From f61fec141157dc45e8660d7c089e906ccd4d4dde Mon Sep 17 00:00:00 2001 From: Maximilian Stolzle Date: Wed, 16 Oct 2024 13:46:03 -0400 Subject: [PATCH 01/13] Start implementing operational space dynamics for planar pcs --- src/jsrm/symbolic_derivation/planar_pcs.py | 16 +- .../symbolic_expressions/planar_pcs_ns-1.dill | Bin 6739 -> 8069 bytes src/jsrm/systems/planar_pcs.py | 177 ++++++++++++++++-- 3 files changed, 172 insertions(+), 21 deletions(-) diff --git a/src/jsrm/symbolic_derivation/planar_pcs.py b/src/jsrm/symbolic_derivation/planar_pcs.py index 4a96d68..c931ae4 100644 --- a/src/jsrm/symbolic_derivation/planar_pcs.py +++ b/src/jsrm/symbolic_derivation/planar_pcs.py @@ -3,7 +3,7 @@ import sympy as sp from typing import Callable, Dict, Optional, Tuple, Union -from .symbolic_utils import compute_coriolis_matrix +from .symbolic_utils import compute_coriolis_matrix, compute_dAdt def symbolically_derive_planar_pcs_model( @@ -55,8 +55,8 @@ def symbolically_derive_planar_pcs_model( # matrix with symbolic expressions to derive the poses along each segment chi_sms = [] - # Jacobians (positional + orientation) in each segment as a function of the point coordinate s - J_sms = [] + # Jacobians (positional + orientation) in each segment as a function of the point coordinate s and its time derivative + J_sms, J_d_sms = [], [] # cross-sectional area of each segment A = sp.zeros(num_segments) # second area moment of inertia of each segment @@ -118,6 +118,10 @@ def symbolically_derive_planar_pcs_model( J = Jp.col_join(Jo) J_sms.append(J) + # compute the time derivative of the Jacobian + J_d = compute_dAdt(J, xi, xi_d) # time derivative of the end-effector Jacobian + J_d_sms.append(J_d) + # derivative of mass matrix with respect to the point coordinate s dB_ds = rho[i] * A[i] * Jp.T @ Jp + rho[i] * I[i] * Jo.T @ Jo if simplify_expressions: @@ -179,8 +183,10 @@ def symbolically_derive_planar_pcs_model( "chiee": chi_sms[-1].subs( s, l[-1] ), # expression for end-effector pose of shape (3, ) - "J_sms": J_sms, - "Jee": J_sms[-1].subs(s, l[-1]), + "J_sms": J_sms, # list of Jacobians (for each segment) of shape (3, num_dof) + "Jee": J_sms[-1].subs(s, l[-1]), # end-effector Jacobian of shape (3, num_dof) + "J_d_sms": J_d_sms, # list of time derivatives of Jacobians (for each segment) + "Jee_d": J_d_sms[-1].subs(s, l[-1]), # time derivative of end-effector Jacobian of shape (3, num_dof) "B": B, # mass matrix "C": C, # coriolis matrix "G": G, # gravity vector diff --git a/src/jsrm/symbolic_expressions/planar_pcs_ns-1.dill b/src/jsrm/symbolic_expressions/planar_pcs_ns-1.dill index 57a26ef72f816d9f3b3fd411bf5a16da81a3bbc8..9d68b6183816c1bea6a35d145bd942f64a0e5a85 100644 GIT binary patch literal 8069 zcmb_hU5H#)9p5`Mo0z1QbW{ikEfUyn5vR?z8O4-n(rl!2jZNEFXxTbDJA1Qd4)ev_ z8Fx|=Fi7J*9ECQwAXEgAnuk2-LlOF*KKP>BKv_h5&Vx@PA_@hq#{chsKJK|QcXl_$ zU1s)t{6ByHk8|$b@08wp?U6bDxt1)dBmKsp(TVHvl}?;sp*R#zBz|apgy*LUn4OJY7p57_ZD7zPI(9R;1Y+&O$>)Tl3VKh>Q<6&bM 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select_params_for_lambdify_fn(params: Dict[str, Array]) -> List[Array]: """ Select the parameters for lambdify Args: @@ -101,6 +101,27 @@ def select_params_for_lambdify(params: Dict[str, Array]) -> List[Array]: "jax", ) chi_lambda_sms.append(chi_lambda) + J_lambda_sms = [] + for J_exp in sym_exps["exps"]["J_sms"]: + J_lambda = sp.lambdify( + params_syms_cat + + sym_exps["state_syms"]["xi"] + + [sym_exps["state_syms"]["s"]], + J_exp, + "jax", + ) + J_lambda_sms.append(J_lambda) + J_d_lambda_sms = [] + for J_d_exp in sym_exps["exps"]["J_d_sms"]: + J_d_lambda = sp.lambdify( + params_syms_cat + + sym_exps["state_syms"]["xi"] + + sym_exps["state_syms"]["xi_d"] + + [sym_exps["state_syms"]["s"]], + J_d_exp, + "jax", + ) + J_d_lambda_sms.append(J_d_lambda) B_lambda = sp.lambdify( params_syms_cat + sym_exps["state_syms"]["xi"], sym_exps["exps"]["B"], "jax" @@ -153,6 +174,30 @@ def apply_eps_to_bend_strains(xi: Array, _eps: float) -> Array: return xi_epsed + def classify_segment(params: Dict[str, Array], s: Array) -> Tuple[Array, Array] : + """ + Classify the point along the robot to the corresponding segment + Args: + params: Dictionary of robot parameters + s: point coordinate along the robot in the interval [0, L]. + Returns: + segment_idx: index of the segment + s_segment: point coordinate along the segment in the interval [0, l_segment + """ + # cumsum of the segment lengths + l_cum = jnp.cumsum(params["l"]) + # add zero to the beginning of the array + l_cum_padded = jnp.concatenate([jnp.array([0.0]), l_cum], axis=0) + # determine in which segment the point is located + # use argmax to find the last index where the condition is true + segment_idx = ( + l_cum.shape[0] - 1 - jnp.argmax((s >= l_cum_padded[:-1])[::-1]).astype(int) + ) + # point coordinate along the segment in the interval [0, l_segment] + s_segment = s - l_cum_padded[segment_idx] + + return segment_idx, s_segment + @jit def forward_kinematics_fn( params: Dict[str, Array], q: Array, s: Array, eps: float = global_eps @@ -172,24 +217,14 @@ def forward_kinematics_fn( """ # map the configuration to the strains xi = xi_eq + B_xi @ q - # add a small number to the bending strain to avoid singularities xi_epsed = apply_eps_to_bend_strains(xi, eps) - # cumsum of the segment lengths - l_cum = jnp.cumsum(params["l"]) - # add zero to the beginning of the array - l_cum_padded = jnp.concatenate([jnp.array([0.0]), l_cum], axis=0) - # determine in which segment the point is located - # use argmax to find the last index where the condition is true - segment_idx = ( - l_cum.shape[0] - 1 - jnp.argmax((s >= l_cum_padded[:-1])[::-1]).astype(int) - ) - # point coordinate along the segment in the interval [0, l_segment] - s_segment = s - l_cum_padded[segment_idx] + # classify the point along the robot to the corresponding segment + segment_idx, s_segment = classify_segment(params, s) # convert the dictionary of parameters to a list, which we can pass to the lambda function - params_for_lambdify = select_params_for_lambdify(params) + params_for_lambdify = select_params_for_lambdify_fn(params) chi = lax.switch( segment_idx, chi_lambda_sms, *params_for_lambdify, *xi_epsed, s_segment @@ -197,6 +232,42 @@ def forward_kinematics_fn( return chi + @jit + def jacobian_fn( + params: Dict[str, Array], q: Array, s: Array, eps: float = global_eps + ) -> Array: + """ + Evaluate the forward kinematics the tip of the links + Args: + params: Dictionary of robot parameters + q: generalized coordinates of shape (n_q, ) + s: point coordinate along the rod in the interval [0, L]. + eps: small number to avoid singularities (e.g., division by zero) + Returns: + J: Jacobian matrix of shape (3, n_q) of the backbone point in Cartesian-space + Relates the configuration-space velocity q_d to the Cartesian-space velocity chi_d, + where chi_d = J @ q_d. Chi_d consists of [p_x_d, p_y_d, theta_d] + """ + # map the configuration to the strains + xi = xi_eq + B_xi @ q + # add a small number to the bending strain to avoid singularities + xi_epsed = apply_eps_to_bend_strains(xi, eps) + + # classify the point along the robot to the corresponding segment + segment_idx, s_segment = classify_segment(params, s) + + # convert the dictionary of parameters to a list, which we can pass to the lambda function + params_for_lambdify = select_params_for_lambdify_fn(params) + + J = lax.switch( + segment_idx, J_lambda_sms, *params_for_lambdify, *xi_epsed, s_segment + ).squeeze() + + # apply the strain basis to the Jacobian + J = J @ B_xi + + return J + @jit def dynamical_matrices_fn( params: Dict[str, Array], q: Array, q_d: Array, eps: float = 1e4 * global_eps @@ -239,7 +310,7 @@ def dynamical_matrices_fn( # dissipative matrix from the parameters D = params.get("D", jnp.zeros((n_xi, n_xi))) - params_for_lambdify = select_params_for_lambdify(params) + params_for_lambdify = select_params_for_lambdify_fn(params) B = B_xi.T @ B_lambda(*params_for_lambdify, *xi_epsed) @ B_xi C_xi = C_lambda(*params_for_lambdify, *xi_epsed, *xi_d) @@ -303,7 +374,7 @@ def potential_energy_fn(params: Dict[str, Array], q: Array, eps: float = 1e4 * g U_K = (xi - xi_eq).T @ K @ (xi - xi_eq) # evaluate K(xi) = K @ xi # gravitational potential energy - params_for_lambdify = select_params_for_lambdify(params) + params_for_lambdify = select_params_for_lambdify_fn(params) U_G = U_lambda(*params_for_lambdify, *xi_epsed) # total potential energy @@ -327,11 +398,85 @@ def energy_fn(params: Dict[str, Array], q: Array, q_d: Array) -> Array: return E + def operational_space_dynamical_matrices_fn( + params: Dict[str, Array], + q: Array, + q_d: Array, + s: Array, + B: Array, + C: Array, + eps: float = 1e4 * global_eps, + ) -> Tuple[Array, Array, Array, Array, Array]: + """ + Compute the dynamics in operational space. + The implementation is based on Chapter 7.8 of "Modelling, Planning and Control of Robotics" by + Siciliano, Sciavicco, Villani, Oriolo. + Args: + params: dictionary of parameters + q: generalized coordinates of shape (n_q,) + q_d: generalized velocities of shape (n_q,) + s: point coordinate along the robot in the interval [0, L]. + B: inertia matrix in the generalized coordinates of shape (n_q, n_q) + C: coriolis matrix derived with Christoffer symbols in the generalized coordinates of shape (n_q, n_q) + eps: small number to avoid singularities (e.g., division by zero) + Returns: + Lambda: inertia matrix in the operational space of shape (3, 3) + mu: matrix with corioli and centrifugal terms in the operational space of shape (3, 3) + J: Jacobian of the Cartesian pose with respect to the generalized coordinates of shape (3, n_q) + J: time-derivative of the Jacobian of the end-effector pose with respect to the generalized coordinates + of shape (3, n_q) + JB_pinv: Dynamically-consistent pseudo-inverse of the Jacobian. Allows the mapping of torques + from the generalized coordinates to the operational space: f = JB_pinv.T @ tau_q + Shape (n_q, 3) + """ + ## map the configuration to the strains + xi = xi_eq + B_xi @ q + xi_d = B_xi @ q_d + # add a small number to the bending strain to avoid singularities + xi_epsed = apply_eps_to_bend_strains(xi, eps) + + # classify the point along the robot to the corresponding segment + segment_idx, s_segment = classify_segment(params, s) + + # convert the dictionary of parameters to a list, which we can pass to the lambda function + params_for_lambdify = select_params_for_lambdify_fn(params) + + # Jacobian and its time-derivative + J = lax.switch( + segment_idx, J_lambda_sms, *params_for_lambdify, *xi_epsed, s_segment + ).squeeze() + J_d = lax.switch( + segment_idx, J_d_lambda_sms, *params_for_lambdify, *xi_epsed, *xi_d, s_segment + ).squeeze() + # apply the strain basis to the J and J_d + J = J @ B_xi + J_d = J_d @ B_xi + + # inverse of the inertia matrix in the configuration space + B_inv = jnp.linalg.inv(B) + + Lambda = jnp.linalg.inv( + J @ B_inv @ J.T + ) # inertia matrix in the operational space + mu = Lambda @ ( + J @ B_inv @ C - J_d + ) # coriolis and centrifugal matrix in the operational space + + JB_pinv = ( + B_inv @ J.T @ Lambda + ) # dynamically-consistent pseudo-inverse of the Jacobian + # apply TODO: remove + # JB_pinv = B_xi.T @ JB_pinv + + return Lambda, mu, J, J_d, JB_pinv + auxiliary_fns = { "apply_eps_to_bend_strains": apply_eps_to_bend_strains, + "jacobian_fn": jacobian_fn, "kinetic_energy_fn": kinetic_energy_fn, "potential_energy_fn": potential_energy_fn, "energy_fn": energy_fn, + "operational_space_dynamical_matrices_fn": operational_space_dynamical_matrices_fn, } return B_xi, forward_kinematics_fn, dynamical_matrices_fn, auxiliary_fns From 05904bdaa4a94352af9dc993d8fb1ec57bc928e8 Mon Sep 17 00:00:00 2001 From: Maximilian Stolzle Date: Wed, 16 Oct 2024 16:52:33 -0400 Subject: [PATCH 02/13] Fix sign of gravitational potential energy --- src/jsrm/symbolic_derivation/planar_hsa.py | 18 +++++++++--------- src/jsrm/symbolic_derivation/planar_pcs.py | 20 ++++++++++---------- src/jsrm/systems/planar_pcs.py | 11 +++++------ 3 files changed, 24 insertions(+), 25 deletions(-) diff --git a/src/jsrm/symbolic_derivation/planar_hsa.py b/src/jsrm/symbolic_derivation/planar_hsa.py index 2cfe74c..7feda0d 100644 --- a/src/jsrm/symbolic_derivation/planar_hsa.py +++ b/src/jsrm/symbolic_derivation/planar_hsa.py @@ -219,7 +219,7 @@ def symbolically_derive_planar_hsa_model( # inertia matrix B = sp.zeros(num_dof, num_dof) # potential energy - U = sp.Matrix([[0]]) + U_g = sp.Matrix([[0]]) # stiffness matrix Shat = sp.zeros(3 * num_segments, 3 * num_segments) # elastic vector @@ -299,11 +299,11 @@ def symbolically_derive_planar_hsa_model( B = B + Br_ij # derivative of the potential energy with respect to the point coordinate s - dUr_ds = sp.simplify(rhor[i, j] * Ar[i, j] * g.T @ pr) + dU_g_r_ds = sp.simplify(-rhor[i, j] * Ar[i, j] * g.T @ pr) # potential energy of the current segment - U_ij = sp.simplify(sp.integrate(dUr_ds, (s, 0, l[i]))) + U_g_ij = sp.simplify(sp.integrate(dU_g_r_ds, (s, 0, l[i]))) # add potential energy of segment to previous segments - U = U + U_ij + U_g = U_g + U_g_ij # strains in physical HSA rod pxir = _sym_beta_fn(vxi, roff[i, j]) @@ -466,8 +466,8 @@ def symbolically_derive_planar_hsa_model( Bp = sp.simplify(Bp) B = B + Bp # potential energy of the platform - Up = sp.simplify(mp * g.T @ pCoGp) - U = U + Up + U_g_p = sp.simplify(-mp * g.T @ pCoGp) + U_g = U_g + U_g_p # update the orientation for the next segment th_prev = th.subs(s, l[i]) @@ -507,8 +507,8 @@ def symbolically_derive_planar_hsa_model( Bpl = sp.simplify(Bpl) B = B + Bpl # add the gravitational potential energy of the payload - Upl = sp.simplify(mpl * g.T @ pCoGpl) - U = U + Upl + Upl = sp.simplify(- mpl * g.T @ pCoGpl) + U_g = U_g + Upl # simplify mass matrix if simplify: @@ -519,7 +519,7 @@ def symbolically_derive_planar_hsa_model( print("C =\n", C) # compute the gravity force vector - G = -U.jacobian(xi).transpose() + G = U_g.jacobian(xi).transpose() if simplify: G = sp.simplify(G) print("G =\n", G) diff --git a/src/jsrm/symbolic_derivation/planar_pcs.py b/src/jsrm/symbolic_derivation/planar_pcs.py index c931ae4..e3ecfc8 100644 --- a/src/jsrm/symbolic_derivation/planar_pcs.py +++ b/src/jsrm/symbolic_derivation/planar_pcs.py @@ -64,7 +64,7 @@ def symbolically_derive_planar_pcs_model( # inertia matrix B = sp.zeros(num_dof, num_dof) # potential energy - U = sp.Matrix([[0]]) + U_g = sp.Matrix([[0]]) # symbol for the point coordinate s = sp.symbols("s", real=True, nonnegative=True) @@ -134,15 +134,15 @@ def symbolically_derive_planar_pcs_model( B = B + B_i # derivative of the potential energy with respect to the point coordinate s - dU_ds = rho[i] * A[i] * g.T @ p + dU_g_ds = -rho[i] * A[i] * g.T @ p if simplify_expressions: - dU_ds = sp.simplify(dU_ds) - # potential energy of the current segment - U_i = sp.integrate(dU_ds, (s, 0, l[i])) + dU_g_ds = sp.simplify(dU_g_ds) + # gravitational potential energy of the current segment + U_gi = sp.integrate(dU_g_ds, (s, 0, l[i])) if simplify_expressions: - U_i = sp.simplify(U_i) + U_gi = sp.simplify(U_gi) # add potential energy of segment to previous segments - U = U + U_i + U_g = U_g + U_gi # update the orientation for the next segment th_prev = th.subs(s, l[i]) @@ -155,11 +155,11 @@ def symbolically_derive_planar_pcs_model( B = sp.simplify(B) print("B =\n", B) - C = compute_coriolis_matrix(B, xi, xi_d) + C = compute_coriolis_matrix(B, xi, xi_d, simplify=simplify_expressions) print("C =\n", C) # compute the gravity force vector - G = -U.jacobian(xi).transpose() + G = U_g.jacobian(xi).transpose() if simplify_expressions: G = sp.simplify(G) print("G =\n", G) @@ -190,7 +190,7 @@ def symbolically_derive_planar_pcs_model( "B": B, # mass matrix "C": C, # coriolis matrix "G": G, # gravity vector - "U": U, # gravitational potential energy + "U_g": U_g, # gravitational potential energy }, } diff --git a/src/jsrm/systems/planar_pcs.py b/src/jsrm/systems/planar_pcs.py index bad4a48..9b4635f 100644 --- a/src/jsrm/systems/planar_pcs.py +++ b/src/jsrm/systems/planar_pcs.py @@ -132,8 +132,8 @@ def select_params_for_lambdify_fn(params: Dict[str, Array]) -> List[Array]: G_lambda = sp.lambdify( params_syms_cat + sym_exps["state_syms"]["xi"], sym_exps["exps"]["G"], "jax" ) - U_lambda = sp.lambdify( - params_syms_cat + sym_exps["state_syms"]["xi"], sym_exps["exps"]["U"], "jax" + U_g_lambda = sp.lambdify( + params_syms_cat + sym_exps["state_syms"]["xi"], sym_exps["exps"]["U_g"], "jax" ) compute_stiffness_matrix_for_all_segments_fn = vmap( @@ -299,10 +299,9 @@ def dynamical_matrices_fn( Ib = A**2 / (4 * jnp.pi) # elastic and shear modulus - E, G = params["E"], params["G"] - + elastic_modulus, shear_modulus = params["E"], params["G"] # stiffness matrix of shape (num_segments, 3, 3) - S = compute_stiffness_matrix_for_all_segments_fn(A, Ib, E, G) + S = compute_stiffness_matrix_for_all_segments_fn(A, Ib, elastic_modulus, shear_modulus) # we define the elastic matrix of shape (n_xi, n_xi) as K(xi) = K @ xi where K is equal to K = blk_diag(S) @@ -375,7 +374,7 @@ def potential_energy_fn(params: Dict[str, Array], q: Array, eps: float = 1e4 * g # gravitational potential energy params_for_lambdify = select_params_for_lambdify_fn(params) - U_G = U_lambda(*params_for_lambdify, *xi_epsed) + U_G = U_g_lambda(*params_for_lambdify, *xi_epsed) # total potential energy U = (U_G + U_K).squeeze() From f9b2543b0911490f5afd9fe43c4573a67498fe81 Mon Sep 17 00:00:00 2001 From: Maximilian Stolzle Date: Wed, 16 Oct 2024 16:52:51 -0400 Subject: [PATCH 03/13] Add more plotting to the planar pcs simulation example --- examples/simulate_planar_pcs.py | 23 ++++++++++++++++++++++- 1 file changed, 22 insertions(+), 1 deletion(-) diff --git a/examples/simulate_planar_pcs.py b/examples/simulate_planar_pcs.py index ba84afb..44fc4e0 100644 --- a/examples/simulate_planar_pcs.py +++ b/examples/simulate_planar_pcs.py @@ -43,7 +43,7 @@ strain_selector = jnp.array([True, False, False]) # define initial configuration -q0 = jnp.array([10 * jnp.pi]) +q0 = jnp.array([5 * jnp.pi]) # number of generalized coordinates n_q = q0.shape[0] @@ -142,6 +142,27 @@ def draw_robot( # the evolution of the generalized velocities q_d_ts = sol.ys[:, n_q:] + # evaluate the forward kinematics along the trajectory + chi_ee_ts = vmap(forward_kinematics_fn, in_axes=(None, 0, None))(params, q_ts, jnp.array([jnp.sum(params["l"])])) + # plot the end-effector position along the trajectory + plt.figure() + plt.plot(chi_ee_ts[0, :], chi_ee_ts[1, :]) + plt.axis("equal") + plt.grid(True) + plt.xlabel("x [m]") + plt.ylabel("y [m]") + plt.show() + # plot end-effector position vs time + plt.figure() + plt.plot(video_ts, chi_ee_ts[:, 0], label="x") + plt.plot(video_ts, chi_ee_ts[:, 1], label="y") + plt.xlabel("Time [s]") + plt.ylabel("Position [m]") + plt.legend() + plt.grid(True) + plt.box(True) + plt.show() + # plot the energy along the trajectory kinetic_energy_fn_vmapped = vmap(partial(auxiliary_fns["kinetic_energy_fn"], params)) potential_energy_fn_vmapped = vmap(partial(auxiliary_fns["potential_energy_fn"], params)) From ced3f11f6c4c384aa772d9f6fbf6ffda8d26142a Mon Sep 17 00:00:00 2001 From: Maximilian Stolzle Date: Wed, 16 Oct 2024 17:38:13 -0400 Subject: [PATCH 04/13] Improve labels for simulation data analysis plots --- examples/simulate_planar_pcs.py | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/examples/simulate_planar_pcs.py b/examples/simulate_planar_pcs.py index 44fc4e0..4db4176 100644 --- a/examples/simulate_planar_pcs.py +++ b/examples/simulate_planar_pcs.py @@ -149,15 +149,15 @@ def draw_robot( plt.plot(chi_ee_ts[0, :], chi_ee_ts[1, :]) plt.axis("equal") plt.grid(True) - plt.xlabel("x [m]") - plt.ylabel("y [m]") + plt.xlabel("End-effector x [m]") + plt.ylabel("End-effector y [m]") plt.show() # plot end-effector position vs time plt.figure() plt.plot(video_ts, chi_ee_ts[:, 0], label="x") plt.plot(video_ts, chi_ee_ts[:, 1], label="y") plt.xlabel("Time [s]") - plt.ylabel("Position [m]") + plt.ylabel("End-effector Position [m]") plt.legend() plt.grid(True) plt.box(True) From a57b2c893776460e3cb0c5865c2044e611bffeb7 Mon Sep 17 00:00:00 2001 From: Maximilian Stolzle Date: Wed, 16 Oct 2024 17:38:35 -0400 Subject: [PATCH 05/13] Do not simplify symbolic expressions if we are deriving dynamics for more than 2 segments --- examples/derive_planar_pcs.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/examples/derive_planar_pcs.py b/examples/derive_planar_pcs.py index 8462062..0206a74 100644 --- a/examples/derive_planar_pcs.py +++ b/examples/derive_planar_pcs.py @@ -12,5 +12,5 @@ / f"planar_pcs_ns-{NUM_SEGMENTS}.dill" ) symbolically_derive_planar_pcs_model( - num_segments=NUM_SEGMENTS, filepath=sym_exp_filepath, simplify_expressions=True + num_segments=NUM_SEGMENTS, filepath=sym_exp_filepath, simplify_expressions=True if NUM_SEGMENTS < 3 else False ) From ae2032e6b27a4624a5393d3a34faea5425f28d30 Mon Sep 17 00:00:00 2001 From: Maximilian Stolzle Date: Wed, 16 Oct 2024 18:22:19 -0400 Subject: [PATCH 06/13] Add more symbolic expressions for planar pcs --- .../symbolic_expressions/planar_pcs_ns-1.dill | Bin 8069 -> 8068 bytes .../symbolic_expressions/planar_pcs_ns-2.dill | Bin 70962 -> 75819 bytes .../symbolic_expressions/planar_pcs_ns-3.dill | Bin 406278 -> 819749 bytes .../symbolic_expressions/planar_pcs_ns-4.dill | Bin 0 -> 3292575 bytes 4 files changed, 0 insertions(+), 0 deletions(-) create mode 100644 src/jsrm/symbolic_expressions/planar_pcs_ns-4.dill diff --git a/src/jsrm/symbolic_expressions/planar_pcs_ns-1.dill b/src/jsrm/symbolic_expressions/planar_pcs_ns-1.dill index 9d68b6183816c1bea6a35d145bd942f64a0e5a85..9118c75ec1f8f7e596640975ac0089007aa7e4c1 100644 GIT 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def operational_space_dynamical_matrices_fn( J @ B_inv @ J.T ) # inertia matrix in the operational space mu = Lambda @ ( - J @ B_inv @ C - J_d + J @ B_inv @ C - J_d ) # coriolis and centrifugal matrix in the operational space JB_pinv = ( - B_inv @ J.T @ Lambda + B_inv @ J.T @ Lambda ) # dynamically-consistent pseudo-inverse of the Jacobian - # apply TODO: remove - # JB_pinv = B_xi.T @ JB_pinv return Lambda, mu, J, J_d, JB_pinv From 5a0a5f15ecb08214444754af5c2e8f94f1fb7bc4 Mon Sep 17 00:00:00 2001 From: Maximilian Stolzle Date: Wed, 16 Oct 2024 18:59:58 -0400 Subject: [PATCH 08/13] Add symbolic expression for 5 segments --- .../symbolic_expressions/planar_pcs_ns-5.dill | Bin 0 -> 12853390 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 src/jsrm/symbolic_expressions/planar_pcs_ns-5.dill diff --git a/src/jsrm/symbolic_expressions/planar_pcs_ns-5.dill b/src/jsrm/symbolic_expressions/planar_pcs_ns-5.dill new file mode 100644 index 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