Kinematic chain using NumPy capable of doing batched FK.

numpy_chain.py

import numpy as np
import networkx as nx
import matplotlib.pyplot as plt
from networkx.algorithms.traversal.depth_first_search import dfs_edges

"""
sys.path.append('../../package/kinematics_helper/') # for 'transforms'
"""
from transforms import (
    rodrigues,
    rodrigues_batch,
    quat2r,
    pr2t,
    t2p,
    t2r,
)

class NumpyChainClass(object):
    """ 
        Kinematic chain using Numpy
    """
    def __init__(self,name='Numpy Chain'):
        """
        Initialize Chain Class
        Parameters:
            name: str - Name of the chain.
        """
        self.chain = None
        self.init_chain(name=name) # initialize chain
        
    def init_chain(self,name=None):
        """
        Initialize chain
        Parameters:
            name: str - Name of the chain.
        """
        # Set name
        self.name = name
        
        # Clear and instantiate chain
        if self.chain is not None:
            self.chain.clear()
        self.chain = nx.DiGraph(name=name)
        
        # Clear body and joint names
        self.body_names  = []
        self.joint_names = []
        
    def get_n_body(self):
        """
        Get the number of bodies.
        Returns:
            int - Number of bodies in the chain.
        """
        return self.chain.number_of_nodes()
    
    def get_body_idx(self,body_name):
        """
        Get the index of a body.
        Parameters:
            body_name: str - Name of the body.
        Returns:
            int - Index of the body.
        """
        body_idx = self.body_names.index(body_name)
        return body_idx
    
    def get_body_idxs(self,body_names):
        """
        Get the indices of bodies.
        Parameters:
            body_names: list of str - Names of the bodies.
        Returns:
            list of int - Indices of the bodies.
        """
        body_idxs = [self.body_names.index(name) 
                     if name in self.body_names else None 
                     for name in body_names]
        return body_idxs
    
    def get_root_body_idx(self):
        """
        Get the root body index.
        Returns:
            int - Index of the root body.
        """
        for node in self.chain.nodes:
            if self.chain.in_degree(node) == 0:  # 루트 노드는 in-degree가 0인 노드
                return list(self.chain.nodes).index(node)
        raise ValueError("No root node found in the chain.")
    
    def get_joint_idx(self,joint_name):
        """
        Get the index of a joint.
        Parameters:
            joint_name: str - Name of the joint.
        Returns:
            int - Index of the joint.
        """
        joint_idx = self.joint_names.index(joint_name)
        return joint_idx
    
    def get_body(self,body_idx):
        """
        Get body information.
        Parameters:
            body_idx: int - Index of the body.
        Returns:
            dict - Information of the body.
        """
        body = self.chain.nodes[body_idx]
        return body
    
    def get_p_body(self,body_name=None,body_idx=None):
        """
        Get the position of a body.
        Parameters:
            body_name: str, optional - Name of the body.
            body_idx: int, optional - Index of the body.
        Returns:
            np.ndarray - Position of the body.
        """
        if body_name is not None:
            body_idx = self.get_body_idx(body_name=body_name)
        elif body_idx is not None:
            body_idx = body_idx
        else:
            raise ValueError("Either body name or index should be given.")
        return self.chain.nodes[body_idx]['p']
    
    def get_p_batch_body(self,body_name=None,body_idx=None):
        """
        Get batched positions of a body.
        Parameters:
            body_name: str, optional - Name of the body.
            body_idx: int, optional - Index of the body.
        Returns:
            np.ndarray - Batched positions of the body.
        """
        if body_name is not None:
            body_idx = self.get_body_idx(body_name=body_name)
        elif body_idx is not None:
            body_idx = body_idx
        else:
            raise ValueError("Either body name or index should be given.")
        return self.chain.nodes[body_idx]['p_batch']
    
    def get_R_body(self,body_name=None,body_idx=None):
        """
        Get the rotation matrix of a body.
        Parameters:
            body_name: str, optional - Name of the body.
            body_idx: int, optional - Index of the body.
        Returns:
            np.ndarray - Rotation matrix of the body.
        """
        if body_name is not None:
            body_idx = self.get_body_idx(body_name=body_name)
        elif body_idx is not None:
            body_idx = body_idx
        else:
            raise ValueError("Either body name or index should be given.")
        return self.chain.nodes[body_idx]['R']
    
    def get_R_batch_body(self,body_name=None,body_idx=None):
        """
        Get batched rotation matrices of a body.
        Parameters:
            body_name: str, optional - Name of the body.
            body_idx: int, optional - Index of the body.
        Returns:
            np.ndarray - Batched rotation matrices of the body.
        """
        if body_name is not None:
            body_idx = self.get_body_idx(body_name=body_name)
        elif body_idx is not None:
            body_idx = body_idx
        else:
            raise ValueError("Either body name or index should be given.")
        return self.chain.nodes[body_idx]['R_batch']
    
    def get_T_body(self,body_name=None,body_idx=None):
        """
        Get the transformation matrix of a body.
        Parameters:
            body_name: str, optional - Name of the body.
            body_idx: int, optional - Index of the body.
        Returns:
            np.ndarray - Transformation matrix of the body.
        """
        return pr2t(
            p = self.get_p_body(body_name,body_idx),
            R = self.get_R_body(body_name,body_idx),
            )
    
    def set_body_info(self,body_idx,key,value):
        """
        Set body information using a key and value.
        Parameters:
            body_idx: int - Index of the body.
            key: str - Key of the information.
            value: Any - Value to set.
        """
        self.chain.nodes[body_idx][key] = value
        
    def set_p_body(self,body_name=None,body_idx=None,p=None):
        """
        Set the position of a body.
        Parameters:
            body_name: str, optional - Name of the body.
            body_idx: int, optional - Index of the body.
            p: np.ndarray - Position to set.
        """
        if body_name is not None:
            body_idx = self.get_body_idx(body_name=body_name)
        elif body_idx is not None:
            body_idx = body_idx
        else:
            raise ValueError("Either body name or index should be given.")
        self.chain.nodes[body_idx]['p'] = p
        
    def set_R_body(self,body_name=None,body_idx=None,R=None):
        """
        Set the rotation matrix of a body.
        Parameters:
            body_name: str, optional - Name of the body.
            body_idx: int, optional - Index of the body.
            R: np.ndarray - Rotation matrix to set.
        """
        if body_name is not None:
            body_idx = self.get_body_idx(body_name=body_name)
        elif body_idx is not None:
            body_idx = body_idx
        else:
            raise ValueError("Either body name or index should be given.")
        self.chain.nodes[body_idx]['R'] = R
        
    def set_T_body(self,body_name=None,body_idx=None,T=None):
        """
        Set the transformation matrix of a body.
        Parameters:
            body_name: str, optional - Name of the body.
            body_idx: int, optional - Index of the body.
            T: np.ndarray - Transformation matrix to set.
        """
        if body_name is not None:
            body_idx = self.get_body_idx(body_name=body_name)
        elif body_idx is not None:
            body_idx = body_idx
        else:
            raise ValueError("Either body name or index should be given.")
        self.chain.nodes[body_idx]['p'] = t2p(T)
        self.chain.nodes[body_idx]['R'] = t2r(T)
        
    def set_q_joint(self,joint_name,q):
        """
        Set the joint angle for a joint.
        Parameters:
            joint_name: str - Name of the joint.
            q: float - Joint angle to set.
        """
        self.chain.nodes[self.get_joint_idx(joint_name)]['q'] = q
            
    def set_qs_joints(self,joint_names,qs,forward=False,root_body_name=None):
        """
        Set joint angles for multiple joints.
        Parameters:
            joint_names: list of str - Names of the joints.
            qs: list or np.ndarray - Joint angles to set.
            forward: bool, optional - Whether to perform forward kinematics after setting.
            root_body_name: str, optional - Name of the root body.
        """
        for (joint_name,q) in zip(joint_names,qs):
            self.set_q_joint(joint_name=joint_name,q=q)
        if forward:
            self.forward(root_body_name=root_body_name)
            
    def set_qs_joints_batch(self, joint_names, q_batch):
        """
        Set batched joint angles for multiple joints.
        Parameters:
            joint_names: list of str - Names of the joints.
            q_batch: np.ndarray, shape [B, N] - Batch of joint angles for all joints.
        """
        B, N = q_batch.shape
        for i, joint_name in enumerate(joint_names):
            q_values = q_batch[:, i]  # shape [B]
            self.chain.nodes[self.get_joint_idx(joint_name)]['q_batch'] = q_values
    
    def add_body(
            self,
            body_name        = '',
            parent_body_name = '',
            joint_name       = '',
            p_offset         = np.zeros(3),
            R_offset         = np.eye(3),
            a                = np.zeros(3),
        ):
        """
        Add a body to the chain.
        Parameters:
            body_name: str - Name of the body.
            parent_body_name: str - Name of the parent body.
            joint_name: str - Name of the joint associated with the body.
            p_offset: np.ndarray - Positional offset of the body.
            R_offset: np.ndarray - Rotational offset of the body.
            a: np.ndarray - Joint axis of the body.
        """
        
        # Add new body (='node' in 'chain)
        new_body_idx = self.get_n_body()
        self.chain.add_node(new_body_idx) # add new node (=body)
        
        # Update body information
        body_info = {
            'name':body_name,
            'parent_name':parent_body_name,
            'joint_name':joint_name,
            'p_offset':p_offset,
            'R_offset':R_offset,
            'a':a,
            'q':0.0,
            'p':np.zeros(3),
            'R':np.eye(3),
            'parent':[],
            'childs':[],
        }
        self.chain.update(nodes=[(new_body_idx,body_info)])
        
        # Append body and joint names
        self.body_names.append(body_name)
        self.joint_names.append(joint_name)
        
        # Add parent body (if necessary)
        if (parent_body_name is not None) and (body_name != parent_body_name):
            # Add parent index
            parent_body_idx = self.get_body_idx(parent_body_name)
            self.chain.nodes[new_body_idx]['parent'] = parent_body_idx
            # Connect parent and child
            self.chain.add_edge(u_of_edge=parent_body_idx,v_of_edge=new_body_idx)
            
        # Append childs to the parent
        parent_body_idx = self.get_body_idx(body_name)
        parent_childs = self.chain.nodes[parent_body_idx]['childs']
        parent_childs.append(new_body_idx)
        
    def build_chain_from_mujoco_env(
            self,
            env        = None,
            init_first = True,
        ):
        """
        Build a kinematic chain from a MuJoCo environment.
        Parameters:
            env: MuJoCo environment - The environment to parse.
            init_first: bool, optional - Whether to reset the chain before building.
        """
        # Reset first
        if init_first:
            self.init_chain(name=env.name)
        for body_idx in range(env.n_body):
            # Parse body information
            body_name = env.body_names[body_idx]
            body = env.model.body(body_name) 
            parent_body_name = env.body_names[body.parentid[0]]
            p_body_offset,quat_body_offset = body.pos,body.quat
            # Parse joint information
            n_joint = body.jntnum # number of attached joints 
            if n_joint == 1:
                joint = env.model.joint(body.jntadr[0]) # joint attached joint
                joint_name = joint.name
                p_joint_offset,joint_axis = joint.pos,joint.axis # currently not supported
            else:
                joint_name = ''
                p_joint_offset,joint_axis = np.zeros(3),np.zeros(3)
            # Add body to the chain
            self.add_body(
                body_name        = body_name,
                parent_body_name = parent_body_name,
                joint_name       = joint_name,
                p_offset         = p_body_offset,
                R_offset         = quat2r(quat_body_offset),
                a                = joint_axis,
            )
        
    def forward(self,joint_names=None,q=None,root_body_name=None):
        """
        Perform forward kinematics.
        Parameters:
            joint_names: list of str, optional - Names of the joints.
            q: np.ndarray, optional - Joint angles.
            root_body_name: str, optional - Name of the root body.
        """
        # Set joint angles (optional)
        if joint_names is not None:
            self.set_qs_joints(joint_names=joint_names,qs=q)
        
        # Get root body index
        if root_body_name is None:
            root_body_idx = self.get_root_body_idx()
        else:
            root_body_idx = self.get_body_idx(root_body_name)
            
        # Recuresively update p and R
        for edge in dfs_edges(self.chain,source=root_body_idx):
            idx_fr  = edge[0]
            idx_to  = edge[1]
            body_fr = self.get_body(idx_fr)
            body_to = self.get_body(idx_to)
            # Update p
            p = body_fr['R']@body_to['p_offset'] + body_fr['p'] # [3]
            self.set_body_info(body_idx=idx_to,key='p',value=p)
            # Update R
            a_to = body_to['a'] 
            if abs(np.linalg.norm(a_to)-1) < 1e-6: # revolute joint
                q_to = body_to['q'] # [1]
                R = body_fr['R']@body_to['R_offset']@rodrigues(a=a_to,q_rad=q_to) # [3x3]
            else:
                R = body_fr['R']@body_to['R_offset'] # [3x3]
            self.set_body_info(body_idx=idx_to,key='R',value=R)
            
    def forward_batch(self, joint_names=None, q_batch=None, root_body_name=None):
        """
        Perform batched forward kinematics.
        Parameters:
            joint_names: list of str, optional - Names of the joints.
            q_batch: np.ndarray, shape [B, N], optional - Batch of joint angles for all joints.
            root_body_name: str, optional - Name of the root body.
        """
        if joint_names is not None:
            self.set_qs_joints_batch(joint_names=joint_names, q_batch=q_batch)

        root_body_idx = self.get_root_body_idx() if root_body_name is None else self.get_body_idx(root_body_name)

        B = q_batch.shape[0]  # Number of batches

        # Initialize root body's p and R for batch
        root_body = self.get_body(root_body_idx)
        root_p = root_body['p']  # shape [3]
        root_R = root_body['R']  # shape [3, 3]

        # Broadcast root position and rotation to batch size
        root_p_batch = np.tile(root_p, (B, 1))  # shape [B, 3]
        root_R_batch = np.tile(root_R, (B, 1, 1))  # shape [B, 3, 3]

        # Update batched position and rotation for the root body
        root_body['p_batch'] = root_p_batch
        root_body['R_batch'] = root_R_batch

        for edge in dfs_edges(self.chain, source=root_body_idx):
            idx_fr = edge[0]
            idx_to = edge[1]
            body_fr = self.get_body(idx_fr)
            body_to = self.get_body(idx_to)

            # Update p_batch
            p_fr_batch = body_fr['p_batch']  # shape [B, 3]
            R_fr_batch = body_fr['R_batch']  # shape [B, 3, 3]
            p_offset = body_to['p_offset']  # shape [3]

            p_to_batch = np.einsum('bij,j->bi', R_fr_batch, p_offset) + p_fr_batch  # shape [B, 3]
            body_to['p_batch'] = p_to_batch

            # Update R_batch
            a_to = body_to['a']  # shape [3]
            if abs(np.linalg.norm(a_to) - 1) < 1e-6:  # Revolute joint
                q_to_batch = body_to['q_batch']  # shape [B]
                R_to_batch = np.matmul(
                    np.matmul(R_fr_batch, body_to['R_offset']),
                    rodrigues_batch(a=np.tile(a_to, (B, 1)), q_rad=q_to_batch)
                )  # shape [B, 3, 3]
            else:
                R_to_batch = np.matmul(R_fr_batch, body_to['R_offset'])  # shape [B, 3, 3]

            body_to['R_batch'] = R_to_batch
            
    def plot_graph(
            self,
            align           = 'horizontal',
            figsize         = (6,4),
            node_size       = 100,
            nose_font_size  = 6,
            node_colors     = None,
            title_font_size = 10,
            root_on_top     = True,
        ):
        """
        Plot the kinematic chain graph.
        Parameters:
            align: str, optional - Layout alignment ('horizontal' or 'vertical').
            figsize: tuple, optional - Figure size.
            node_size: int, optional - Size of the nodes.
            nose_font_size: int, optional - Font size for node labels.
            node_colors: list, optional - Colors of the nodes.
            title_font_size: int, optional - Font size of the title.
            root_on_top: bool, optional - Whether to place the root node on top.
        """
        n_body = self.get_n_body()
        tree = self.chain
        for layer, nodes in enumerate(nx.topological_generations(tree)):
            for node in nodes:
                tree.nodes[node]['layer'] = layer
        pos = nx.multipartite_layout(
            tree,
            align      = align,
            scale      = 1.0,
            subset_key ='layer',
        )
        # Invert the tree so that the root node comes on the top
        if root_on_top:
            pos = {node: (x, -y) for node, (x, y) in pos.items()} 
        # Plot nodes
        fig,ax = plt.subplots(figsize=figsize)
        if node_colors is None: # set colors
            node_colors = []
            for body_idx in range(n_body):
                a = self.get_body(body_idx)['a']
                if np.linalg.norm(a) < 1e-6:
                    node_color = (1,1,1,0.5)
                else:
                    node_color = [0,0,0,0.5]
                    node_color[np.argmax(a)] = 1
                    node_color = tuple(node_color)
                node_colors.append(node_color)
                
        nx.draw_networkx(
            tree,
            pos         = pos,
            ax          = ax,
            with_labels = True,
            node_size   = node_size,
            font_size   = nose_font_size,
            node_color  = node_colors,
            linewidths  = 1,
            edgecolors  = 'k'
        )
        ax.set_title('%s'%(tree.name),fontsize=title_font_size)
        fig.tight_layout()
        plt.show()

    def plot_chain_mujoco(
            self,
            env, # <= assumed to be instantiated from 'MuJoCoParserClass'
            plot_link        = True,
            r_link           = 0.01,
            rgba_link        = (0,0,1,0.25),
            root_body_name   = None,
            plot_body        = True,
            plot_body_name   = False,
            plot_body_axis   = True,
            axis_len         = 0.025,
            axis_width       = 0.0025,
            rate             = 1.0,
            plot_body_sphere = False,
            r_body           = 0.025,
            rgba_body        = (0,0,0,0.5),
            plot_rev_axis    = True,
            r_axis           = 0.01,
            h_axis           = 0.05,
            alpha_axis       = 0.5,
        ):
        """
        Plot the kinematic chain in a MuJoCo environment.
        Parameters:
            env: MuJoCo environment - Environment to plot.
            plot_link: bool, optional - Whether to plot links.
            r_link: float, optional - Radius of the links.
            rgba_link: tuple, optional - Color of the links (RGBA).
            root_body_name: str, optional - Name of the root body.
            plot_body: bool, optional - Whether to plot bodies.
            plot_body_name: bool, optional - Whether to display body names.
            plot_body_axis: bool, optional - Whether to plot body axes.
            axis_len: float, optional - Length of the axes.
            axis_width: float, optional - Width of the axes.
            rate: float, optional - Scaling factor.
            plot_body_sphere: bool, optional - Whether to plot bodies as spheres.
            r_body: float, optional - Radius of the body spheres.
            rgba_body: tuple, optional - Color of the bodies (RGBA).
            plot_rev_axis: bool, optional - Whether to plot revolute axes.
            r_axis: float, optional - Radius of the axes.
            h_axis: float, optional - Height of the axes.
            alpha_axis: float, optional - Transparency of the axes.
        """
        if root_body_name is None:
            root_body_idx = self.get_root_body_idx()
        else:
            root_body_idx = self.get_body_idx(body_name=root_body_name)
            
        # Plot link
        if plot_link:
            for idx,edge in enumerate(dfs_edges(self.chain,source=root_body_idx)):
                body_fr = self.get_body(edge[0])
                body_to = self.get_body(edge[1])
                env.plot_cylinder_fr2to(
                    p_fr = body_fr['p'],
                    p_to = body_to['p'],
                    r    = r_link,
                    rgba = rgba_link,
                )
                
        # Plot body
        if plot_body:
            subtree = nx.dfs_tree(self.chain,source=root_body_idx)
            for body_idx in list(subtree.nodes):
                body = self.get_body(body_idx)
                if plot_body_name:
                    body_name = body['name']
                else:
                    body_name = ''
                env.plot_T(
                    p           = body['p'],
                    R           = body['R'],
                    plot_axis   = plot_body_axis,
                    axis_len    = rate*axis_len,
                    axis_width  = rate*axis_width,
                    plot_sphere = plot_body_sphere,
                    sphere_r    = r_body,
                    sphere_rgba = rgba_body,
                    label       = body_name,
                )
                
        # Plot revolute axis
        if plot_rev_axis:
            subtree = nx.dfs_tree(self.chain,source=root_body_idx)
            for body_idx in list(subtree.nodes):
                body = self.get_body(body_idx)
                a = body['a']
                if np.linalg.norm(a) > 1e-6:
                    p,R = body['p'],body['R']
                    p2 = p + R@a*rate*h_axis
                    axis_color = [0,0,0,alpha_axis]
                    axis_color[np.argmax(a)] = 1
                    env.plot_arrow_fr2to(p_fr=p,p_to=p2,r=rate*r_axis,rgba=axis_color)

Initialize numpy chain

nc = NumpyChainClass(name=env.name)
nc.build_chain_from_mujoco_env(env=env)

Forward kinematics

nc.forward(root_body_name='pelvis')

Plot graph

nc.plot_graph(figsize=(6,4),node_size=100,nose_font_size=6)
print ("Done.")

Set pelvis position

env.forward()
p_pelvis = env.get_p_body(body_name='pelvis')
nc.set_p_body(body_name='pelvis',p=p_pelvis)

Batched FK using NumPy Chain

B = 10000 # batchsize
q0_batch = np.random.randn(B,env.n_rev_joint) # [B x 37]
env.tic()
nc.forward_batch(joint_names=env.rev_joint_names,
q_batch=q0_batch,root_body_name='pelvis')
esec_batch = env.toc()

Batched FK using MuJoCo (GT)

env.tic()
for b_idx in range(B):
q0 = q0_batch[b_idx,:]
env.forward(q=q0,joint_names=env.rev_joint_names)
esec_seq = env.toc()
print ("Done. esec_batch:[%.2fms] and esec_seq[%.2fms] for [%d] batched FK"%
(esec_batch1000,esec_seq1000,B))

Check batched FK

body_name_to_check = 'right_six_link'
p_batch_nc_check = nc.get_p_batch_body(body_name=body_name_to_check) # [B x 3]
p_errs = np.zeros(B)
for b_idx in range(B):
q0 = q0_batch[b_idx,:]
env.forward(q=q0,joint_names=env.rev_joint_names)
p_env_check = env.get_p_body(body_name=body_name_to_check)
p_nc_check = p_batch_nc_check[b_idx,:]
p_err = np.linalg.norm(p_env_check-p_nc_check)
# Append error
p_errs[b_idx] = p_err
# Print
p_err_th = 1e-8
if p_err > p_err_th:
color_err = 'green' if p_err < p_err_th else 'red'
print ("[%d/%d] p_gt:[%.2f,%.2f,%.2f] p_nc:[%.2f,%.2f,%.2f] p_err:[%s]"%
(b_idx,B,p_env_check[0],p_env_check[1],p_env_check[2],
p_nc_check[0],p_nc_check[1],p_nc_check[2],
colored('%.2e'%(p_err),color_err)))

Print results

print ("[%d] batched FK and the maximum error is:[%.3e]"%
(B,p_errs.max()))
print ("Done.")