From 22c2224deafbe8b0c404b62598717fd4651df273 Mon Sep 17 00:00:00 2001 From: sergeypdev Date: Thu, 20 Mar 2025 00:46:50 +0400 Subject: [PATCH] Tweak tyres, fix asymmetry in pacejka formula --- game/game.odin | 4 +- game/physics/pacejka.odin | 4 +- game/physics/simulation.odin | 5 +-- research/pacejka96.ipynb | 84 ++++++++++++++++++++++-------------- 4 files changed, 58 insertions(+), 39 deletions(-) diff --git a/game/game.odin b/game/game.odin index d92ab1a..70b3fa1 100644 --- a/game/game.odin +++ b/game/game.odin @@ -320,7 +320,7 @@ update_runtime_world :: proc(runtime_world: ^Runtime_World, dt: f32) { wheel_extent_x := f32(1.7) wheel_y := f32(-0.5) rest := f32(1) - natural_frequency := f32(0.3) + natural_frequency := f32(0.4) damping := f32(0.08) radius := f32(0.6) wheel_front_z := f32(3.05) @@ -393,7 +393,7 @@ update_runtime_world :: proc(runtime_world: ^Runtime_World, dt: f32) { front_wheels := turn_wheels back_wheels := drive_wheels - DRIVE_IMPULSE :: 2000 + DRIVE_IMPULSE :: 3000 BRAKE_IMPULSE :: 500 TURN_ANGLE :: -f32(30) * math.RAD_PER_DEG // 68% front, 32% rear diff --git a/game/physics/pacejka.odin b/game/physics/pacejka.odin index 364151a..e389d15 100644 --- a/game/physics/pacejka.odin +++ b/game/physics/pacejka.odin @@ -4,7 +4,7 @@ import "core:math" Pacejka96_Params :: [11]f32 -DEFAULT_PACEJKA96_PARAMS :: Pacejka96_Params{1.65, 1, 1750, 0, 229, 0.0, 0, 0, -12, 0, 0} +DEFAULT_PACEJKA96_PARAMS :: Pacejka96_Params{1.65, -200, 1900, 0, 229, 0.0, 0, 0, 0, 0, 0} // X is slip ratio percentage [-100, 100] or slip angle in degrees, where positive angle is turning left // Output is the friction coefficient @@ -12,7 +12,7 @@ pacejka_96 :: proc(b: Pacejka96_Params, x: f32, f_z: f32, s_v: f32 = 0) -> f32 { C := b[0] D := (b[1] * f_z + b[2]) * f_z B := ((b[3] * f_z * f_z + b[4] * f_z) * math.exp(-b[5] * f_z)) / (C * D) - E := -(1 - (b[6] * f_z * f_z + b[7] * f_z + b[8])) + E := (b[6] * f_z * f_z + b[7] * f_z + b[8]) s_h := b[9] * f_z + b[10] X := x + s_h diff --git a/game/physics/simulation.odin b/game/physics/simulation.odin index 337b442..81feba8 100644 --- a/game/physics/simulation.odin +++ b/game/physics/simulation.odin @@ -550,7 +550,6 @@ pgs_solve_suspension :: proc(sim_state: ^Sim_State, config: Solver_Config, dt: f apply_velocity_correction(body, incremental_impulse * dir, wheel_world_pos) } - body_right := body_local_to_world_vec(body, Vec3{1, 0, 0}) right := wheel_get_right_vec(body, v) // Positive means spinning forward @@ -638,7 +637,7 @@ pgs_solve_suspension :: proc(sim_state: ^Sim_State, config: Solver_Config, dt: f applied_impulse := new_total_impulse - v.lateral_impulse v.lateral_impulse = new_total_impulse - apply_velocity_correction(body, applied_impulse * body_right, v.hit_point) + apply_velocity_correction(body, applied_impulse * right, v.hit_point) } } else { v.lateral_impulse = 0 @@ -693,7 +692,7 @@ pgs_substep :: proc(sim_state: ^Sim_State, config: Solver_Config, dt: f32, inv_d p := body_local_to_world(body, s.rel_pos) hit_p := body_local_to_world(body, s.rel_pos + s.rel_dir * s.hit_t) forward := wheel_get_forward_vec(body, s) - right := body_local_to_world_vec(body, Vec3{1, 0, 0}) + right := wheel_get_right_vec(body, s) apply_velocity_correction( body, diff --git a/research/pacejka96.ipynb b/research/pacejka96.ipynb index c09928e..e581bce 100644 --- a/research/pacejka96.ipynb +++ b/research/pacejka96.ipynb @@ -2,51 +2,63 @@ "cells": [ { "cell_type": "code", - "execution_count": 94, + "execution_count": 102, "metadata": {}, "outputs": [], "source": [ - "from sympy import Symbol, sin, atan, exp\n", - "from sympy.plotting import plot\n" + "%matplotlib widget" ] }, { "cell_type": "code", - "execution_count": 95, + "execution_count": 103, "metadata": {}, "outputs": [], "source": [ - "def pacejka96(b, x, Fz, Sv, Sh):\n", + "from sympy import Symbol, sin, atan, exp, solve, diff, simplify,Eq\n", + "from sympy.plotting import plot, plot3d\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "b = [Symbol(f'b_{i}', positive=True, real=True) for i in range(11)]\n", + "Fz = Symbol('F_z', positive=True, real=True)\n", + "x = Symbol('x', real=True)\n", + "\n", + "def pacejka96():\n", " C = b[0]\n", " D = (b[1] * Fz + b[2]) * Fz\n", - " B=((b[3]*Fz^2+b[4]*Fz)*exp(-b[5]*Fz))/(C*D)\n", - " E = -(1 - (b[6] * Fz^2 +b[7] * Fz + b[8]))\n", + " B=((b[3]*Fz**2+b[4]*Fz)*exp(-b[5]*Fz))/(C*D)\n", + " E = b[6] * Fz**2 +b[7] * Fz + b[8]\n", " Sh=b[9]*Fz+b[10]\n", - " Sv=0\n", " \n", " X = x + Sh\n", " y = D * sin(C * atan(B * X - E * ( B * X - atan(B * X))))\n", - " Y = y + Sv\n", + " Y = y\n", " return Y" ] }, { "cell_type": "code", - "execution_count": 96, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Pacejka coefficients\n", - "b = [\n", - " 1.6,\n", - " 0,\n", - " 2500,\n", + "b_vals = [\n", + " 1.65,\n", + " -150,\n", + " 1750,\n", " 0,\n", " 229,\n", " 0.0,\n", " 0,\n", " 0,\n", - " -12,\n", + " 0,\n", " 0,\n", " 0\n", "]" @@ -54,24 +66,29 @@ }, { "cell_type": "code", - "execution_count": 97, + "execution_count": 106, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", - "text/plain": [ - "
" + "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, @@ -80,20 +97,23 @@ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 97, + "execution_count": 106, "metadata": {}, "output_type": "execute_result" } ], "source": [ + "%matplotlib widget\n", + "\n", "slip_ratio = Symbol('slip_ratio')\n", "slip_angle = Symbol('slip_angle')\n", "\n", - "plot(pacejka96(b, slip_ratio, 2, 0, 0) / 2000, (slip_ratio, -10, 20))\n", - "plot(pacejka96(b, slip_angle, 2, 0, 0) / 2000, (slip_angle, 0, 15))" + "slip_ratio_formula = pacejka96().subs({sym: val for sym, val in zip(b, b_vals)})\n", + "\n", + "plot(abs((slip_ratio_formula / (Fz * 1000)).subs({Fz: 2})), (x, -100, 100))" ] } ],