File syn_kinematics.h

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Multi-Axis Robot Forward & Inverse Kinematics Engine (Q16.16 fixed-point). More...

• #include "../common/syn_defs.h"
• #include "../util/syn_matrix.h"
• #include "../util/syn_qmath.h"
• #include <stdbool.h>
• #include <stddef.h>
• #include <stdint.h>

Classes

Type	Name
struct	SYN_DH_Param Single joint Denavit-Hartenberg parameter specification.
struct	SYN_Kinematics_6DOFConfig Configuration parameters for 6-DOF Articulated Arm with Spherical Wrist.
struct	SYN_Kinematics_DeltaConfig Configuration parameters for 3-Axis Delta Parallel Robot.
struct	SYN_Kinematics_Planar3Config Configuration parameters for 3-DOF Planar Arm.
struct	SYN_Kinematics_SCARAConfig Configuration parameters for 4-DOF SCARA Robot.
struct	SYN_Orientation3D 3D Orientation (Roll, Pitch, Yaw Euler angles) in Q16.16 radians.
struct	SYN_Pose6D Complete 6-DOF Spatial Pose (Position + Orientation).
struct	SYN_Position3D 3D Cartesian Position (X, Y, Z) in Q16.16.

Public Types

Type	Name
enum	SYN_ArmElbow Elbow configuration for 2D/3D arm inverse kinematics.
enum	SYN_DH_Convention Denavit-Hartenberg parameter convention.

Public Functions

Type	Name
SYN_Status	syn_dh_matrix (const SYN_DH_Param * param, q16_t joint_val, SYN_DH_Convention conv, SYN_Matrix * out_t44) Compute single-link 4x4 Homogeneous Transformation Matrix from DH parameters.
SYN_Status	syn_kinematics_6dof_fk (const SYN_Kinematics_6DOFConfig * cfg, const q16_t q, SYN_Pose6D * out_pose) Forward kinematics for 6-DOF articulated arm.
SYN_Status	syn_kinematics_6dof_ik (const SYN_Kinematics_6DOFConfig * cfg, const SYN_Pose6D * target, SYN_ArmElbow elbow, bool wrist_flip, q16_t out_q) Closed-form inverse kinematics for 6-DOF arm with spherical wrist (Pieper solution).
SYN_Status	syn_kinematics_delta_fk (const SYN_Kinematics_DeltaConfig * cfg, q16_t theta1, q16_t theta2, q16_t theta3, SYN_Position3D * out_pos) Forward kinematics for 3-axis Delta parallel robot.
SYN_Status	syn_kinematics_delta_ik (const SYN_Kinematics_DeltaConfig * cfg, const SYN_Position3D * target, q16_t * out_theta1, q16_t * out_theta2, q16_t * out_theta3) Inverse kinematics for 3-axis Delta parallel robot.
SYN_Status	syn_kinematics_forward (const SYN_DH_Param * chain, size_t num_joints, const q16_t * joint_vals, SYN_DH_Convention conv, SYN_Matrix * out_t44, SYN_Pose6D * out_pose) Compute Forward Kinematics for a general serial DH chain.
SYN_Status	syn_kinematics_jacobian (const SYN_DH_Param * chain, size_t num_joints, const q16_t * joint_vals, SYN_DH_Convention conv, SYN_Matrix * out_j6xn) Calculate Geometric 6xN Jacobian Matrix for a serial link chain.
SYN_Status	syn_kinematics_planar3_fk (const SYN_Kinematics_Planar3Config * cfg, q16_t q1, q16_t q2, q16_t q3, q16_t * out_x, q16_t * out_y, q16_t * out_phi) Forward kinematics for 3-DOF planar arm.
SYN_Status	syn_kinematics_planar3_ik (const SYN_Kinematics_Planar3Config * cfg, q16_t x, q16_t y, q16_t phi, SYN_ArmElbow elbow, q16_t * out_q1, q16_t * out_q2, q16_t * out_q3) Closed-form inverse kinematics for 3-DOF planar arm.
SYN_Status	syn_kinematics_scara_fk (const SYN_Kinematics_SCARAConfig * cfg, q16_t q1, q16_t q2, q16_t d3, q16_t q4, SYN_Pose6D * out_pose) Forward kinematics for 4-DOF SCARA robot.
SYN_Status	syn_kinematics_scara_ik (const SYN_Kinematics_SCARAConfig * cfg, const SYN_Pose6D * target, SYN_ArmElbow elbow, q16_t * out_q1, q16_t * out_q2, q16_t * out_d3, q16_t * out_q4) Closed-form inverse kinematics for 4-DOF SCARA robot.

Macros

Type	Name
define	SYN_KINEMATICS_MAX_JOINTS 8U

Detailed Description

Provides a zero-heap robotics kinematics engine for embedded microcontrollers: * Standard & Modified Denavit-Hartenberg (DH) parameter chain transforms. * Multi-joint forward kinematics with position vector and orientation extraction. * Closed-form inverse kinematics solvers for: * 3-DOF Planar Articulated Arm. * 4-DOF SCARA Robot (X, Y, Z, Yaw) with elbow-left / elbow-right configurations. * 6-DOF Articulated Robot Arm with spherical wrist (Pieper's decoupling). * 3-Axis Delta Parallel Robot.

• Geometric Jacobian computation (6 x N) for differential velocity kinematics.

Public Types Documentation

enum SYN_ArmElbow

Elbow configuration for 2D/3D arm inverse kinematics.

enum SYN_ArmElbow {
    SYN_ARM_ELBOW_UP = 0,
    SYN_ARM_ELBOW_DOWN = 1
};

---

enum SYN_DH_Convention

Denavit-Hartenberg parameter convention.

enum SYN_DH_Convention {
    SYN_DH_CONVENTION_STANDARD = 0,
    SYN_DH_CONVENTION_MODIFIED = 1
};

---

Public Functions Documentation

function syn_dh_matrix

Compute single-link 4x4 Homogeneous Transformation Matrix from DH parameters.

SYN_Status syn_dh_matrix (
    const SYN_DH_Param * param,
    q16_t joint_val,
    SYN_DH_Convention conv,
    SYN_Matrix * out_t44
) 

Parameters:

• param DH parameters for link.
• joint_val Joint variable (angle in rad for revolute, displacement for prismatic).
• conv DH convention (standard or modified).
• out_t44 Output 4x4 matrix (must be initialized with 4 rows, 4 cols).

Returns:

SYN_OK on success, SYN_INVALID_PARAM on NULL or dimension error.

---

function syn_kinematics_6dof_fk

Forward kinematics for 6-DOF articulated arm.

SYN_Status syn_kinematics_6dof_fk (
    const SYN_Kinematics_6DOFConfig * cfg,
    const q16_t q,
    SYN_Pose6D * out_pose
) 

Parameters:

• cfg 6-DOF arm configuration.
• q Array of 6 joint angles in radians.
• out_pose Output 6-DOF Cartesian pose.

Returns:

SYN_OK on success.

---

function syn_kinematics_6dof_ik

Closed-form inverse kinematics for 6-DOF arm with spherical wrist (Pieper solution).

SYN_Status syn_kinematics_6dof_ik (
    const SYN_Kinematics_6DOFConfig * cfg,
    const SYN_Pose6D * target,
    SYN_ArmElbow elbow,
    bool wrist_flip,
    q16_t out_q
) 

Parameters:

• cfg 6-DOF arm configuration.
• target Target 6-DOF pose.
• elbow Shoulder/elbow solution choice.
• wrist_flip Invert wrist pitch/yaw solution if true.
• out_q Output array of 6 joint angles in radians.

Returns:

SYN_OK on success, SYN_ERROR if target position or orientation unreachable.

---

function syn_kinematics_delta_fk

Forward kinematics for 3-axis Delta parallel robot.

SYN_Status syn_kinematics_delta_fk (
    const SYN_Kinematics_DeltaConfig * cfg,
    q16_t theta1,
    q16_t theta2,
    q16_t theta3,
    SYN_Position3D * out_pos
) 

Parameters:

• cfg Delta robot geometry configuration.
• theta1 Actuator 1 angle (rad).
• theta2 Actuator 2 angle (rad).
• theta3 Actuator 3 angle (rad).
• out_pos Output 3D Cartesian position of traveling plate center.

Returns:

SYN_OK on success, SYN_ERROR if no real geometric intersection exists.

---

function syn_kinematics_delta_ik

Inverse kinematics for 3-axis Delta parallel robot.

SYN_Status syn_kinematics_delta_ik (
    const SYN_Kinematics_DeltaConfig * cfg,
    const SYN_Position3D * target,
    q16_t * out_theta1,
    q16_t * out_theta2,
    q16_t * out_theta3
) 

Parameters:

• cfg Delta robot geometry configuration.
• target Target 3D Cartesian position (X, Y, Z).
• out_theta1 Output actuator 1 angle (rad).
• out_theta2 Output actuator 2 angle (rad).
• out_theta3 Output actuator 3 angle (rad).

Returns:

SYN_OK on success, SYN_ERROR if position is outside workspace.

---

function syn_kinematics_forward

Compute Forward Kinematics for a general serial DH chain.

SYN_Status syn_kinematics_forward (
    const SYN_DH_Param * chain,
    size_t num_joints,
    const q16_t * joint_vals,
    SYN_DH_Convention conv,
    SYN_Matrix * out_t44,
    SYN_Pose6D * out_pose
) 

Parameters:

• chain Array of DH joint parameters.
• num_joints Number of joints in chain (<= SYN_KINEMATICS_MAX_JOINTS).
• joint_vals Array of joint values.
• conv DH convention.
• out_t44 Optional output 4x4 end-effector transform matrix (can be NULL).
• out_pose Optional output 6-DOF pose (can be NULL).

Returns:

SYN_OK on success, SYN_INVALID_PARAM on invalid inputs.

---

function syn_kinematics_jacobian

Calculate Geometric 6xN Jacobian Matrix for a serial link chain.

SYN_Status syn_kinematics_jacobian (
    const SYN_DH_Param * chain,
    size_t num_joints,
    const q16_t * joint_vals,
    SYN_DH_Convention conv,
    SYN_Matrix * out_j6xn
) 

Parameters:

• chain Array of DH joint parameters.
• num_joints Number of joints in chain.
• joint_vals Current joint positions.
• conv DH convention.
• out_j6xn Output 6xN matrix (rows=6, cols=num_joints).

Returns:

SYN_OK on success, SYN_INVALID_PARAM on invalid inputs.

---

function syn_kinematics_planar3_fk

Forward kinematics for 3-DOF planar arm.

SYN_Status syn_kinematics_planar3_fk (
    const SYN_Kinematics_Planar3Config * cfg,
    q16_t q1,
    q16_t q2,
    q16_t q3,
    q16_t * out_x,
    q16_t * out_y,
    q16_t * out_phi
) 

Parameters:

• cfg Planar arm configuration.
• q1 Joint 1 angle (rad).
• q2 Joint 2 angle (rad).
• q3 Joint 3 angle (rad).
• out_x Pointer to receive X position.
• out_y Pointer to receive Y position.
• out_phi Pointer to receive tool orientation angle (rad).

Returns:

SYN_OK on success.

---

function syn_kinematics_planar3_ik

Closed-form inverse kinematics for 3-DOF planar arm.

SYN_Status syn_kinematics_planar3_ik (
    const SYN_Kinematics_Planar3Config * cfg,
    q16_t x,
    q16_t y,
    q16_t phi,
    SYN_ArmElbow elbow,
    q16_t * out_q1,
    q16_t * out_q2,
    q16_t * out_q3
) 

Parameters:

• cfg Planar arm configuration.
• x Target X position.
• y Target Y position.
• phi Target end-effector orientation angle (rad).
• elbow Elbow configuration (up or down).
• out_q1 Output joint 1 angle.
• out_q2 Output joint 2 angle.
• out_q3 Output joint 3 angle.

Returns:

SYN_OK on success, SYN_ERROR if target unreachable.

---

function syn_kinematics_scara_fk

Forward kinematics for 4-DOF SCARA robot.

SYN_Status syn_kinematics_scara_fk (
    const SYN_Kinematics_SCARAConfig * cfg,
    q16_t q1,
    q16_t q2,
    q16_t d3,
    q16_t q4,
    SYN_Pose6D * out_pose
) 

Parameters:

• cfg SCARA configuration.
• q1 Joint 1 shoulder angle (rad).
• q2 Joint 2 elbow angle (rad).
• d3 Joint 3 prismatic vertical displacement (distance down).
• q4 Joint 4 wrist roll angle (rad).
• out_pose Output 4-DOF pose (X, Y, Z, Yaw).

Returns:

SYN_OK on success.

---

function syn_kinematics_scara_ik

Closed-form inverse kinematics for 4-DOF SCARA robot.

SYN_Status syn_kinematics_scara_ik (
    const SYN_Kinematics_SCARAConfig * cfg,
    const SYN_Pose6D * target,
    SYN_ArmElbow elbow,
    q16_t * out_q1,
    q16_t * out_q2,
    q16_t * out_d3,
    q16_t * out_q4
) 

Parameters:

• cfg SCARA configuration.
• target Target 6-DOF pose (X, Y, Z, Yaw).
• elbow Elbow configuration (up/left or down/right).
• out_q1 Output joint 1 angle.
• out_q2 Output joint 2 angle.
• out_d3 Output joint 3 vertical position.
• out_q4 Output joint 4 wrist angle.

Returns:

SYN_OK on success, SYN_ERROR if target unreachable.

---

Macro Definition Documentation

define SYN_KINEMATICS_MAX_JOINTS

#define SYN_KINEMATICS_MAX_JOINTS `8U`

Maximum supported joints in a kinematic chain

---

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The documentation for this class was generated from the following file src/syntropic/motor/syn_kinematics.h