Chapter 13: Walking a Quadruped

Sample code

• Directory: docs/os-on-arduino/code/13_quadruped

uv run pio run -d 13_quadruped -t upload
uv run pio device monitor -b 115200

Source code

The sketch for this chapter. Click a file name to expand. The code is mirrored automatically from the manuscript repository, so what you see here is always current.

src/main.cpp — 203 lines

Open on GitHub

// 第13章 四脚ロボット — 50 Hz の制御ループ
//
//   iktest        FK/IK の往復テスト (脚は動かない)
//   stand         home 姿勢へ 2 秒かけて立ち上がり、保持する
//   trot          naive 歩行 (本文 13.5)
//   rl <vx> <wz>  学習済みポリシーで歩く (本文 13.6, 13.7)
//   drive <vx> <wz>
//                 rl と同じだが、300 ms 途切れると home 保持に戻る。
//                 PC のキーボード操作 (host/quad_host.py serial) が送り続ける
//   stop          ポリシーを切り離して home 姿勢を保持。IMU を使う方策では
//                 ポリシーを速度 0 で回し続け、押されても IMU を見て踏ん張る
//   zero          全関節を 0 度 (脚をまっすぐ) へ移して保持。吊るして使う
//   free          トルクを切る
//   raw           (RCB-4 版だけ) 関節ごとのサーボ番号とパルスを出す。校正に使う
//   imu           (IMU を使う方策だけ) 胴体座標の角速度と重力の向き、関節の目標角を出す
//
// 安全: サーボの電源はバッテリから取ること。最初の trot と rl は必ず機体を
// 吊るすか支えた状態で。
#include <Arduino.h>
#include <math.h>
#include <stdlib.h>
#include <string.h>

#include "leg_ik.h"
#include "servo_bus.h"
#include "quad_calib.h"
#include "quad_control.h"
#include "quad_imu.h"

#define NJ           QUAD_NUM_JOINTS
#define CONTROL_US   ((unsigned long)(QUAD_CONTROL_DT * 1e6f))

extern void gait_step(float dt, float *q_out);
extern void gait_reset(void);

enum Mode { MODE_FREE, MODE_HOLD, MODE_TROT, MODE_RL };

static Mode          g_mode = MODE_HOLD;
static quad_state_t  g_policy;
static float         g_q[NJ], g_q_prev[NJ], g_qd[NJ], g_target[NJ];
static float         g_cmd[3] = {0.0f, 0.0f, 0.0f};
static unsigned long g_step = 0, g_skipped = 0, g_read_fail = 0;
static unsigned long g_last_read_us = 0;
#if QUAD_USES_IMU
// 方策が IMU を観測に使うときだけ読む。IMU が無い (起動時に見つからない・校正に
// 失敗した) ときと読めなかった周期は、水平に止まっている値を渡して歩かせる。
// そのときは傾いても方策には伝わらないので、毎秒の行に imu=level と出す。
static quad_imu_t    g_imu;
static bool          g_imu_ok = false;
static unsigned long g_imu_fail = 0;
#endif
static float         g_hold_from[NJ];
static const float  *g_hold_goal = QUAD_DEFAULT_JOINT_POS;
static int           g_hold_k = 0;

// zero で向かう姿勢。サーボの 0 点 (2048) を合わせた、脚がまっすぐの姿勢。
static const float   ZERO_POSE[NJ] = {0};

// drive はこの間隔より長く途切れたら止まる。PC 側が固まったりケーブルが
// 抜けたりしても、最後の速度で歩き続けないように。
#define DRIVE_TIMEOUT_MS 300UL
static bool          g_drive_armed = false;
static unsigned long g_last_drive_ms = 0;

static void begin_hold(const float *goal)
{
    memcpy(g_hold_from, g_target, sizeof(g_hold_from));
    g_hold_goal = goal;
    g_hold_k = 0;
}

// 停止はポリシーの整定に任せてはいけない。速度 0 を指令してもネットは動き続け、
// 実機ではその場で足踏みを続けることがある。ここはポリシーを迂回して、関節目標を
// home (または 0 度) へ直接歩かせる。
static void hold_target(float *out)
{
    const int steps = 100;                       // 2 秒
    float a = (g_hold_k >= steps) ? 1.0f : (float)g_hold_k / steps;
    for (int i = 0; i < NJ; ++i)
        out[i] = g_hold_from[i] + a * (g_hold_goal[i] - g_hold_from[i]);
    if (g_hold_k < steps) g_hold_k++;
}

// rl と drive の共通部分。歩いている最中なら速度だけを差し替え、ポリシーの
// 内部状態 (直前の行動と歩容の位相) は初期化しない。キーを押すたびに初期化
// すると、そのたびに歩容が頭から始まってつまずく。
// 歩き始めたときは true を返す。
static bool set_walk_command(const char *args, const __FlashStringHelper *name)
{
    // sscanf の %f は使わない。Arduino の newlib-nano は -u _scanf_float を
    // リンクしないと浮動小数を読まず、黙って 0 のまま返す。実機で
    // "rl 0.15 0" が vx=0.00 になり、ポリシーは速度 0 で回り続けた。
    // strtof はリンク指定に関係なく読める。
    char *rest;
    float vx = strtof(args, &rest);
    float wz = strtof(rest, NULL);
    g_cmd[0] = vx; g_cmd[1] = 0.0f; g_cmd[2] = wz;
    if (g_mode != MODE_RL) {
        servo_bus_torque(true);
        quad_init(&g_policy);
        g_mode = MODE_RL;
        Serial.print(F("mode=rl vx=")); Serial.print(vx, 2);
        Serial.print(F(" wz=")); Serial.print(wz, 2);
        Serial.print(F(" (")); Serial.print(name); Serial.println(')');
        return true;
    }
    return false;
}

static void shell(char c)
{
    static char buf[32];
    static int len = 0;
    if (c != '\r' && c != '\n') {
        if (len < 31) buf[len++] = c;
        return;
    }
    buf[len] = '\0';
    int n = len;
    len = 0;
    if (n == 0) return;

    if (!strcmp(buf, "iktest")) {
        test_ik_roundtrip();
#if QUAD_USES_IMU
    } else if (!strcmp(buf, "stop") && g_imu_ok) {
        // 歩いた後の停止も IMU のフィードバックを切らない。速度 0 の指令は
        // 位相のしきい値 (QUAD_PHASE_CMD_MIN) を下回るので、ポリシーは足踏みを
        // やめて立つ。歩行中なら内部状態はそのままで、指令だけを 0 にする。
        // 見張りは外すので、PC が送るのをやめても立ったまま踏ん張り続ける。
        g_drive_armed = false;
        g_cmd[0] = g_cmd[1] = g_cmd[2] = 0.0f;
        if (g_mode != MODE_RL) {
            servo_bus_torque(true);
            quad_init(&g_policy);
            g_mode = MODE_RL;
        }
        Serial.println(F("mode=balance (IMU で姿勢を保つ。固定するなら stand)"));
#endif
    } else if (!strcmp(buf, "stand") || !strcmp(buf, "stop")) {
        g_drive_armed = false;
        servo_bus_torque(true);
        begin_hold(QUAD_DEFAULT_JOINT_POS);
        g_mode = MODE_HOLD;
        Serial.println(F("mode=hold"));
    } else if (!strcmp(buf, "zero")) {
        g_drive_armed = false;
        servo_bus_torque(true);
        begin_hold(ZERO_POSE);
        g_mode = MODE_HOLD;
        Serial.println(F("mode=zero"));
    } else if (!strcmp(buf, "trot")) {
        g_drive_armed = false;
        servo_bus_torque(true);
        gait_reset();
        g_mode = MODE_TROT;
        Serial.println(F("mode=trot"));
    } else if (!strncmp(buf, "drive", 5)) {
        // 送り続けられる前提なので、歩き始めた 1 回だけ返事をする。
        set_walk_command(buf + 5, F("drive"));
        g_drive_armed = true;
        g_last_drive_ms = millis();
    } else if (!strncmp(buf, "rl", 2)) {
        // 手で打つ前提なので見張りは掛けない。
        g_drive_armed = false;
        if (!set_walk_command(buf + 2, F("rl"))) {
            Serial.print(F("cmd vx=")); Serial.print(g_cmd[0], 2);
            Serial.print(F(" wz=")); Serial.println(g_cmd[2], 2);
        }
#if QUAD_USES_IMU
    } else if (!strcmp(buf, "imu")) {
        if (!g_imu_ok) Serial.print(F("(IMU 無し。水平の値を渡している) "));
        quad_imu_print(&g_imu);
        // IMU が方策に届いているかは、balance 中に傾けてこの値が変わるかで見る。
        Serial.print(F("target rad:"));
        for (int i = 0; i < NJ; ++i) {
            Serial.print(' ');
            Serial.print(g_target[i], 3);
        }
        Serial.println();
#endif
#ifdef QUAD_SERVO_RCB4
    } else if (!strcmp(buf, "raw")) {
        servo_bus_print_raw();
#endif
    } else if (!strcmp(buf, "free")) {
        g_drive_armed = false;
        servo_bus_torque(false);
        g_mode = MODE_FREE;
        Serial.println(F("mode=free"));
    } else {
        Serial.print(F("unknown: ")); Serial.println(buf);
    }
}

void setup()
{
    Serial.begin(115200);
    servo_bus_init();

    int found = servo_bus_ping_all();
    Serial.print(F("サーボ応答: ")); Serial.print(found);
    Serial.print(F(" / ")); Serial.println(NJ);

#ifdef QUAD_SERVO_RCB4
    // RCB-4 には速度上限のレジスタが無い。速度は書き込みごとの補間フレーム数で決まる。
    servo_bus_apply_limits();
    Serial.println(F("速度設定: RCB-4 には無い (補間 1 フレームで送る)"));
#else
    // 速度レジスタは SRAM にあるので電源のたびに出荷値へ戻る。何も報告されず、
    // ロボットが遅くなるだけなので、開いたら必ず書く (補遺 13.9.1)。
    int limits = servo_bus_apply_limits();
    Serial.print(F("速度設定: ")); Serial.print(limits);
    Serial.print(F(" / ")); Serial.print(NJ * 2);
    Serial.println(limits == NJ * 2 ? F(" 適用") : F(" !! 一部失敗 (遅く歩きます)"));
#endif

#if QUAD_USES_IMU
    // ジャイロのゼロ点を取るので、トルクを入れる (脚が動く) 前に、静止した状態で。
    Serial.println(F("IMU: 起動中。約 10 秒、ロボットを動かさないこと"));
    quad_imu_level(&g_imu);
    if (!quad_imu_begin()) {
        Serial.println(F("!! IMU (QMI8658, 0x6B) が見つかりません。Qwiic の配線を確認"));
    } else if (!quad_imu_calibrate(1000)) {
        Serial.println(F("!! IMU の校正に失敗 (動いていた?)。静止させて再起動"));
    } else {
        g_imu_ok = true;
        quad_imu_update(QUAD_CONTROL_DT, &g_imu);
        Serial.print(F("IMU: "));
        quad_imu_print(&g_imu);
    }
    if (!g_imu_ok)
        Serial.println(F("!! IMU 無しで動かす: 方策には水平に止まっている値を渡す。"
                         "傾いても押されても方策には伝わらない"));
#endif

    if (!servo_bus_read(g_q)) Serial.println(F("!! 起動時の関節読み取りに失敗"));
    for (int i = 0; i < NJ; ++i) {
        g_q_prev[i] = g_q[i];
        g_qd[i] = 0.0f;
        g_target[i] = g_q[i];
    }
    quad_init(&g_policy);
    servo_bus_torque(true);
    begin_hold(QUAD_DEFAULT_JOINT_POS);

    // home の値はコメントではなくこの出力が正。立ち高さを変えて再学習すると
    // 変わるので、脚の格好はここに出る数字と突き合わせること (補遺 13.8.1)。
    Serial.print(F("home rad:"));
    for (int i = 0; i < NJ; ++i) {
        Serial.print(' ');
        Serial.print(QUAD_DEFAULT_JOINT_POS[i], 4);
    }
    Serial.println();
    Serial.println(F("commands: iktest / stand / trot / rl <vx> <wz> / drive <vx> <wz> / stop / zero / free"));
#if QUAD_USES_IMU
    Serial.println(F("          imu"));
#endif
}

void loop()
{
    static unsigned long next_us = 0;
    static unsigned long report_us = 0;
    static unsigned long loop_sum = 0, loop_max = 0, loop_n = 0, late_n = 0;

    while (Serial.available()) shell((char)Serial.read());

    if (g_drive_armed && g_mode == MODE_RL &&
        millis() - g_last_drive_ms > DRIVE_TIMEOUT_MS) {
        g_drive_armed = false;
        begin_hold(QUAD_DEFAULT_JOINT_POS);
        g_mode = MODE_HOLD;
        Serial.println(F("mode=hold (drive が途切れた)"));
    }

    if (next_us == 0) next_us = micros();
    if ((long)(micros() - next_us) < 0) return;
    unsigned long t0 = micros();

    if (g_mode == MODE_FREE) {
        next_us = micros() + CONTROL_US;
        return;
    }

    if (!servo_bus_read(g_q)) {
        g_read_fail++;
    } else {
        // 公称周期ではなく実経過時間で割る。周期が乱れているときこそ関節速度が
        // 効くのに、そこで一番大きな誤差が乗る (本文 13.4.5)。
        unsigned long now = micros();
        float dt = (g_last_read_us == 0) ? QUAD_CONTROL_DT
                                         : (float)(now - g_last_read_us) * 1e-6f;
        g_last_read_us = now;
        for (int i = 0; i < NJ; ++i) {
            g_qd[i] = 0.6f * g_qd[i] + 0.4f * ((g_q[i] - g_q_prev[i]) / dt);
            g_q_prev[i] = g_q[i];
        }
#if QUAD_USES_IMU
        // 重力の向きのフィルタは止めずに回し続ける (歩き出した瞬間に古い値を使わない)。
        if (g_imu_ok && !quad_imu_update(dt, &g_imu)) {
            g_imu_fail++;
            quad_imu_level(&g_imu);
        }
        const quad_imu_t *imu = &g_imu;
#else
        const quad_imu_t *imu = NULL;
#endif

        if (g_mode == MODE_HOLD)      hold_target(g_target);
        else if (g_mode == MODE_TROT) gait_step(QUAD_CONTROL_DT, g_target);
        else                          quad_step(&g_policy, g_q, g_qd, g_cmd,
                                                imu, (long)g_step, g_target, NULL);
        servo_bus_write(g_target);
    }
    g_step++;

    unsigned long spent = micros() - t0;
    loop_sum += spent; loop_n++;
    if (spent > loop_max) loop_max = spent;
    if (spent > CONTROL_US) late_n++;

    if (micros() - report_us > 1000000UL) {
        report_us = micros();
        Serial.print(F("loop avg ")); Serial.print(loop_n ? loop_sum / loop_n : 0);
        Serial.print(F(" us  max ")); Serial.print(loop_max);
        Serial.print(F(" us  late ")); Serial.print(late_n);
        Serial.print('/'); Serial.print(loop_n);
        Serial.print(F("  skipped ")); Serial.print(g_skipped);
        Serial.print(F("  read_fail ")); Serial.print(g_read_fail);
#if QUAD_USES_IMU
        Serial.print(F("  imu_fail ")); Serial.print(g_imu_fail);
        if (!g_imu_ok) Serial.print(F("  imu=level"));
#endif
#ifdef QUAD_SERVO_RCB4
        Serial.print(F("  write_fail ")); Serial.print(servo_bus_write_fail());
#endif
        Serial.println();
        loop_sum = loop_n = loop_max = late_n = 0;
    }

    next_us += CONTROL_US;
    long behind = (long)(micros() - next_us);
    if (behind > 0) {
        // 落とした周期を連続実行しても時間は戻らず、歩容クロックだけが遅れる。
        // 歩容の位相は step_i * dt で作られているので、遅れを後から詰めようと
        // すると位相が実時間から離れていく。落とした分は捨てて、step カウンタを
        // 進めて実時間に合わせ直す (本文 13.4.4)。
        long lost = behind / (long)CONTROL_US + 1;
        g_step += lost;
        g_skipped += lost;
        next_us += (unsigned long)lost * CONTROL_US;
    }
}

include/arduino_quad_policy.h — 81 lines

Open on GitHub

// GENERATED by scripts/export_quad_policy.py -- do not edit.
// export env=ArduinoQuad-Robust  ckpt=model_3998.pt
// trained in run=2026-09-23_01-24-04_gait_best_robust  robustified=True
// verified against the PyTorch actor: max abs diff 2.384e-06
//
// Observation layout (float, in this order; each term keeps its own
// history, oldest step first):
//   [  0..  9) command      3 x 3
//   [  9.. 15) phase        3 x 2
//   [ 15.. 39) joint_pos    3 x 8
//   [ 39.. 63) joint_vel    3 x 8
//   [ 63.. 87) actions      3 x 8
//
// Joint order for the 8 outputs (and for joint_pos/joint_vel):
//   FL_hip_joint, FL_knee_joint, RL_hip_joint, RL_knee_joint, RR_hip_joint, RR_knee_joint, FR_hip_joint, FR_knee_joint
// Servo target = default_joint_pos + action_scale * action.
// Control period 0.0200 s, gait period 0.320 s.
#pragma once
#include <math.h>

#define QUAD_OBS_DIM 87
#define QUAD_ACT_DIM 8
#define QUAD_HISTORY 3
#define QUAD_CONTROL_DT 0.020000f
#define QUAD_GAIT_PERIOD 0.320000f
#define QUAD_PHASE_CMD_MIN 0.020000f
// Observation terms this policy needs, and where each one starts.
// quad_control.h switches on these: a policy trained with an IMU and
// firmware built without one is a compile error, not a wrong vector.
#define QUAD_HAS_ANG_VEL 0
#define QUAD_OFF_ANG_VEL 0
#define QUAD_HAS_GRAVITY 0
#define QUAD_OFF_GRAVITY 0
#define QUAD_OFF_COMMAND 0
#define QUAD_OFF_PHASE 9
#define QUAD_OFF_JOINT_POS 15
#define QUAD_OFF_JOINT_VEL 39
#define QUAD_OFF_ACTIONS 63
#define QUAD_ACTION_CLIP 0.000000f

static const float QUAD_OBS_MEAN[87] = {0.0336035304f,0.0f,0.000134267888f,0.0336029939f,0.0f,0.000134225978f,0.0336029977f,0.0f,0.000134162023f,0.0110033667f,0.00654149521f,0.0103664529f,0.00227296422f,0.00929618068f,-0.00165605138f,-0.0996681377f,0.21970816f,0.077660881f,0.169342697f,-0.0304191243f,0.077332288f,0.0811016783f,0.132261127f,-0.0996234193f,0.220510602f,0.0776216015f,0.169613168f,-0.030668335f,0.0776234567f,0.0812870935f,0.132598132f,-0.0995837077f,0.221297294f,0.0776126236f,0.169875041f,-0.030933721f,0.0778916627f,0.0814921185f,0.132950306f,0.00609073788f,0.0403407291f,-0.000798478024f,0.0144634321f,-0.0090560317f,0.0152415503f,0.0126855699f,0.0161864664f,0.00607235963f,0.0399002135f,0.00117849896f,0.0146543263f,-0.00956137851f,0.014461848f,0.0141154667f,0.0168822799f,0.00573631888f,0.0391197391f,0.00247046934f,0.0141154183f,-0.0104320208f,0.0132169276f,0.0149195008f,0.0175817255f,-0.391827792f,0.901990294f,0.318310052f,0.71057415f,-0.106905602f,0.352199078f,0.33024767f,0.545584857f,-0.39171651f,0.905018806f,0.31870535f,0.711841762f,-0.10799633f,0.353262544f,0.331238031f,0.54714942f,-0.391681403f,0.907944858f,0.318968683f,0.712882936f,-0.109152049f,0.354198903f,0.332167447f,0.548754096f};
static const float QUAD_OBS_STD[87] = {0.0671391338f,0.00999999978f,0.216168553f,0.0671399534f,0.00999999978f,0.21616894f,0.0671404824f,0.00999999978f,0.216170803f,0.673015237f,0.678779483f,0.674248397f,0.677592456f,0.675450802f,0.676410854f,0.17257759f,0.102742665f,0.0867881551f,0.146485358f,0.12975359f,0.0987313241f,0.180292308f,0.109146483f,0.172825217f,0.101989299f,0.0873046592f,0.146410659f,0.129906371f,0.0987481102f,0.180468425f,0.108966805f,0.173074663f,0.101238959f,0.0877866074f,0.146330297f,0.130064458f,0.0987621546f,0.180644408f,0.108783685f,0.780099809f,1.31468689f,0.738246143f,0.878351092f,0.746443689f,0.86755389f,1.03046823f,1.12464714f,0.785301268f,1.31828809f,0.746920228f,0.884548604f,0.753174245f,0.87294817f,1.03535092f,1.12901533f,0.790504098f,1.32186151f,0.754448712f,0.890129447f,0.759538412f,0.878232837f,1.04009128f,1.13304901f,0.67247802f,0.453431576f,0.340066582f,0.571589649f,0.494885802f,0.394169956f,0.709146678f,0.460726321f,0.673773885f,0.451424807f,0.342248291f,0.571398735f,0.496058017f,0.394684911f,0.710151851f,0.460463703f,0.67499429f,0.449484199f,0.344396263f,0.571387291f,0.497275323f,0.395209879f,0.711106062f,0.460166365f};
static const float QUAD_DEFAULT_JOINT_POS[8] = {1.03069997f,-1.76289999f,1.03069997f,-1.76289999f,1.03069997f,-1.76289999f,1.03069997f,-1.76289999f};
static const float QUAD_ACTION_SCALE[8] = {0.25f,0.25f,0.25f,0.25f,0.25f,0.25f,0.25f,0.25f};
// layer 0: 87 -> 96
static const float QUAD_W0[8352] = 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static const float QUAD_B0[96] = {-0.348703623f,-0.0456410907f,0.36792928f,0.389547706f,0.255178601f,-0.012251908f,-0.102271348f,-0.037445914f,-0.134179145f,0.00323434779f,-0.196916878f,-0.575582266f,0.0938698426f,-0.202945858f,0.221416995f,0.0359954871f,-0.4682661f,0.120148726f,-0.0192725286f,-0.301232308f,0.0771779045f,0.172857642f,0.017783463f,-0.0907984525f,-0.112053871f,0.153566584f,-0.484333038f,0.0686802492f,-0.076091662f,0.0441725776f,-0.00587740866f,-0.0377555862f,0.253019333f,-0.147345766f,0.112960465f,-0.283983856f,0.0923316032f,0.0971832052f,0.237561956f,-0.255763352f,-0.0604527742f,-0.251665324f,0.159823269f,-0.361796349f,-0.0489391126f,0.303704351f,-0.0591195524f,0.0399659351f,0.0205135215f,0.0799346343f,-0.6844064f,-0.350118726f,-0.689281225f,-0.00505075371f,-0.38831386f,0.00352159399f,-0.337154537f,-0.058584027f,-0.383617461f,0.0201607905f,0.263953567f,-0.251626581f,-0.0588156544f,0.121364832f,0.0414783247f,0.0389873348f,0.0867573917f,-0.182563454f,-0.174277112f,0.226010397f,-0.21465531f,-0.25773567f,-0.0114152394f,-0.268191844f,0.0311002396f,-0.193009019f,-0.0987791941f,0.211044282f,0.179092363f,-0.0608258843f,0.00310953171f,-0.00687270984f,-0.133010611f,-0.432063609f,0.0132349236f,0.138969362f,0.329235107f,-0.352024317f,0.0785005018f,-0.424467564f,-0.0346929729f,-0.276835293f,0.326326698f,-0.0495057255f,-0.28982684f,-0.0429760888f};
// layer 1: 96 -> 64
static const float QUAD_W1[6144] = 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static const float QUAD_B1[64] = {-0.0780039281f,-0.225751579f,-0.341019124f,-0.150478497f,-0.325764269f,-0.0723779872f,-0.0261174235f,-0.132607937f,-0.162098408f,-0.261525184f,-0.326918453f,-0.00762997381f,-0.272505671f,-0.234043241f,-0.20703204f,0.117178023f,-0.124287173f,-0.431641817f,0.179903373f,0.124851428f,-0.177675739f,0.164610445f,-0.202714995f,0.151253819f,-0.15824151f,-0.175458089f,0.0909161121f,-0.0867407918f,0.0656070188f,-0.328341961f,-0.306190759f,-0.11986915f,0.156478092f,-0.244460478f,-0.134614214f,-0.111356929f,-0.091349557f,-0.00800478365f,-0.143270329f,-0.0858665407f,-0.361652702f,-0.0897944048f,-0.0416552499f,-0.0401792601f,-0.0196617059f,-0.152328283f,-0.0315670855f,-0.261898488f,0.244171798f,-0.168292537f,-0.160600111f,0.0544917397f,-0.187967151f,-0.424891561f,0.205664083f,-0.323031157f,-0.257215858f,-0.254151464f,-0.0177750234f,-0.178067461f,-0.265624583f,-0.401156187f,0.1829146f,0.011388707f};
// layer 2: 64 -> 8
static const float QUAD_W2[512] = {-0.0328935049f,0.00454363273f,0.175112739f,0.0181658361f,0.0522269309f,-0.0540712178f,0.00295709562f,-0.0556951053f,-0.0258971378f,-0.0196563303f,0.0160496049f,0.0337346196f,0.0129301958f,0.00935716089f,0.0829395503f,0.0755343288f,0.0364815146f,-0.0558753312f,0.014032444f,-0.0399873257f,-0.00933451019f,-0.00932216179f,-0.00370264705f,-0.00177527906f,0.0348587893f,-0.0208172388f,0.0177912656f,-0.0673444569f,-0.0127092917f,0.0178685822f,0.0210783686f,-0.0206429549f,-0.0369172394f,0.118200004f,-0.0513224863f,-0.0527939536f,0.00704606809f,0.0569383502f,-0.00154811156f,0.033079233f,0.0378239341f,0.0467534885f,-0.00797281321f,0.0396993123f,-0.0770339444f,0.00529282494f,-0.013825193f,0.028144069f,-0.068384558f,-0.00677561993f,0.0133961625f,-0.0558479019f,0.00985220447f,0.0454073362f,0.0333826616f,-0.0220118724f,-0.0411452055f,-0.041173391f,-0.085457325f,0.00127518049f,-0.0181648191f,0.0360735841f,-0.0385605842f,0.0831081048f,0.0198048912f,-0.0410422124f,0.0145807024f,0.025357971f,-0.0736060292f,-0.00313304807f,0.0593524538f,-0.00987926312f,-0.0626416504f,0.121731445f,-0.0202170834f,-0.0261848215f,-0.0139467809f,-0.0233121589f,-0.0465194695f,0.0120087797f,-0.0162060019f,-0.0995653421f,0.0138943586f,-0.0730096474f,-0.0324096233f,0.0275556203f,-0.0585049056f,-0.00450076163f,0.0527050942f,0.0335893854f,0.0146024385f,-0.0492415726f,0.0299717616f,0.0191697013f,-0.123629063f,0.0257768314f,0.0232778788f,0.0184325688f,0.0308093913f,-0.000994545291f,-0.0112678753f,0.0401571244f,-0.00510870945f,-0.0869607553f,-0.0352860764f,-0.0170906093f,0.0372504666f,0.0211658124f,-0.0365504399f,-0.000681690639f,0.034909606f,-0.0439860895f,0.122022174f,-0.037427716f,0.0564757809f,-0.0119972993f,-0.0278499629f,-0.181543216f,0.0818822682f,-0.148134068f,-0.0438900106f,-0.0311496742f,0.0514024235f,0.0449103341f,-0.00451535871f,-0.0584380329f,-0.0445392132f,0.0245600231f,0.0330109335f,-0.0306945369f,0.0336441621f,0.0245770458f,-0.0192166623f,-0.00114800874f,0.0140271327f,-0.0468382798f,0.00663414551f,0.0204309616f,-0.130107492f,0.0389319547f,0.00538587291f,-0.0475660004f,0.00443699863f,0.018293269f,0.0504850708f,-0.0806426033f,0.0152550759f,0.0281093623f,-0.0338997953f,-0.0170977339f,-0.0086056944f,0.0464549325f,-0.00509200105f,-0.000736162765f,-0.0170533415f,0.0274650231f,-0.00446090568f,-0.0199820492f,-0.0345627144f,-0.0317037404f,0.0487297811f,-0.0589423254f,0.028707169f,0.0333441794f,0.00399636198f,-0.0582362115f,-0.00787804555f,0.00521550095f,-0.0090130819f,-0.0345052704f,-0.0499099828f,-0.0178059936f,0.018982796f,-0.0109610092f,-0.00805162732f,-0.0463294424f,-0.00266859168f,-0.0187695101f,-0.0659777373f,0.00270399614f,0.0889670849f,-0.00105078891f,0.0302064754f,-0.0381135978f,-0.029424794f,-0.0012788187f,0.0165050607f,-0.0205571726f,-0.0160836428f,-0.0549022183f,-0.00190423243f,-0.0255200956f,-0.00810632482f,0.104016475f,-0.0201121755f,-0.0153929396f,-0.0431664661f,0.0370446406f,-0.0261014812f,-0.0183956344f,0.0549611598f,0.00501520187f,-0.0658977926f,0.0563890263f,-0.105447106f,-0.0372724347f,-0.0239615887f,0.0260184482f,0.0159357395f,-0.0880594477f,0.0422453023f,0.00137172942f,-0.0512881763f,0.101667181f,0.00470794039f,0.00960721821f,-0.0603914708f,0.0176759325f,-0.00842359941f,-0.0360481516f,0.013331851f,-0.198727757f,-0.0639660209f,0.030028088f,0.0183479637f,-0.0719854683f,-0.0578705594f,0.00708010932f,0.00744193187f,0.0577129759f,-0.0670250282f,-0.031993974f,0.00117866031f,-0.0005136283f,0.00178368599f,-0.0143554723f,-0.0233332794f,-0.00044407f,-0.0375969075f,0.0248441044f,0.0171479601f,-0.0261833444f,0.0115062818f,0.0192347169f,-0.0497185849f,-0.131313369f,-0.0130507573f,-0.0387052931f,-0.0519661792f,-0.0203324854f,-0.0383444279f,-0.0329843871f,-0.110675529f,-0.108498238f,0.0343881622f,0.0273784418f,-0.00529764593f,0.0164715648f,0.0421199389f,0.0567735732f,0.00488652848f,-0.0172803346f,0.0555005483f,0.00310770026f,0.0257714298f,-0.0334594287f,-0.0560556725f,-0.00932615343f,0.0265598837f,-0.00191686186f,-0.0188796651f,0.0216538813f,0.023108352f,-0.00443345681f,-0.0141110383f,-0.0192478169f,-0.0374209769f,0.0329855941f,0.0240477864f,-0.0583143234f,-0.0191074274f,-0.0579558201f,-0.0148029905f,-0.0225220378f,0.0303868745f,-0.038682647f,0.0632866621f,0.0324926749f,0.0195811987f,-0.0216782931f,-0.0349471197f,-0.0518481247f,-0.0143600991f,0.0164155662f,-0.0352247506f,0.0359312966f,0.0673455745f,0.0329288282f,0.0341473818f,-0.0114600454f,-0.0158208963f,-0.0428808816f,-0.00823597703f,0.0319003761f,0.033558201f,0.00205523358f,-0.0111736823f,0.00918042473f,0.0175029282f,0.00877502002f,-0.0488642752f,-0.100411691f,-0.127350226f,-0.0125087835f,0.0157816969f,-0.00229322049f,-0.0402057096f,-0.00284263561f,-0.0115660159f,-0.0132869333f,-0.0046346318f,-0.0605339706f,0.0420443714f,0.0638423115f,-0.0680264607f,0.0270700678f,0.00430453662f,0.0226855297f,-0.0324182808f,-0.00939063821f,-0.00774952536f,0.0779359415f,-0.0479278825f,0.0156652834f,-0.0511422753f,-0.00207308098f,0.0220343042f,-0.0297145583f,0.0174928475f,-0.0358159468f,-0.00389878708f,-0.00985997915f,0.00349078584f,0.0143236667f,0.0386589766f,-0.071375221f,-0.0215424411f,0.00172293291f,0.00342096318f,0.0491247885f,-0.106341965f,0.0237705018f,-0.0867223218f,-0.0220595878f,-0.0181072615f,-0.0447468944f,-0.108234189f,0.0386281051f,0.00525399577f,-0.0363734141f,0.0896141455f,0.015122734f,-0.0521720387f,-0.016744202f,-0.0191304963f,0.0319653042f,0.0668615252f,0.0129099684f,0.0100445589f,-0.0252566617f,0.0197488796f,-0.0241162032f,-0.00464488892f,-0.119820274f,-0.036582645f,-0.0313879773f,-0.0440700091f,0.0158395749f,-0.0336504206f,-0.0212850627f,-0.0449435115f,-0.0130204996f,0.0105142826f,-0.0323759802f,-0.0984397978f,-0.0820181593f,-0.0601655915f,-0.0108385617f,-0.0668410435f,-0.0625047311f,0.00926630013f,0.0176455844f,-0.0344405659f,-0.0681064725f,0.014322917f,-0.0237254091f,-0.0225720294f,-0.017987946f,0.0164755303f,0.016263647f,-0.00315208849f,-0.0646057054f,-0.010992256f,0.0262708049f,0.0589277297f,-0.00690538809f,0.0524173304f,0.0482075661f,0.0672673509f,-0.05629839f,0.0212435499f,-0.0522714965f,0.00370819657f,-0.0238392092f,-0.00436585676f,-0.0175193269f,0.0938035473f,-0.0317085944f,-0.0191617571f,-0.03211312f,0.0546284765f,-0.00146638835f,-0.0242609438f,-0.00118011713f,0.0127807464f,0.0512515344f,0.0185293257f,0.0685456395f,-0.0542289019f,0.0771553367f,-0.0532696471f,0.00732418755f,0.0270429794f,-0.115556188f,0.0195816383f,0.00379014341f,-0.000719690754f,-0.0338939801f,-0.0101148458f,-0.0528272688f,-0.0321593881f,-0.0590101518f,-0.0755888075f,0.0181631818f,-0.0255750939f,-0.0107415915f,0.0830448419f,-0.0396252312f,0.01333082f,-0.0374885947f,-0.0367818773f,0.0399071537f,0.0115164313f,0.00957157556f,0.036543835f,0.026402941f,-0.040213421f,0.00661818078f,-0.110263579f,0.050286904f,-0.0574310683f,-0.0162984505f,0.078583315f,0.037622571f,-0.0554130524f,-0.0596961863f,0.0709842518f,-0.000959481928f,-0.0249564145f,0.0174582712f,0.0154987304f,-0.0853776708f,0.00388626452f,0.00380389323f,0.0106417369f,-0.0183877572f,0.0490305834f,-0.0303858947f,0.00756881898f,-0.0585386269f,-0.0729041696f,-0.0188894942f,-0.157666802f,0.0622627363f,-0.0248188805f,0.0138328355f,0.0332117192f,0.123401038f,-0.0115693789f,0.078080602f,0.0133205177f,0.081870012f,-0.027581973f,0.0378378108f,0.0557461195f,-0.00203458173f,-0.0270400643f,0.0129224267f,-0.047261294f,0.0814955011f,0.0386988148f,-0.0593194962f,0.0693327338f,0.023084987f,-0.00810745545f,-0.0820308179f,0.0709728673f,0.0390855074f,0.0167535432f,-0.012808484f,0.111686453f,0.0175213963f};
static const float QUAD_B2[8] = {0.0756532028f,0.233209416f,0.0950364545f,0.0209171865f,-0.0113339247f,0.183389544f,-0.0129895825f,0.077193141f};

static inline float quad_elu(float x) { return x > 0.0f ? x : expm1f(x); }

// obs: QUAD_OBS_DIM raw (un-normalised) values; act: QUAD_ACT_DIM out.
static inline void quad_policy_forward(const float *obs, float *act) {
  float a[96], b[96];
  for (int i = 0; i < 87; ++i) a[i] = (obs[i] - QUAD_OBS_MEAN[i]) / QUAD_OBS_STD[i];
  for (int o = 0; o < 96; ++o) {
    float s = QUAD_B0[o];
    const float *w = &QUAD_W0[o * 87];
    for (int i = 0; i < 87; ++i) s += w[i] * a[i];
    b[o] = quad_elu(s);
  }
  for (int o = 0; o < 96; ++o) a[o] = b[o];
  for (int o = 0; o < 64; ++o) {
    float s = QUAD_B1[o];
    const float *w = &QUAD_W1[o * 96];
    for (int i = 0; i < 96; ++i) s += w[i] * a[i];
    b[o] = quad_elu(s);
  }
  for (int o = 0; o < 64; ++o) a[o] = b[o];
  for (int o = 0; o < 8; ++o) {
    float s = QUAD_B2[o];
    const float *w = &QUAD_W2[o * 64];
    for (int i = 0; i < 64; ++i) s += w[i] * a[i];
    b[o] = s;
  }
  for (int o = 0; o < 8; ++o) act[o] = b[o];
}

include/leg_ik.h — 13 lines

Open on GitHub

// 1 脚 2 自由度の順運動学・逆運動学 (本文 13.3)
//
// この機体の脚は矢状面の中だけで動く (外転軸が無い)。3 次元へ広げる必要が
// ないので、平面 2 リンクの式がそのまま脚の全部になる。
#pragma once

// x は前が正、r は股の軸から下向きが正 [m]。
// t2 は股、t3 は膝の関節角 [rad]。符号は URDF に合わせてある。
void leg_fk(float t2, float t3, float *fx, float *fr);
void leg_ik(float fx, float fr, float *t2, float *t3);

// FK と IK を突き合わせて実装を確かめる (本文 13.3.7)
void test_ik_roundtrip(void);

include/quad_calib.h — 26 lines

Open on GitHub

// この機体のサーボ構成 (本文 13.8)。
//
// ポリシーの 8 出力の順に並んでいる。**並べ替えてはいけない。** 順番は学習した
// チェックポイントから来ていて、arduino_quad_policy.h の先頭にも書いてある。
//
// sign と zero は校正で決める値で、機体ごとに違う。ここに書いてあるのは
// 本書の実機のもの。自分の機体では host/quad_host.py calibrate で出し直す
// こと -- ホストとファームが同じ値を持っていないとロボットは暴れる。
#pragma once

#define QUAD_NUM_JOINTS 8

// バス上の ID。FL_hip, FL_knee, RL_hip, RL_knee, RR_hip, RR_knee, FR_hip, FR_knee
static const unsigned char QUAD_SERVO_ID[QUAD_NUM_JOINTS] = {3, 4, 7, 8, 5, 6, 1, 2};

// URDF の関節が回る向きにサーボが回るかどうか。+1 か -1 で、推測しないこと。
static const float QUAD_SERVO_SIGN[QUAD_NUM_JOINTS] = {
    -1.0f, -1.0f, -1.0f, -1.0f, 1.0f, 1.0f, 1.0f, 1.0f};

// 関節角 0 rad に対応するサーボの読み値。
//
// このサーボは絶対角のエンコーダを持っていて機械的な止まりが無いので、
// ホーンを何度で取り付けても、ここを測り直せば辻褄が合う (本文 13.8.1)。
// 下の 2048 は「真ん中」であって、正しい値ではない。校正して置き換えること。
static const float QUAD_SERVO_ZERO[QUAD_NUM_JOINTS] = {
    2048.0f, 2048.0f, 2048.0f, 2048.0f, 2048.0f, 2048.0f, 2048.0f, 2048.0f};

include/quad_control.h — 187 lines

Open on GitHub

// Observation assembly and action decoding for the ArduinoQuad policy.
//
// Pure C99, no Arduino and no servo dependency, so it can be compiled and
// tested on the host against the mjlab environment -- which is the point: the
// bug that kills a sim2real deployment is almost never the network, it is the
// observation vector being assembled in a different order, with a different
// history convention, or from differently-scaled units than the one the policy
// was trained on. scripts/check_quad_control.py replays a trained policy in
// mjlab and asserts this file reproduces the environment's own observation
// vector step for step.
//
// Everything layout-related comes from arduino_quad_policy.h, which is
// generated from the checkpoint, so re-exporting a policy with a different
// observation set cannot silently desync this code -- the constants move with
// it.
//
// Units are the simulation's: radians, radians/second, seconds, metres/second.
// Converting servo counts <-> radians is the caller's job (see the .ino).

#pragma once

#include <math.h>
#include <string.h>

// The *_imu PlatformIO envs define QUAD_POLICY_IMU and get the policy that also
// reads the body IMU. The *_krs envs define QUAD_POLICY_KRS and get the KRS
// robot's own policy (KRS-3302 servos, also reads the IMU). All three headers
// are generated and define the same names.
#if defined(QUAD_POLICY_KRS)
#include "krs_quad_policy.h"
#elif defined(QUAD_POLICY_IMU)
#include "arduino_quad_policy_imu.h"
#else
#include "arduino_quad_policy.h"
#endif

#define QUAD_NJ QUAD_ACT_DIM

// M_PI is not in strict C99 (and the Arduino core does not always define it).
#define QUAD_TWO_PI 6.28318530717958647692f

// What the policy needs from an IMU. Pass NULL to quad_step when the policy was
// trained without one (QUAD_HAS_ANG_VEL and QUAD_HAS_GRAVITY both 0).
//
//   ang_vel  body-frame angular velocity [rad/s], x forward, y left, z up --
//            a raw rate gyro, no filtering or attitude estimate needed.
//   gravity  the gravity direction expressed in the body frame, unit length.
//            Level and upright is {0, 0, -1}. This one DOES need an attitude
//            estimate; it is not the raw accelerometer reading.
typedef struct {
  float ang_vel[3];
  float gravity[3];
} quad_imu_t;

typedef struct {
  // Per-term history ring buffers, oldest-to-newest when flattened out.
#if QUAD_HAS_ANG_VEL
  float angvel[QUAD_HISTORY][3];
#endif
#if QUAD_HAS_GRAVITY
  float grav[QUAD_HISTORY][3];
#endif
  float cmd[QUAD_HISTORY][3];
  float phase[QUAD_HISTORY][2];
  float qpos[QUAD_HISTORY][QUAD_NJ];
  float qvel[QUAD_HISTORY][QUAD_NJ];
  float act[QUAD_HISTORY][QUAD_NJ];
  int head;          // index of the newest entry
  int filled;        // how many slots hold real data
  float t;           // seconds since the policy started (gait clock)
  float last_act[QUAD_NJ];
} quad_state_t;

// Start (or restart) the controller. The history is primed with the standing
// pose and a zero action, which is what a reset looks like in mjlab too.
static inline void quad_init(quad_state_t *s) {
  memset(s, 0, sizeof(*s));
  s->head = QUAD_HISTORY - 1;
  s->filled = 0;
}

static inline void quad__push(quad_state_t *s, const float cmd[3],
                              const float qpos_rel[QUAD_NJ],
                              const float qvel[QUAD_NJ],
                              const float last_act[QUAD_NJ],
                              const float phase[2],
                              const quad_imu_t *imu) {
  s->head = (s->head + 1) % QUAD_HISTORY;
#if QUAD_HAS_ANG_VEL
  memcpy(s->angvel[s->head], imu->ang_vel, sizeof(float) * 3);
#endif
#if QUAD_HAS_GRAVITY
  memcpy(s->grav[s->head], imu->gravity, sizeof(float) * 3);
#endif
  (void)imu;
  memcpy(s->cmd[s->head], cmd, sizeof(float) * 3);
  memcpy(s->phase[s->head], phase, sizeof(float) * 2);
  memcpy(s->qpos[s->head], qpos_rel, sizeof(float) * QUAD_NJ);
  memcpy(s->qvel[s->head], qvel, sizeof(float) * QUAD_NJ);
  memcpy(s->act[s->head], last_act, sizeof(float) * QUAD_NJ);
  if (s->filled < QUAD_HISTORY) {
    // Before the buffer is full, mjlab's CircularBuffer repeats the first
    // sample into every slot, so match that instead of leaving zeros.
    for (int k = 0; k < QUAD_HISTORY; ++k) {
      if (k == s->head) continue;
      if (s->filled == 0) {
        memcpy(s->cmd[k], s->cmd[s->head], sizeof(float) * 3);
        memcpy(s->phase[k], s->phase[s->head], sizeof(float) * 2);
        memcpy(s->qpos[k], s->qpos[s->head], sizeof(float) * QUAD_NJ);
        memcpy(s->qvel[k], s->qvel[s->head], sizeof(float) * QUAD_NJ);
        memcpy(s->act[k], s->act[s->head], sizeof(float) * QUAD_NJ);
      }
    }
    s->filled++;
  }
}

// Flatten one term's history oldest-to-newest into obs[off..].
static inline void quad__flat(const float *ring, int n, int head, int stride,
                              float *out) {
  for (int k = 0; k < QUAD_HISTORY; ++k) {
    int idx = (head + 1 + k) % QUAD_HISTORY;  // oldest first
    memcpy(out + (size_t)k * n, ring + (size_t)idx * stride, sizeof(float) * n);
  }
}

// The gait clock. Must match rl/slow_robot.py::phase: a global sin/cos ramp of
// period QUAD_GAIT_PERIOD, forced to zero whenever |command| is below
// QUAD_PHASE_CMD_MIN (that is how the policy is told "stand still"). The
// exporter writes the threshold the policy was trained with; headers from
// before it did were all trained with 0.1.
#ifndef QUAD_PHASE_CMD_MIN
#define QUAD_PHASE_CMD_MIN 0.1f
#endif
static inline void quad_phase(float t, const float cmd[3], float out[2]) {
  float norm = sqrtf(cmd[0] * cmd[0] + cmd[1] * cmd[1] + cmd[2] * cmd[2]);
  if (norm < QUAD_PHASE_CMD_MIN) {
    out[0] = 0.0f;
    out[1] = 0.0f;
    return;
  }
  float ph = fmodf(t, QUAD_GAIT_PERIOD) / QUAD_GAIT_PERIOD;
  out[0] = sinf(ph * QUAD_TWO_PI);
  out[1] = cosf(ph * QUAD_TWO_PI);
}

// One control step.
//   q       : measured joint angles [rad], in QUAD_ACT_DIM order (see the header)
//   qd      : measured joint velocities [rad/s], same order
//   cmd     : [vx, vy, wz]; vy must be 0 -- this robot has no lateral DoF
//   imu     : body-frame rates / gravity direction. Must be non-NULL when the
//             policy was trained with an IMU (QUAD_HAS_ANG_VEL or
//             QUAD_HAS_GRAVITY); ignored, and may be NULL, when it was not.
//   step_i  : control step counter since quad_init (drives the gait clock)
//   target  : out, joint position targets [rad]
//   obs_out : optional, the assembled QUAD_OBS_DIM observation (NULL to skip)
static inline void quad_step(quad_state_t *s, const float q[QUAD_NJ],
                             const float qd[QUAD_NJ], const float cmd[3],
                             const quad_imu_t *imu,
                             long step_i, float target[QUAD_NJ],
                             float *obs_out) {
  float qpos_rel[QUAD_NJ], phase[2], obs[QUAD_OBS_DIM], act[QUAD_ACT_DIM];
  for (int j = 0; j < QUAD_NJ; ++j) qpos_rel[j] = q[j] - QUAD_DEFAULT_JOINT_POS[j];

  s->t = (float)step_i * QUAD_CONTROL_DT;
  quad_phase(s->t, cmd, phase);
  quad__push(s, cmd, qpos_rel, qd, s->last_act, phase, imu);

  // Offsets come from arduino_quad_policy.h, which reads them out of the
  // trained checkpoint. They are NOT computed here: adding an IMU term puts a
  // term at offset 0 and shifts every other one, and code that assumed a fixed
  // order would keep filling the old slots without any error.
  int h = s->head;
#if QUAD_HAS_ANG_VEL
  quad__flat(&s->angvel[0][0], 3, h, 3, obs + QUAD_OFF_ANG_VEL);
#endif
#if QUAD_HAS_GRAVITY
  quad__flat(&s->grav[0][0], 3, h, 3, obs + QUAD_OFF_GRAVITY);
#endif
  quad__flat(&s->cmd[0][0], 3, h, 3, obs + QUAD_OFF_COMMAND);
  quad__flat(&s->phase[0][0], 2, h, 2, obs + QUAD_OFF_PHASE);
  quad__flat(&s->qpos[0][0], QUAD_NJ, h, QUAD_NJ, obs + QUAD_OFF_JOINT_POS);
  quad__flat(&s->qvel[0][0], QUAD_NJ, h, QUAD_NJ, obs + QUAD_OFF_JOINT_VEL);
  quad__flat(&s->act[0][0], QUAD_NJ, h, QUAD_NJ, obs + QUAD_OFF_ACTIONS);

  quad_policy_forward(obs, act);

  // Runtime, not #if: QUAD_ACTION_CLIP is a float literal and the preprocessor
  // cannot compare those. The compiler folds this away when the clip is 0.
  if (QUAD_ACTION_CLIP > 0.0f) {
    for (int j = 0; j < QUAD_ACT_DIM; ++j) {
      if (act[j] > QUAD_ACTION_CLIP) act[j] = QUAD_ACTION_CLIP;
      if (act[j] < -QUAD_ACTION_CLIP) act[j] = -QUAD_ACTION_CLIP;
    }
  }

  for (int j = 0; j < QUAD_NJ; ++j) {
    target[j] = QUAD_DEFAULT_JOINT_POS[j] + QUAD_ACTION_SCALE[j] * act[j];
  }
  memcpy(s->last_act, act, sizeof(act));
  if (obs_out) memcpy(obs_out, obs, sizeof(obs));
}

include/servo_bus.h — 24 lines

Open on GitHub

// シリアルバスサーボの最小ドライバ (本文 13.2.2)
//
// PWM と違って返事が返る。返事が返るということは、返らなかったときにどうする
// かを決めなければならないということで、そこから 20 ms の締切の話が始まる。
#pragma once

#include <stdbool.h>

void  servo_bus_init(void);

// 応答した個数。起動時に 8 個そろわなければ先へ進まないこと。
int   servo_bus_ping_all(void);

// 速度制限のレジスタを書いて読み返す。戻り値は成立した書き込みの数 (最大 16)。
// SRAM にあるので電源のたびに消える。詳しくは本文 13.9.1。
int   servo_bus_apply_limits(void);

void  servo_bus_torque(bool on);

// 全関節を 1 回の往復で読む。1 個でも黙っていたら false。
bool  servo_bus_read(float *q_rad);

// 8 個ぶんの目標角を 1 パケットで送る (sync write)。返事は無い。
void  servo_bus_write(const float *q_rad);

#ifdef QUAD_SERVO_RCB4
// RCB-4 mini 版 (servo_bus_rcb4.cpp) だけにある。RCB-4 は書き込みにも ACK を
// 返すので、返らなかった回数を数えられる。apply_limits は書くものが無いので 0。
unsigned long servo_bus_write_fail(void);

// 関節ごとの ID・RCB-4 のサーボ番号・パルス・角度を出す (コマンド raw)。
// quad_calib_rcb4.h のゼロ点と向きはこれで測る。
void servo_bus_print_raw(void);
#endif

src/gait.cpp — 56 lines

Open on GitHub

// naive 歩行: 状態機械 + trot gait (本文 13.5)
//
// ポリシーを使わずに歩かせる側。平地では動くが、この機体は前後が非対称なので
// 向きによって性能が倍以上違う (0.156 m/s と 0.089 m/s)。係数を手で回して
// どちらかには合わせられるが、両方には合わせられない。そこが RL へ行く動機。
#include <Arduino.h>
#include <math.h>
#include "leg_ik.h"
#include "quad_calib.h"

#define GAIT_PERIOD_MS  320      // 学習したポリシーと同じ歩容周期
#define LEG_FL 0
#define LEG_RL 1
#define LEG_RR 2
#define LEG_FR 3

static float STEP_X   = 0.06f;   // 前進ストライド長 [m]
static float STEP_H   = 0.030f;  // 遊脚の持ち上げ [m]
static float STANCE_R = 0.1205f; // 接地時の股軸からの下向き距離 [m]

static float g_phase = 0.0f;     // 0..1

// 各脚の位相オフセット。対角の 2 本が同じ値になるのが trot。
// 並びは quad_calib.h の関節順 (FL, RL, RR, FR) に対応する。
static const float PHASE_OFFSET[4] = {0.0f, 0.5f, 0.0f, 0.5f};

// 遊脚は前へ出しながら山なりに持ち上がり、接地脚は体の下を後ろへ流れる。
// 外転が無いので横方向は無く、2 変数で足りる (本文 13.5.2)。
static void compute_swing_foot(float phi, float *fx, float *fr)
{
    if (phi < 0.5f) {
        float t = phi * 2.0f;
        *fx = (t - 0.5f) * STEP_X;
        *fr = STANCE_R - STEP_H * sinf((float)M_PI * t);
    } else {
        float t = (phi - 0.5f) * 2.0f;
        *fx = (0.5f - t) * STEP_X;
        *fr = STANCE_R;
    }
}

void gait_reset(void) { g_phase = 0.0f; }

void gait_set_stride(float step_x) { STEP_X = step_x; }

// dt [s] ぶん位相を進めて、8 関節の目標角を書く。
void gait_step(float dt, float *q_out)
{
    g_phase = fmodf(g_phase + dt * 1000.0f / GAIT_PERIOD_MS, 1.0f);
    for (int leg = 0; leg < 4; ++leg) {
        float phi = fmodf(g_phase + PHASE_OFFSET[leg], 1.0f);
        float fx, fr;
        compute_swing_foot(phi, &fx, &fr);
        leg_ik(fx, fr, &q_out[leg * 2 + 0], &q_out[leg * 2 + 1]);
    }
}

src/leg_ik.cpp — 44 lines

Open on GitHub

#include <math.h>
#include "leg_ik.h"

// CAD から測った値。股軸→膝軸、膝軸→足先球の中心。
static const float L2 = 0.0883f;   // 大腿  88.3 mm
static const float L3 = 0.1087f;   // 下腿 108.7 mm

// 下腿ブラケットの折れ (本文 13.3.5)。膝角 0 でも 4.36 度だけ前に折れている。
// 無視しても脚は動くが、足先が狙いから 8 mm 前へずれる。しかもそのずれは
// ログには出ない -- IK が返した角度にサーボは行き、読み戻せば一致するので、
// 辻褄は完璧に合ったまま足の位置だけが違う。
static const float KNEE_OFFSET = -0.0761f;

// x は前を正、r は股軸から下向きを正。URDF の関節符号は「正で足が後ろへ」
// なので、前後を入れ替えて平面 2 リンクの式へ渡す。ここを合わせておかないと、
// IK は正しい角度を返すのに脚は逆へ振れる。
void leg_fk(float t2, float t3, float *fx, float *fr)
{
    float a = t2;
    float b = t2 + t3 + KNEE_OFFSET;
    *fx = -(L2 * sinf(a) + L3 * sinf(b));
    *fr =   L2 * cosf(a) + L3 * cosf(b);
}

void leg_ik(float fx, float fr, float *t2, float *t3)
{
    float u = -fx;                       // 平面 2 リンクの向きへ直す
    float d2 = u * u + fr * fr;

    // 余弦定理で膝の曲がり角 (本文 13.3.3 手順その1)
    float c = (d2 - L2 * L2 - L3 * L3) / (2.0f * L2 * L3);
    if (c >  1.0f) c =  1.0f;            // 届かないときの保険 (本文 13.3.8)
    if (c < -1.0f) c = -1.0f;

    // acosf が返すのは 0..pi の側だが、この機体の膝は後ろへ折れる。立ち姿勢の
    // 膝角が -101 度である以上、負のほうの解を採るのが正しい (本文 13.3.4)。
    float gamma = -acosf(c);

    // 引き算で股の角度 (本文 13.3.3 手順その2)
    float a = atan2f(u, fr);
    float b = atan2f(L3 * sinf(gamma), L2 + L3 * cosf(gamma));
    *t2 = a - b;
    *t3 = gamma - KNEE_OFFSET;
}

src/leg_ik_test.cpp — 33 lines

Open on GitHub

// FK と IK は互いに逆向きの計算なので、通して元に戻るかで実装を確かめられる
// (本文 13.3.7)。実機へ載せる前に必ず通しておくこと。
#include <Arduino.h>
#include <math.h>
#include "leg_ik.h"

void test_ik_roundtrip(void)
{
    // (x, r) [m]。x は前が正、r は股軸から下向き
    const float targets[][2] = {
        { 0.000f, 0.1600f},   // ほぼ真下、脚を伸ばし気味
        { 0.040f, 0.1400f},   // 前へ
        {-0.040f, 0.1400f},   // 後ろへ
        { 0.000f, 0.1205f},   // 立ち姿勢 (home) の高さ
        { 0.000f, 0.2500f},   // 届かない位置。切り詰めが効くか
    };

    for (unsigned i = 0; i < sizeof(targets) / sizeof(targets[0]); i++) {
        float t2, t3, gx, gr;
        leg_ik(targets[i][0], targets[i][1], &t2, &t3);
        leg_fk(t2, t3, &gx, &gr);

        float err = fabsf(gx - targets[i][0]) + fabsf(gr - targets[i][1]);

        Serial.print(F("target=(")); Serial.print(targets[i][0], 3);
        Serial.print(F(", "));       Serial.print(targets[i][1], 4);
        Serial.print(F(")  hip="));  Serial.print(t2 * 57.2958f, 2);
        Serial.print(F("  knee=")); Serial.print(t3 * 57.2958f, 2);
        Serial.print(F("  err="));  Serial.println(err, 6);
    }
    Serial.println(F("err が 0.00001 を下回れば式は正しい。"
                     "最後の 1 行だけは届かない位置なので 0.05 前後になる。"));
}

src/servo_bus.cpp — 176 lines

Open on GitHub

#include <Arduino.h>
#include "servo_bus.h"
#include "quad_calib.h"

#define BUS          Serial1        // D0(RX) / D1(TX)
#define BUS_BAUD     1000000        // 本文 13.2.2: 50 Hz 制御にはこれが要る
#define INST_PING    0x01
#define INST_READ    0x02
#define INST_WRITE   0x03
#define INST_SYNC    0x83
#define ADDR_TORQUE  40
#define ADDR_ACC     41             // 加速度 (1) の直後に目標位置 (2)・時間 (2)・速度 (2)
#define ADDR_POS     56
#define SYNC_LEN     7              // ADDR_ACC から 7 バイト = 41..47

// データシートに無い SRAM の速度上限。出荷値は 50 と 1 で、無負荷速度の 21%
// しか出ない (実測 1.00 rad/s に対しポリシーが要求するのは 5.34 rad/s)。SRAM な
// ので電源を切ると戻る。何も報告されず、ロボットが遅くなるだけ。補遺 13.9.1。
#define ADDR_MAX_ACC   85
#define ADDR_ACC_MULT  86
#define VAL_MAX_ACC   254
#define VAL_ACC_MULT    0

#define NJ QUAD_NUM_JOINTS
#define RAD_PER_COUNT (6.28318530717958647692f / 4096.0f)

static uint8_t checksum(const uint8_t *b, int n)
{
    int s = 0;
    for (int i = 0; i < n; ++i) s += b[i];
    return (uint8_t)(~s);
}

// 1 往復。戻り値は受け取ったパラメータ数、負なら失敗。
//
// timeout_us は制御周期より必ず短くすること。既定 100 ms のライブラリをその
// まま使うと、サーボ 1 個が黙るだけで制御周期 5 回分を失う (本文 13.4.3)。
static int txrx(uint8_t id, uint8_t inst, const uint8_t *par, int npar,
                uint8_t *out, int outmax, uint32_t timeout_us)
{
    uint8_t pkt[16];
    int n = 0;
    pkt[n++] = 0xFF; pkt[n++] = 0xFF;
    pkt[n++] = id; pkt[n++] = (uint8_t)(npar + 2); pkt[n++] = inst;
    for (int i = 0; i < npar; ++i) pkt[n++] = par[i];
    pkt[n] = checksum(pkt + 2, n - 2); n++;

    // このバスは半二重なので、アダプタによっては自分の送信がそのまま受信
    // バッファに現れる。ヘッダを探し直すことでそれを読み飛ばす (本文 13.2.2)。
    while (BUS.available()) BUS.read();
    BUS.write(pkt, n);
    BUS.flush();

    uint32_t t0 = micros();
    int prev = -1, cur = -1;
    while (micros() - t0 < timeout_us) {
        if (!BUS.available()) continue;
        prev = cur; cur = BUS.read();
        if (prev == 0xFF && cur == 0xFF) break;
    }
    if (!(prev == 0xFF && cur == 0xFF)) return -1;

    uint8_t head[2];
    for (int i = 0; i < 2; ++i) {
        while (!BUS.available()) if (micros() - t0 > timeout_us) return -2;
        head[i] = BUS.read();
    }
    int len = head[1];
    if (len < 2 || len > 32) return -3;
    uint8_t body[34];
    for (int i = 0; i < len; ++i) {
        while (!BUS.available()) if (micros() - t0 > timeout_us) return -2;
        body[i] = BUS.read();
    }
    uint8_t sum[36];
    sum[0] = head[0]; sum[1] = head[1];
    for (int i = 0; i < len; ++i) sum[2 + i] = body[i];
    if (checksum(sum, len + 1) != body[len - 1]) return -4;
    if (head[0] != id) return -5;

    int np = len - 2;
    for (int i = 0; i < np && i < outmax; ++i) out[i] = body[1 + i];
    return np;
}

void servo_bus_init(void)
{
    BUS.begin(BUS_BAUD);
    delay(200);
}

int servo_bus_ping_all(void)
{
    int found = 0;
    for (int i = 0; i < NJ; ++i) {
        uint8_t o[4];
        if (txrx(QUAD_SERVO_ID[i], INST_PING, NULL, 0, o, 4, 3000) >= 0) found++;
    }
    return found;
}

// 書いて読み返す。応答が無かった書き込みと、届かなかった書き込みは区別が
// つかない -- 黙って適用されない速度上限こそが、この関数の存在理由。
static bool write_verify(uint8_t id, uint8_t addr, uint8_t value, int tries)
{
    for (int t = 0; t < tries; ++t) {
        uint8_t p[2] = {addr, value}, o[4];
        txrx(id, INST_WRITE, p, 2, o, 4, 3000);
        uint8_t r[2] = {addr, 1};
        if (txrx(id, INST_READ, r, 2, o, 1, 3000) == 1 && o[0] == value) return true;
        delay(20);
    }
    return false;
}

int servo_bus_apply_limits(void)
{
    int ok = 0;
    for (int i = 0; i < NJ; ++i) {
        if (write_verify(QUAD_SERVO_ID[i], ADDR_MAX_ACC,  VAL_MAX_ACC,  6)) ok++;
        if (write_verify(QUAD_SERVO_ID[i], ADDR_ACC_MULT, VAL_ACC_MULT, 6)) ok++;
    }
    return ok;
}

void servo_bus_torque(bool on)
{
    for (int i = 0; i < NJ; ++i) {
        uint8_t p[2] = {ADDR_TORQUE, (uint8_t)(on ? 1 : 0)}, o[4];
        txrx(QUAD_SERVO_ID[i], INST_WRITE, p, 2, o, 2, 3000);
    }
}

bool servo_bus_read(float *q_rad)
{
    bool ok = true;
    for (int i = 0; i < NJ; ++i) {
        uint8_t p[2] = {ADDR_POS, 2}, o[2];
        if (txrx(QUAD_SERVO_ID[i], INST_READ, p, 2, o, 2, 3000) != 2) {
            ok = false;
            continue;
        }
        float counts = (float)(o[0] | (o[1] << 8));
        q_rad[i] = (counts - QUAD_SERVO_ZERO[i]) * RAD_PER_COUNT * QUAD_SERVO_SIGN[i];
    }
    return ok;
}

void servo_bus_write(const float *q_rad)
{
    // 8 個ぶんを 1 パケットで送る。1 個ずつ書くと往復が 8 倍になり、
    // 20 ms の予算が崩れる (本文 13.4.2)。
    uint8_t pkt[8 + NJ * (SYNC_LEN + 1)];
    int k = 0;
    pkt[k++] = 0xFF; pkt[k++] = 0xFF;
    pkt[k++] = 0xFE;                                   // broadcast
    pkt[k++] = (uint8_t)((SYNC_LEN + 1) * NJ + 4);
    pkt[k++] = INST_SYNC;
    // 加速度 (41) から書き始める。以前は 42 (目標位置) から 7 バイト書き、最後の
    // 「加速度」の 0 が実際には 48 番地 = トルク上限の下位バイトに入っていた。
    // 出荷値 1000 (0x03E8) が 768 (0x0300) に落ち、荷重のかかる脚が沈んで転ぶ。
    // 加速度は一度も書かれず、サーボに残っていた値のまま動いていた。
    pkt[k++] = ADDR_ACC;
    pkt[k++] = SYNC_LEN;
    for (int i = 0; i < NJ; ++i) {
        float counts = q_rad[i] / RAD_PER_COUNT * QUAD_SERVO_SIGN[i]
                     + QUAD_SERVO_ZERO[i];
        if (counts < 0.0f) counts = 0.0f;
        if (counts > 4095.0f) counts = 4095.0f;
        int c = (int)(counts + 0.5f);
        pkt[k++] = QUAD_SERVO_ID[i];
        pkt[k++] = 0;                                  // 加速度 0 = 上限なし
        pkt[k++] = (uint8_t)(c & 0xFF);                // 目標位置
        pkt[k++] = (uint8_t)((c >> 8) & 0xFF);
        pkt[k++] = 0; pkt[k++] = 0;                    // 時間
        pkt[k++] = 0; pkt[k++] = 0;                    // 速度 0 = 上限なし
    }
    pkt[k] = checksum(pkt + 2, k - 2); k++;
    BUS.write(pkt, k);
    BUS.flush();
}

On the board

The quadruped walking on your own OS, driving 8 servos (1.5x speed)

Pitfalls

(Collected from reader questions — ask via GitHub Issues.)