| """Bounded variants of two held-out test plants. |
| |
| cartpole_b cart-pole with the pole-balancing loop PLUS a weak, slow cart-centering loop |
| (a balancing controller on a finite track), so the cart position stays bounded |
| two_link_arm_b two-link arm with an elbow torsion spring (rest pose: straight elbow), so the |
| second link swings but cannot spin full revolutions (not part of the benchmark |
| episodes; kept for completeness) |
| |
| Same contract as systems.py. The existing CartPole / TwoLinkArm classes are not modified; these |
| subclasses only add terms. |
| """ |
|
|
| from __future__ import annotations |
|
|
| import torch |
|
|
| from .systems import CartPole, TwoLinkArm, register |
|
|
|
|
| @register("cartpole_b") |
| class CartPoleBounded(CartPole): |
| """CartPole (same physics, same partial model) with cart feedback added to the stabilising loop. |
| |
| F = f_scale (u - K x), K = (k_x, k_v, k_th, k_om): the pole gains are the original K_BAL; |
| k_x = -0.8, k_v = -0.6 (input units per m, per m/s) add a slow centering loop. Linearised closed |
| loop (with the saturating actuator's back-EMF): pole pair -7.85 +- 0.75j (tau 0.13 s), centering |
| pair -0.345 +- 1.07j (tau 2.9 s, zeta 0.31); static gain x_ss / u = -1.25 m per unit command, so |
| the protocol box |u| <= 1 keeps the cart within a gym-like +-2.4 m track. The negative signs are |
| the non-minimum-phase cart-pole structure (to move the cart one way, the base must first lean |
| the pole that way). f_known (the modeller's model) uses the same K: the controller is known; |
| the UNMODELLED large-angle terms are exactly those of CartPole. |
| """ |
| K_BAL = (-0.8, -0.6, -9.889688, -2.181384) |
| UNMODELLED = CartPole.UNMODELLED |
|
|
|
|
| @register("two_link_arm_b") |
| class TwoLinkArmBounded(TwoLinkArm): |
| """TwoLinkArm (same physics, same partial model) plus an elbow torsion spring tau_2 = -k_e q2. |
| |
| k_e = m2 g lc2 (= 4.905 N m / rad at nominal parameters): the spring is as stiff as link 2's |
| own gravity stiffness, so the static gravity sag of the elbow is at most 1 rad and the second |
| link swings but cannot wind up. Elbow natural frequency sqrt(k_e / (m2 lc2^2 + I2)) = 3.8 rad/s, |
| close to the shoulder pendulum (~3 rad/s): both links stay excited. A generalised force on joint 2 |
| enters through M(q)^-1 like the input torque on joint 1. k_e is tied to (m2, g, lc2), so it |
| follows the 30 % mismatch of those parameters (a physical spring sized for the link). The spring |
| is part of the known model; UNMODELLED stays the Coriolis / centrifugal terms of TwoLinkArm. |
| """ |
| UNMODELLED = TwoLinkArm.UNMODELLED |
| KE_FACTOR = 1.0 |
|
|
| def _spring_acc(self, x): |
| q2 = x[:, 1] |
| a = self.m1 * self.lc1 ** 2 + self.I1 + self.m2 * (self.l1 ** 2 + self.lc2 ** 2) + self.I2 |
| b = self.m2 * self.l1 * self.lc2 |
| d = self.m2 * self.lc2 ** 2 + self.I2 |
| c2 = torch.cos(q2) |
| m11, m12, m22 = a + 2 * b * c2, d + b * c2, d + 0 * c2 |
| det = m11 * m22 - m12 ** 2 |
| t2 = -self.KE_FACTOR * (self.m2 * self.g * self.lc2) * q2 |
| z = 0 * q2 |
| return torch.stack([z, z, -m12 * t2 / det, m11 * t2 / det], 1) |
|
|
| def f(self, x, u): |
| return super().f(x, u) + self._spring_acc(x) |
|
|
| def f_known(self, x, u): |
| return super().f_known(x, u) + self._spring_acc(x) |
|
|
