        let cmat2 = r2.gcross_matrix();
+
+        #[allow(unused_mut)] // The mut is needed for 3D
+        let mut ang_basis = frame1.rotation.diff_conj1_2(&frame2.rotation).transpose();
+        #[allow(unused_mut)] // The mut is needed for 3D
+        let mut ang_err = frame1.rotation.inverse() * frame2.rotation;
+
+        #[cfg(feature = "dim3")]
+        {
+            let sgn = N::one().simd_copysign(frame1.rotation.dot(&frame2.rotation));
+            ang_basis *= sgn;
+            *ang_err.as_mut_unchecked() *= sgn;
+        }
+
+        Self {
+            basis,
+            cmat1_basis: cmat1 * basis,
+            cmat2_basis: cmat2 * basis,
+            ang_basis,
+            lin_err,
+            ang_err,
+        }
+    }
+
+    pub fn limit_linear<const LANES: usize>(
+        &self,
+        params: &IntegrationParameters,
+        joint_id: [JointIndex; LANES],
+        body1: &SolverBody<N, LANES>,
+        body2: &SolverBody<N, LANES>,
+        limited_axis: usize,
+        limits: [N; 2],
+        writeback_id: WritebackId,
+    ) -> JointVelocityConstraint<N, LANES> {
+        let zero = N::zero();
+        let mut constraint =
+            self.lock_linear(params, joint_id, body1, body2, limited_axis, writeback_id);
+
+        let dist = self.lin_err.dot(&constraint.lin_jac);
+        let min_enabled = dist.simd_lt(limits[0]);
+        let max_enabled = limits[1].simd_lt(dist);
+
+        let erp_inv_dt = N::splat(params.erp_inv_dt());
+        let rhs_bias =
+            ((dist - limits[1]).simd_max(zero) - (limits[0] - dist).simd_max(zero)) * erp_inv_dt;
+        constraint.rhs = constraint.rhs_wo_bias + rhs_bias;
+        constraint.impulse_bounds = [
+            N::splat(-Real::INFINITY).select(min_enabled, zero),
+            N::splat(Real::INFINITY).select(max_enabled, zero),
+        ];
+
+        constraint
+    }
+
+    pub fn motor_linear<const LANES: usize>(
+        &self,
+        params: &IntegrationParameters,
+        joint_id: [JointIndex; LANES],
+        body1: &SolverBody<N, LANES>,
+        body2: &SolverBody<N, LANES>,
+        _locked_ang_axes: u8,
+        motor_axis: usize,
+        motor_params: &MotorParameters<N>,
+        writeback_id: WritebackId,
+    ) -> JointVelocityConstraint<N, LANES> {
+        let mut constraint =
+            self.lock_linear(params, joint_id, body1, body2, motor_axis, writeback_id);
+
+        // if locked_ang_axes & (1 << motor_axis) != 0 {
+        //     // FIXME: check that this also works for cases
+        //     // when not all the angular axes are locked.
+        //     constraint.ang_jac1 = na::zero();
+        //     constraint.ang_jac2 = na::zero();
+        // }
+
+        let mut rhs_wo_bias = N::zero();
+        if motor_params.stiffness != N::zero() {
+            let dist = self.lin_err.dot(&constraint.lin_jac);
+            rhs_wo_bias += (dist - motor_params.target_pos) * motor_params.stiffness;
+        }
+
+        if motor_params.damping != N::zero() {
+            let dvel = constraint.lin_jac.dot(&(body2.linvel - body1.linvel))
+                + (constraint.ang_jac2.gdot(body2.angvel) - constraint.ang_jac1.gdot(body1.angvel));
+            rhs_wo_bias += (dvel - motor_params.target_vel) * motor_params.damping;
+        }
+
+        constraint.impulse_bounds = [-motor_params.max_impulse, motor_params.max_impulse];
+        constraint.rhs = rhs_wo_bias;
+        constraint.rhs_wo_bias = rhs_wo_bias;
+        constraint
+    }
+
+    pub fn lock_linear<const LANES: usize>(
+        &self,
+        params: &IntegrationParameters,
+        joint_id: [JointIndex; LANES],
+        body1: &SolverBody<N, LANES>,
+        body2: &SolverBody<N, LANES>,
+        locked_axis: usize,
+        writeback_id: WritebackId,
+    ) -> JointVelocityConstraint<N, LANES> {
+        let lin_jac = self.basis.column(locked_axis).into_owned();
+        #[cfg(feature = "dim2")]
+        let mut ang_jac1 = self.cmat1_basis[locked_axis];
+        #[cfg(feature = "dim2")]
+        let mut ang_jac2 = self.cmat2_basis[locked_axis];
+        #[cfg(feature = "dim3")]
+        let mut ang_jac1 = self.cmat1_basis.column(locked_axis).into_owned();
+        #[cfg(feature = "dim3")]
+        let mut ang_jac2 = self.cmat2_basis.column(locked_axis).into_owned();
+
+        let dvel = lin_jac.dot(&(body2.linvel - body1.linvel))
+            + (ang_jac2.gdot(body2.angvel) - ang_jac1.gdot(body1.angvel));
+        let rhs_wo_bias = dvel * N::splat(params.velocity_solve_fraction);
+
+        let erp_inv_dt = params.erp_inv_dt();
+        let rhs_bias = lin_jac.dot(&self.lin_err) * N::splat(erp_inv_dt);
+
+        ang_jac1 = body1.sqrt_ii * ang_jac1;
+        ang_jac2 = body2.sqrt_ii * ang_jac2;
+
+        JointVelocityConstraint {
+            joint_id,
+            mj_lambda1: body1.mj_lambda,
+            mj_lambda2: body2.mj_lambda,
+            im1: body1.im,
+            im2: body2.im,
+            impulse: N::zero(),
+            impulse_bounds: [-N::splat(Real::MAX), N::splat(Real::MAX)],
+            lin_jac,
+            ang_jac1,
+            ang_jac2,
+            inv_lhs: N::zero(), // Will be set during ortogonalization.
+            rhs: rhs_wo_bias + rhs_bias,
+            rhs_wo_bias,
+            writeback_id,
+        }
+    }
+
+    pub fn limit_angular<const LANES: usize>(
+        &self,
+        params: &IntegrationParameters,
+        joint_id: [JointIndex; LANES],
+        body1: &SolverBody<N, LANES>,
+        body2: &SolverBody<N, LANES>,
+        limited_axis: usize,
+        limits: [N; 2],
+        writeback_id: WritebackId,
+    ) -> JointVelocityConstraint<N, LANES> {
+        let zero = N::zero();
+        let half = N::splat(0.5);
+        let s_limits = [(limits[0] * half).simd_sin(), (limits[1] * half).simd_sin()];
+        #[cfg(feature = "dim2")]
+        let s_ang = self.ang_err.im;
+        #[cfg(feature = "dim3")]
+        let s_ang = self.ang_err.imag()[limited_axis];
+        let min_enabled = s_ang.simd_lt(s_limits[0]);
+        let max_enabled = s_limits[1].simd_lt(s_ang);
+
+        let impulse_bounds = [
+            N::splat(-Real::INFINITY).select(min_enabled, zero),
+            N::splat(Real::INFINITY).select(max_enabled, zero),
+        ];
+
+        #[cfg(feature = "dim2")]
+        let ang_jac = self.ang_basis[limited_axis];
+        #[cfg(feature = "dim3")]
+        let ang_jac = self.ang_basis.column(limited_axis).into_owned();
+        let dvel = ang_jac.gdot(body2.angvel) - ang_jac.gdot(body1.angvel);
+        let rhs_wo_bias = dvel * N::splat(params.velocity_solve_fraction);
+
+        let erp_inv_dt = params.erp_inv_dt();
+        let rhs_bias = ((s_ang - s_limits[1]).simd_max(zero)
+            - (s_limits[0] - s_ang).simd_max(zero))
+            * N::splat(erp_inv_dt);
+
+        let ang_jac1 = body1.sqrt_ii * ang_jac;
+        let ang_jac2 = body2.sqrt_ii * ang_jac;
+
+        JointVelocityConstraint {
+            joint_id,
+            mj_lambda1: body1.mj_lambda,
+            mj_lambda2: body2.mj_lambda,
+            im1: body1.im,
+            im2: body2.im,
+            impulse: N::zero(),
+            impulse_bounds,
+            lin_jac: na::zero(),
+            ang_jac1,
+            ang_jac2,
+            inv_lhs: N::zero(), // Will be set during ortogonalization.
+            rhs: rhs_wo_bias + rhs_bias,
+            rhs_wo_bias,
+            writeback_id,
+        }
+    }
+
+    pub fn motor_angular<const LANES: usize>(
+        &self,
+        joint_id: [JointIndex; LANES],
+        body1: &SolverBody<N, LANES>,
+        body2: &SolverBody<N, LANES>,
+        _motor_axis: usize,
+        motor_params: &MotorParameters<N>,
+        writeback_id: WritebackId,
+    ) -> JointVelocityConstraint<N, LANES> {
+        // let mut ang_jac = self.ang_basis.column(_motor_axis).into_owned();
+        #[cfg(feature = "dim2")]
+        let ang_jac = N::one();
+        #[cfg(feature = "dim3")]
+        let ang_jac = self.basis.column(_motor_axis).into_owned();
+
+        let mut rhs_wo_bias = N::zero();
+        if motor_params.stiffness != N::zero() {
+            #[cfg(feature = "dim2")]
+            let s_ang_dist = self.ang_err.im;
+            #[cfg(feature = "dim3")]
+            let s_ang_dist = self.ang_err.imag()[_motor_axis];
+            let s_target_ang = motor_params.target_pos.simd_sin();
+            rhs_wo_bias += (s_ang_dist - s_target_ang) * motor_params.stiffness;
+        }
+
+        if motor_params.damping != N::zero() {
+            let dvel = ang_jac.gdot(body2.angvel) - ang_jac.gdot(body1.angvel);
+            rhs_wo_bias +=
+                (dvel - motor_params.target_vel/* * ang_jac.norm() */) * motor_params.damping;
+        }
+
+        let ang_jac1 = body1.sqrt_ii * ang_jac;
+        let ang_jac2 = body2.sqrt_ii * ang_jac;
+
+        JointVelocityConstraint {
+            joint_id,
+            mj_lambda1: body1.mj_lambda,
+            mj_lambda2: body2.mj_lambda,
+            im1: body1.im,
+            im2: body2.im,
+            impulse: N::zero(),
+            impulse_bounds: [-motor_params.max_impulse, motor_params.max_impulse],
+            lin_jac: na::zero(),
+            ang_jac1,
+            ang_jac2,
+            inv_lhs: N::zero(), // Will be set during ortogonalization.
+            rhs: rhs_wo_bias,
+            rhs_wo_bias,
+            writeback_id,
+        }
+    }
+
+    pub fn lock_angular<const LANES: usize>(
+        &self,
+        params: &IntegrationParameters,
+        joint_id: [JointIndex; LANES],
+        body1: &SolverBody<N, LANES>,
+        body2: &SolverBody<N, LANES>,
+        locked_axis: usize,
+        writeback_id: WritebackId,
+    ) -> JointVelocityConstraint<N, LANES> {
+        #[cfg(feature = "dim2")]
+        let ang_jac = self.ang_basis[locked_axis];
+        #[cfg(feature = "dim3")]
+        let ang_jac = self.ang_basis.column(locked_axis).into_owned();
+
+        let dvel = ang_jac.gdot(body2.angvel) - ang_jac.gdot(body1.angvel);
+        let rhs_wo_bias = dvel * N::splat(params.velocity_solve_fraction);
+
+        let erp_inv_dt = params.erp_inv_dt();
+        #[cfg(feature = "dim2")]
+        let rhs_bias = self.ang_err.im * N::splat(erp_inv_dt);
+        #[cfg(feature = "dim3")]
+        let rhs_bias = self.ang_err.imag()[locked_axis] * N::splat(erp_inv_dt);
+
+        let ang_jac1 = body1.sqrt_ii * ang_jac;
+        let ang_jac2 = body2.sqrt_ii * ang_jac;
+
+        JointVelocityConstraint {
+            joint_id,
+            mj_lambda1: body1.mj_lambda,
+            mj_lambda2: body2.mj_lambda,
+            im1: body1.im,
+            im2: body2.im,
+            impulse: N::zero(),
+            impulse_bounds: [-N::splat(Real::MAX), N::splat(Real::MAX)],
+            lin_jac: na::zero(),
+            ang_jac1,
+            ang_jac2,
+            inv_lhs: N::zero(), // Will be set during ortogonalization.
+            rhs: rhs_wo_bias + rhs_bias,
+            rhs_wo_bias,
+            writeback_id,
+        }
+    }
+
+    /// Orthogonalize the constraints and set their inv_lhs field.
+    pub fn finalize_constraints<const LANES: usize>(
+        constraints: &mut [JointVelocityConstraint<N, LANES>],
+    ) {
+        let len = constraints.len();
+        let imsum = constraints[0].im1 + constraints[0].im2;
+
+        // Use the modified Gram-Schmidt orthogonalization.
+        for j in 0..len {
+            let c_j = &mut constraints[j];
+            let dot_jj = c_j.lin_jac.norm_squared() * imsum
+                + c_j.ang_jac1.gdot(c_j.ang_jac1)
+                + c_j.ang_jac2.gdot(c_j.ang_jac2);
+            let inv_dot_jj = crate::utils::simd_inv(dot_jj);
+            c_j.inv_lhs = inv_dot_jj; // Don’t forget to update the inv_lhs.
+
+            if c_j.impulse_bounds != [-N::splat(Real::MAX), N::splat(Real::MAX)] {
+                // Don't remove constraints with limited forces from the others
+                // because they may not deliver the necessary forces to fulfill
+                // the removed parts of other constraints.
+                continue;
+            }
+
+            for i in (j + 1)..len {
+                let (c_i, c_j) = constraints.index_mut_const(i, j);
+                let dot_ij = c_i.lin_jac.dot(&c_j.lin_jac) * imsum
+                    + c_i.ang_jac1.gdot(c_j.ang_jac1)
+                    + c_i.ang_jac2.gdot(c_j.ang_jac2);
+                let coeff = dot_ij * inv_dot_jj;
+
+                c_i.lin_jac -= c_j.lin_jac * coeff;
+                c_i.ang_jac1 -= c_j.ang_jac1 * coeff;
+                c_i.ang_jac2 -= c_j.ang_jac2 * coeff;
+                c_i.rhs_wo_bias -= c_j.rhs_wo_bias * coeff;
+                c_i.rhs -= c_j.rhs * coeff;
+            }
+        }
+    }
+
+    pub fn limit_linear_ground<const LANES: usize>(
+        &self,
+        params: &IntegrationParameters,
+        joint_id: [JointIndex; LANES],
+        body1: &SolverBody<N, LANES>,
+        body2: &SolverBody<N, LANES>,
+        limited_axis: usize,
+        limits: [N; 2],
+        writeback_id: WritebackId,
+    ) -> JointVelocityGroundConstraint<N, LANES> {
+        let zero = N::zero();
+        let lin_jac = self.basis.column(limited_axis).into_owned();
+        let dist = self.lin_err.dot(&lin_jac);
+        let min_enabled = dist.simd_lt(limits[0]);
+        let max_enabled = limits[1].simd_lt(dist);
+
+        let impulse_bounds = [
+            N::splat(-Real::INFINITY).select(min_enabled, zero),
+            N::splat(Real::INFINITY).select(max_enabled, zero),
+        ];
+
+        let ang_jac1 = self.cmat1_basis.column(limited_axis).into_owned();
+        #[cfg(feature = "dim2")]
+        let mut ang_jac2 = self.cmat2_basis[limited_axis];
+        #[cfg(feature = "dim3")]
+        let mut ang_jac2 = self.cmat2_basis.column(limited_axis).into_owned();
+
+        let dvel = lin_jac.dot(&(body2.linvel - body1.linvel))
+            + (ang_jac2.gdot(body2.angvel) - ang_jac1.gdot(body1.angvel));
+        let rhs_wo_bias = dvel * N::splat(params.velocity_solve_fraction);
+
+        let erp_inv_dt = params.erp_inv_dt();
+        let rhs_bias = ((dist - limits[1]).simd_max(zero) - (limits[0] - dist).simd_max(zero))
+            * N::splat(erp_inv_dt);
+
+        ang_jac2 = body2.sqrt_ii * ang_jac2;
+
+        JointVelocityGroundConstraint {
+            joint_id,
+            mj_lambda2: body2.mj_lambda,
+            im2: body2.im,
+            impulse: zero,
+            impulse_bounds,
+            lin_jac,
+            ang_jac2,
+            inv_lhs: zero, // Will be set during ortogonalization.
+            rhs: rhs_wo_bias + rhs_bias,
+            rhs_wo_bias,
+            writeback_id,
+        }
+    }
+
+    pub fn motor_linear_ground<const LANES: usize>(
+        &self,
+        joint_id: [JointIndex; LANES],
+        body1: &SolverBody<N, LANES>,
+        body2: &SolverBody<N, LANES>,
+        motor_axis: usize,
+        motor_params: &MotorParameters<N>,
+        writeback_id: WritebackId,
+    ) -> JointVelocityGroundConstraint<N, LANES> {
+        let lin_jac = self.basis.column(motor_axis).into_owned();
+        let ang_jac1 = self.cmat1_basis.column(motor_axis).into_owned();
+        #[cfg(feature = "dim2")]
+        let mut ang_jac2 = self.cmat2_basis[motor_axis];
+        #[cfg(feature = "dim3")]
+        let mut ang_jac2 = self.cmat2_basis.column(motor_axis).into_owned();
+
+        let mut rhs_wo_bias = N::zero();
+        if motor_params.stiffness != N::zero() {
+            let dist = self.lin_err.dot(&lin_jac);
+            rhs_wo_bias += (dist - motor_params.target_pos) * motor_params.stiffness;
+        }
+
+        if motor_params.damping != N::zero() {
+            let dvel = lin_jac.dot(&(body2.linvel - body1.linvel))
+                + (ang_jac2.gdot(body2.angvel) - ang_jac1.gdot(body1.angvel));
+            rhs_wo_bias += (dvel - motor_params.target_vel) * motor_params.damping;
+        }
+
+        ang_jac2 = body2.sqrt_ii * ang_jac2;
+
+        JointVelocityGroundConstraint {
+            joint_id,
+            mj_lambda2: body2.mj_lambda,
+            im2: body2.im,
+            impulse: N::zero(),
+            impulse_bounds: [-motor_params.max_impulse, motor_params.max_impulse],
+            lin_jac,
+            ang_jac2,
+            inv_lhs: N::zero(), // Will be set during ortogonalization.
+            rhs: rhs_wo_bias,
+            rhs_wo_bias,
+            writeback_id,
+        }
+    }
+
+    pub fn lock_linear_ground<const LANES: usize>(
+        &self,
+        params: &IntegrationParameters,
+        joint_id: [JointIndex; LANES],
+        body1: &SolverBody<N, LANES>,
+        body2: &SolverBody<N, LANES>,
+        locked_axis: usize,
+        writeback_id: WritebackId,
+    ) -> JointVelocityGroundConstraint<N, LANES> {
+        let lin_jac = self.basis.column(locked_axis).into_owned();
+        let ang_jac1 = self.cmat1_basis.column(locked_axis).into_owned();
+        #[cfg(feature = "dim2")]
+        let mut ang_jac2 = self.cmat2_basis[locked_axis];
+        #[cfg(feature = "dim3")]
+        let mut ang_jac2 = self.cmat2_basis.column(locked_axis).into_owned();
+
+        let dvel = lin_jac.dot(&(body2.linvel - body1.linvel))
+            + (ang_jac2.gdot(body2.angvel) - ang_jac1.gdot(body1.angvel));
+        let rhs_wo_bias = dvel * N::splat(params.velocity_solve_fraction);
+
+        let erp_inv_dt = params.erp_inv_dt();
+        let rhs_bias = lin_jac.dot(&self.lin_err) * N::splat(erp_inv_dt);
+
+        ang_jac2 = body2.sqrt_ii * ang_jac2;
+
+        JointVelocityGroundConstraint {
+            joint_id,
+            mj_lambda2: body2.mj_lambda,
+            im2: body2.im,
+            impulse: N::zero(),
+            impulse_bounds: [-N::splat(Real::MAX), N::splat(Real::MAX)],
+            lin_jac,
+            ang_jac2,
+            inv_lhs: N::zero(), // Will be set during ortogonalization.
+            rhs: rhs_wo_bias + rhs_bias,
+            rhs_wo_bias,
+            writeback_id,
+        }
+    }
+
+    pub fn motor_angular_ground<const LANES: usize>(
+        &self,
+        joint_id: [JointIndex; LANES],
+        body1: &SolverBody<N, LANES>,
+        body2: &SolverBody<N, LANES>,
+        _motor_axis: usize,
+        motor_params: &MotorParameters<N>,
+        writeback_id: WritebackId,
+    ) -> JointVelocityGroundConstraint<N, LANES> {
+        // let mut ang_jac = self.ang_basis.column(_motor_axis).into_owned();
+        #[cfg(feature = "dim2")]
+        let ang_jac = N::one();
+        #[cfg(feature = "dim3")]
+        let ang_jac = self.basis.column(_motor_axis).into_owned();
+
+        let mut rhs_wo_bias = N::zero();
+        if motor_params.stiffness != N::zero() {
+            #[cfg(feature = "dim2")]
+            let s_ang_dist = self.ang_err.im;
+            #[cfg(feature = "dim3")]
+            let s_ang_dist = self.ang_err.imag()[_motor_axis];
+            let s_target_ang = motor_params.target_pos.simd_sin();
+            rhs_wo_bias += (s_ang_dist - s_target_ang) * motor_params.stiffness;
+        }
+
+        if motor_params.damping != N::zero() {
+            let dvel = ang_jac.gdot(body2.angvel) - ang_jac.gdot(body1.angvel);
+            rhs_wo_bias +=
+                (dvel - motor_params.target_vel/* * ang_jac.norm() */) * motor_params.damping;
+        }
+
+        let ang_jac2 = body2.sqrt_ii * ang_jac;
+
+        JointVelocityGroundConstraint {
+            joint_id,
+            mj_lambda2: body2.mj_lambda,
+            im2: body2.im,
+            impulse: N::zero(),
+            impulse_bounds: [-motor_params.max_impulse, motor_params.max_impulse],
+            lin_jac: na::zero(),
+            ang_jac2,
+            inv_lhs: N::zero(), // Will be set during ortogonalization.
+            rhs: rhs_wo_bias,
+            rhs_wo_bias,
+            writeback_id,
+        }
+    }
+
+    pub fn limit_angular_ground<const LANES: usize>(
+        &self,
+        params: &IntegrationParameters,
+        joint_id: [JointIndex; LANES],
+        body1: &SolverBody<N, LANES>,
+        body2: &SolverBody<N, LANES>,
+        limited_axis: usize,
+        limits: [N; 2],
+        writeback_id: WritebackId,
+    ) -> JointVelocityGroundConstraint<N, LANES> {
+        let zero = N::zero();
+        let half = N::splat(0.5);
+        let s_limits = [(limits[0] * half).simd_sin(), (limits[1] * half).simd_sin()];
+        #[cfg(feature = "dim2")]
+        let s_ang = self.ang_err.im;
+        #[cfg(feature = "dim3")]
+        let s_ang = self.ang_err.imag()[limited_axis];
+        let min_enabled = s_ang.simd_lt(s_limits[0]);
+        let max_enabled = s_limits[1].simd_lt(s_ang);
+
+        let impulse_bounds = [
+            N::splat(-Real::INFINITY).select(min_enabled, zero),
+            N::splat(Real::INFINITY).select(max_enabled, zero),
+        ];
+
+        #[cfg(feature = "dim2")]
+        let ang_jac = self.ang_basis[limited_axis];
+        #[cfg(feature = "dim3")]
+        let ang_jac = self.ang_basis.column(limited_axis).into_owned();
+        let dvel = ang_jac.gdot(body2.angvel) - ang_jac.gdot(body1.angvel);
+        let rhs_wo_bias = dvel * N::splat(params.velocity_solve_fraction);
+
+        let erp_inv_dt = params.erp_inv_dt();
+        let rhs_bias = ((s_ang - s_limits[1]).simd_max(zero)
+            - (s_limits[0] - s_ang).simd_max(zero))
+            * N::splat(erp_inv_dt);
+
+        let ang_jac2 = body2.sqrt_ii * ang_jac;
+
+        JointVelocityGroundConstraint {
+            joint_id,
+            mj_lambda2: body2.mj_lambda,
+            im2: body2.im,
+            impulse: zero,
+            impulse_bounds,
+            lin_jac: na::zero(),
+            ang_jac2,
+            inv_lhs: zero, // Will be set during ortogonalization.
+            rhs: rhs_wo_bias + rhs_bias,
+            rhs_wo_bias,
+            writeback_id,
+        }
+    }
+
+    pub fn lock_angular_ground<const LANES: usize>(
+        &self,
+        params: &IntegrationParameters,
+        joint_id: [JointIndex; LANES],
+        body1: &SolverBody<N, LANES>,
+        body2: &SolverBody<N, LANES>,
+        locked_axis: usize,
+        writeback_id: WritebackId,
+    ) -> JointVelocityGroundConstraint<N, LANES> {
+        #[cfg(feature = "dim2")]
+        let ang_jac = self.ang_basis[locked_axis];
+        #[cfg(feature = "dim3")]
+        let ang_jac = self.ang_basis.column(locked_axis).into_owned();
+        let dvel = ang_jac.gdot(body2.angvel) - ang_jac.gdot(body1.angvel);
+        let rhs_wo_bias = dvel * N::splat(params.velocity_solve_fraction);
+
+        let erp_inv_dt = params.erp_inv_dt();
+        #[cfg(feature = "dim2")]
+        let rhs_bias = self.ang_err.im * N::splat(erp_inv_dt);
+        #[cfg(feature = "dim3")]
+        let rhs_bias = self.ang_err.imag()[locked_axis] * N::splat(erp_inv_dt);
+
+        let ang_jac2 = body2.sqrt_ii * ang_jac;
+
+        JointVelocityGroundConstraint {
+            joint_id,
+            mj_lambda2: body2.mj_lambda,
+            im2: body2.im,
+            impulse: N::zero(),
+            impulse_bounds: [-N::splat(Real::MAX), N::splat(Real::MAX)],
+            lin_jac: na::zero(),
+            ang_jac2,
+            inv_lhs: N::zero(), // Will be set during ortogonalization.
+            rhs: rhs_wo_bias + rhs_bias,
+            rhs_wo_bias,
+            writeback_id,
+        }
+    }
+
+    /// Orthogonalize the constraints and set their inv_lhs field.
+    pub fn finalize_ground_constraints<const LANES: usize>(
+        constraints: &mut [JointVelocityGroundConstraint<N, LANES>],
+    ) {
+        let len = constraints.len();
+        let imsum = constraints[0].im2;
+
+        // Use the modified Gram-Schmidt orthogonalization.
+        for j in 0..len {
+            let c_j = &mut constraints[j];
+            let dot_jj = c_j.lin_jac.norm_squared() * imsum + c_j.ang_jac2.gdot(c_j.ang_jac2);
+            let inv_dot_jj = crate::utils::simd_inv(dot_jj);
+            c_j.inv_lhs = inv_dot_jj; // Don’t forget to update the inv_lhs.
+
+            if c_j.impulse_bounds != [-N::splat(Real::MAX), N::splat(Real::MAX)] {
+                // Don't remove constraints with limited forces from the others
+                // because they may not deliver the necessary forces to fulfill
+                // the removed parts of other constraints.
+                continue;
+            }
+
+            for i in (j + 1)..len {
+                let (c_i, c_j) = constraints.index_mut_const(i, j);
+                let dot_ij =
+                    c_i.lin_jac.dot(&c_j.lin_jac) * imsum + c_i.ang_jac2.gdot(c_j.ang_jac2);
+                let coeff = dot_ij * inv_dot_jj;
+
+                c_i.lin_jac -= c_j.lin_jac * coeff;
+                c_i.ang_jac2 -= c_j.ang_jac2 * coeff;
+                c_i.rhs_wo_bias -= c_j.rhs_wo_bias * coeff;
+                c_i.rhs -= c_j.rhs * coeff;
+            }
+        }
+    }
+}