SpotMicroESP32-Leika/app/src/lib/gait.ts

import { get } from 'svelte/store'
import type { body_state_t } from './kinematic'
import { currentKinematic } from './stores/featureFlags'

const { sin } = Math

export interface gait_state_t {
  step_height: number
  step_x: number
  step_z: number
  step_angle: number
  step_velocity: number
  step_depth: number
}

export interface ControllerCommand {
  lx: number
  ly: number
  rx: number
  ry: number
  h: number
  s: number
  s1: number
}

export abstract class GaitState {
  protected abstract name: string

  protected dt = 0.02
  protected body_state!: body_state_t
  protected gait_state: gait_state_t = {
    step_height: 0.4,
    step_x: 0,
    step_z: 0,
    step_angle: 0,
    step_velocity: 1,
    step_depth: 0.002
  }

  public get default_feet_pos() {
    return get(currentKinematic).getDefaultFeetPos()
  }

  protected get default_height() {
    return 0.5
  }

  begin() {
    console.log('Starting', this.name)
  }
  end() {
    console.log('Ending', this.name)
  }
  step(body_state: body_state_t, command: ControllerCommand, dt: number = 0.02) {
    this.map_command(command)
    this.body_state = body_state
    this.dt = dt / 1000
    return body_state
  }

  map_command(command: ControllerCommand) {
    const newCommand = {
      step_height: 0.4 + (command.s1 + 1) / 2,
      step_x: command.ly,
      step_z: -command.lx,
      step_velocity: command.s,
      step_angle: command.rx,
      step_depth: 0.002
    }

    this.gait_state = newCommand
  }
}

export class IdleState extends GaitState {
  protected name = 'Idle'
}

export class CalibrationState extends GaitState {
  protected name = 'Calibration'

  step(body_state: body_state_t, command: ControllerCommand, dt: number = 0.02) {
    body_state.omega = 0
    body_state.phi = 0
    body_state.psi = 0
    body_state.xm = 0
    body_state.ym = this.default_height * 10
    body_state.zm = 0
    body_state.feet = this.default_feet_pos
    return body_state
  }
}

export class RestState extends GaitState {
  protected name = 'Rest'

  step(body_state: body_state_t, command: ControllerCommand, dt: number = 0.02) {
    body_state.omega = 0
    body_state.phi = 0
    body_state.psi = 0
    body_state.xm = 0
    body_state.ym = this.default_height / 2
    body_state.zm = 0
    body_state.feet = this.default_feet_pos
    return body_state
  }
}

export class StandState extends GaitState {
  protected name = 'Stand'

  step(body_state: body_state_t, command: ControllerCommand, dt: number = 0.02) {
    body_state.omega = 0
    body_state.phi = command.rx
    body_state.psi = command.ry
    body_state.xm = command.ly / 4
    body_state.zm = command.lx / 4
    body_state.feet = this.default_feet_pos
    return body_state
  }
}

abstract class PhaseGaitState extends GaitState {
  protected tick = 0
  protected phase = 0
  protected phase_time = 0
  protected abstract num_phases: number
  protected abstract phase_speed_factor: number
  protected abstract swing_stand_ratio: number

  protected contact_phases!: number[][]
  protected shifts!: number[][]

  step(body_state: body_state_t, command: ControllerCommand, dt: number = 0.02) {
    super.step(body_state, command, dt)
    this.update_phase()
    this.update_body_position()
    this.update_feet_positions()
    return this.body_state
  }

  update_phase() {
    this.phase_time += this.dt * this.phase_speed_factor * this.gait_state.step_velocity

    if (this.phase_time >= 1) {
      this.phase += 1
      if (this.phase == this.num_phases) this.phase = 0
      this.phase_time = 0
    }
  }

  update_body_position() {
    if (this.num_phases === 4) return

    const shift = this.shifts[Math.floor(this.phase / 2)]

    this.body_state.xm += (shift[0] - this.body_state.xm) * this.dt * 4
    this.body_state.zm += (shift[2] - this.body_state.zm) * this.dt * 4
  }

  update_feet_positions() {
    for (let i = 0; i < 4; i++) {
      this.body_state.feet[i] = this.update_foot_position(i)
    }
  }

  update_foot_position(index: number): number[] {
    const contact = this.contact_phases[index][this.phase]
    return contact ? this.stand(index) : this.swing(index)
  }

  stand(index: number): number[] {
    const delta_pos = [
      -this.gait_state.step_x * this.dt * this.swing_stand_ratio,
      0,
      -this.gait_state.step_z * this.dt * this.swing_stand_ratio
    ]

    this.body_state.feet[index][0] = this.body_state.feet[index][0] + delta_pos[0]
    this.body_state.feet[index][1] = this.default_feet_pos[index][1]
    this.body_state.feet[index][2] = this.body_state.feet[index][2] + delta_pos[2]
    return this.body_state.feet[index]
  }

  swing(index: number): number[] {
    const delta_pos = [this.gait_state.step_x * this.dt, 0, this.gait_state.step_z * this.dt]

    if (this.gait_state.step_x == 0) {
      delta_pos[0] =
        (this.default_feet_pos[index][0] - this.body_state.feet[index][0]) * this.dt * 8
    }

    if (this.gait_state.step_z == 0) {
      delta_pos[2] =
        (this.default_feet_pos[index][2] - this.body_state.feet[index][2]) * this.dt * 8
    }

    this.body_state.feet[index][0] = this.body_state.feet[index][0] + delta_pos[0]
    this.body_state.feet[index][1] =
      this.default_feet_pos[index][1] + sin(this.phase_time * Math.PI) * this.gait_state.step_height
    this.body_state.feet[index][2] = this.body_state.feet[index][2] + delta_pos[2]
    return this.body_state.feet[index]
  }
}

export class FourPhaseWalkState extends PhaseGaitState {
  protected name = 'Four phase walk'
  protected num_phases = 4
  protected phase_speed_factor = 6
  protected contact_phases = [
    [1, 0, 1, 1],
    [1, 1, 1, 0],
    [1, 1, 1, 0],
    [1, 0, 1, 1]
  ]
  protected swing_stand_ratio = 1 / (this.num_phases - 1)

  begin() {
    super.begin()
  }

  end() {
    super.end()
  }

  step(body_state: body_state_t, command: ControllerCommand, dt: number = 0.02) {
    return super.step(body_state, command, dt)
  }
}

export class EightPhaseWalkState extends PhaseGaitState {
  protected name = 'Eight phase walk'
  protected num_phases = 8
  protected phase_speed_factor = 4
  protected contact_phases = [
    [1, 0, 1, 1, 1, 1, 1, 1],
    [1, 1, 1, 1, 1, 0, 1, 1],
    [1, 1, 1, 1, 1, 1, 1, 0],
    [1, 1, 1, 0, 1, 1, 1, 1]
  ]
  protected shifts = [
    [-0.05, 0, -0.2],
    [0.3, 0, 0.2],
    [-0.05, 0, 0.2],
    [0.3, 0, -0.2]
  ]
  protected swing_stand_ratio = 1 / (this.num_phases - 1)

  begin() {
    super.begin()
  }

  end() {
    super.end()
  }

  step(body_state: body_state_t, command: ControllerCommand, dt: number = 0.02) {
    return super.step(body_state, command, dt)
  }
}

export class BezierState extends GaitState {
  protected name = 'Bezier'
  protected phase = 0
  protected phase_num = 0
  protected step_length: number = 0
  protected stand_offset = 0.75
  offset = [0, 0.5, 0.5, 0]

  begin() {
    super.begin()
  }

  end() {
    super.end()
  }

  step(body_state: body_state_t, command: ControllerCommand, dt: number = 0.02) {
    super.step(body_state, command, dt)
    this.step_length = Math.sqrt(this.gait_state.step_x ** 2 + this.gait_state.step_z ** 2)
    if (this.gait_state.step_x < 0) {
      this.step_length = -this.step_length
    }
    this.update_phase()
    this.update_feet_positions()
    return this.body_state
  }

  update_phase() {
    this.phase += this.dt * this.gait_state.step_velocity * 2
    if (this.phase >= 1) {
      this.phase_num += 1
      this.phase_num %= 2
      this.phase = 0
    }
  }

  update_feet_positions() {
    for (let i = 0; i < 4; i++) {
      this.body_state.feet[i] = this.update_foot_position(i)
    }
  }

  update_foot_position(index: number): number[] {
    let phase = this.phase + this.offset[index]
    if (phase >= 1) {
      phase -= 1
    }
    this.body_state.feet[index][0] = this.default_feet_pos[index][0]
    this.body_state.feet[index][1] = this.default_feet_pos[index][1]
    this.body_state.feet[index][2] = this.default_feet_pos[index][2]
    return phase <= this.stand_offset ?
        this.stand_controller(index, phase / this.stand_offset)
      : this.swing_controller(index, (phase - this.stand_offset) / (1 - this.stand_offset))
  }

  stand_controller(index: number, phase: number) {
    const depth = this.gait_state.step_depth
    return this.controller(index, phase, stance_curve, depth)
  }

  swing_controller(index: number, phase: number) {
    const height = this.gait_state.step_height
    return this.controller(index, phase, bezier_curve, height)
  }

  controller(
    index: number,
    phase: number,
    controller: (length: number, angle: number, ...args: number[]) => number[],
    ...args: number[]
  ) {
    let length = this.step_length / 2
    let angle = Math.atan2(this.gait_state.step_z, this.step_length) * 2
    const delta_pos = controller(length, angle, ...args, phase)

    length = this.gait_state.step_angle * 2
    angle = yawArc(this.default_feet_pos[index], this.body_state.feet[index])

    const delta_rot = controller(length, angle, ...args, phase)

    this.body_state.feet[index][0] += delta_pos[0] + delta_rot[0] * 0.2
    this.body_state.feet[index][2] += delta_pos[2] + delta_rot[2] * 0.2
    if (this.gait_state.step_x || this.gait_state.step_z || this.gait_state.step_angle)
      this.body_state.feet[index][1] += delta_pos[1] + delta_rot[1] * 0.2

    return this.body_state.feet[index]
  }
}

const stance_curve = (length: number, angle: number, depth: number, phase: number): number[] => {
  const X_POLAR = Math.cos(angle)
  const Y_POLAR = Math.sin(angle)

  const step = length * (1 - 2 * phase)
  const X = step * X_POLAR
  const Z = step * Y_POLAR
  let Y = 0

  if (length !== 0) {
    Y = -depth * Math.cos((Math.PI * (X + Y)) / (2 * length))
  }
  return [X, Y, Z]
}

const yawArc = (default_foot_pos: number[], current_foot_pos: number[]): number => {
  const foot_mag = Math.sqrt(default_foot_pos[0] ** 2 + default_foot_pos[2] ** 2)
  const foot_dir = Math.atan2(default_foot_pos[2], default_foot_pos[0])
  const offsets = [
    current_foot_pos[0] - default_foot_pos[0],
    current_foot_pos[2] - default_foot_pos[2],
    current_foot_pos[1] - default_foot_pos[1]
  ]
  const offset_mag = Math.sqrt(offsets[0] ** 2 + offsets[2] ** 2)
  const offset_mod = Math.atan2(offset_mag, foot_mag)

  return Math.PI / 2.0 + foot_dir + offset_mod
}

const bezier_curve = (length: number, angle: number, height: number, phase: number): number[] => {
  const control_points = get_control_points(length, angle, height)
  const n = control_points.length - 1

  const point = [0, 0, 0]
  for (let i = 0; i <= n; i++) {
    const bernstein_poly = comb(n, i) * Math.pow(phase, i) * Math.pow(1 - phase, n - i)
    point[0] += bernstein_poly * control_points[i][0]
    point[1] += bernstein_poly * control_points[i][1]
    point[2] += bernstein_poly * control_points[i][2]
  }
  return point
}
const get_control_points = (length: number, angle: number, height: number): number[][] => {
  const X_POLAR = Math.cos(angle)
  const Z_POLAR = Math.sin(angle)

  const STEP = [
    -length,
    -length * 1.4,
    -length * 1.5,
    -length * 1.5,
    -length * 1.5,
    0.0,
    0.0,
    0.0,
    length * 1.5,
    length * 1.5,
    length * 1.4,
    length
  ]

  const Y = [
    0.0,
    0.0,
    height * 0.9,
    height * 0.9,
    height * 0.9,
    height * 0.9,
    height * 0.9,
    height * 1.1,
    height * 1.1,
    height * 1.1,
    0.0,
    0.0
  ]

  const control_points: number[][] = []

  for (let i = 0; i < STEP.length; i++) {
    const X = STEP[i] * X_POLAR
    const Z = STEP[i] * Z_POLAR
    control_points.push([X, Y[i], Z])
  }

  return control_points
}

const comb = (n: number, k: number): number => {
  if (k < 0 || k > n) return 0
  if (k === 0 || k === n) return 1
  k = Math.min(k, n - k)
  let c = 1
  for (let i = 0; i < k; i++) {
    c = (c * (n - i)) / (i + 1)
  }
  return c
}