| Diana Vandenberg | 19bb9e2 | 2016-02-03 21:24:31 -0800 | [diff] [blame] | 1 | #!/usr/bin/python |
| 2 | |
| 3 | import numpy |
| 4 | |
| 5 | class TrapezoidProfile(object): |
| 6 | """Computes a trapezoidal motion profile |
| 7 | |
| 8 | Attributes: |
| 9 | _acceleration_time: the amount of time the robot will travel at the |
| 10 | specified acceleration (s) |
| 11 | _acceleration: the acceleration the robot will use to get to the target |
| 12 | (unit/s^2) |
| 13 | _constant_time: amount of time to travel at a constant velocity to reach |
| 14 | target (s) |
| 15 | _deceleration_time: amount of time to decelerate (at specified |
| 16 | deceleration) to target (s) |
| 17 | _deceleration: decceleration the robot needs to get to goal velocity |
| 18 | (units/s^2) |
| 19 | _maximum_acceleration: the maximum acceleration (units/s^2) |
| 20 | _maximum_velocity: the maximum velocity (unit/s) |
| 21 | _timestep: time between calls to Update (delta_time) |
| 22 | _output: output array containing distance to goal and velocity |
| 23 | """ |
| 24 | def __init__(self, delta_time): |
| 25 | """Constructs a TrapezoidProfile. |
| 26 | |
| 27 | Args: |
| 28 | delta_time: time between calls to Update (seconds) |
| 29 | """ |
| 30 | self._acceleration_time = 0 |
| 31 | self._acceleration = 0 |
| 32 | self._constant_time = 0 |
| 33 | self._deceleration_time = 0 |
| 34 | self._deceleration = 0 |
| 35 | |
| 36 | self._maximum_acceleration = 0 |
| 37 | self._maximum_velocity = 0 |
| 38 | self._timestep = delta_time |
| 39 | |
| 40 | self._output = numpy.array(numpy.zeros((2,1))) |
| 41 | |
| 42 | # Updates the state |
| 43 | def Update(self, goal_position, goal_velocity): |
| 44 | self._CalculateTimes(goal_position - self._output[0], goal_velocity) |
| 45 | |
| 46 | next_timestep = self._timestep |
| 47 | |
| 48 | # We now have the amount of time we need to accelerate to follow the |
| 49 | # profile, the amount of time we need to move at constant velocity |
| 50 | # to follow the profile, and the amount of time we need to decelerate to |
| 51 | # follow the profile. Do as much of that as we have time left in dt. |
| 52 | if self._acceleration_time > next_timestep: |
| 53 | self._UpdateVals(self._acceleration, next_timestep) |
| 54 | else: |
| 55 | self._UpdateVals(self._acceleration, self._acceleration_time) |
| 56 | |
| 57 | next_timestep -= self._acceleration_time |
| 58 | if self._constant_time > next_timestep: |
| 59 | self._UpdateVals(0, next_timestep) |
| 60 | else: |
| 61 | self._UpdateVals(0, self._constant_time) |
| 62 | next_timestep -= self._constant_time; |
| 63 | if self._deceleration_time > next_timestep: |
| 64 | self._UpdateVals(self._deceleration, next_timestep) |
| 65 | else: |
| 66 | self._UpdateVals(self._deceleration, self._deceleration_time) |
| 67 | next_timestep -= self._deceleration_time |
| 68 | self._UpdateVals(0, next_timestep) |
| 69 | |
| 70 | return self._output |
| 71 | |
| 72 | # Useful for preventing windup etc. |
| 73 | def MoveCurrentState(self, current): |
| 74 | self._output = current |
| 75 | |
| 76 | # Useful for preventing windup etc. |
| 77 | def MoveGoal(self, dx): |
| 78 | self._output[0] += dx |
| 79 | |
| 80 | def SetGoal(self, x): |
| 81 | self._output[0] = x |
| 82 | |
| 83 | def set_maximum_acceleration(self, maximum_acceleration): |
| 84 | self._maximum_acceleration = maximum_acceleration |
| 85 | |
| 86 | def set_maximum_velocity(self, maximum_velocity): |
| 87 | self._maximum_velocity = maximum_velocity |
| 88 | |
| 89 | def _UpdateVals(self, acceleration, delta_time): |
| 90 | self._output[0, 0] += (self._output[1, 0] * delta_time |
| 91 | + 0.5 * acceleration * delta_time * delta_time) |
| 92 | self._output[1, 0] += acceleration * delta_time |
| 93 | |
| 94 | def _CalculateTimes(self, distance_to_target, goal_velocity): |
| 95 | if distance_to_target == 0: |
| 96 | self._acceleration_time = 0 |
| 97 | self._acceleration = 0 |
| 98 | self._constant_time = 0 |
| 99 | self._deceleration_time = 0 |
| 100 | self._deceleration = 0 |
| 101 | return |
| 102 | elif distance_to_target < 0: |
| 103 | # Recurse with everything inverted. |
| 104 | self._output[1] *= -1 |
| 105 | self._CalculateTimes(-distance_to_target, -goal_velocity) |
| 106 | self._output[1] *= -1 |
| 107 | self._acceleration *= -1 |
| 108 | self._deceleration *= -1 |
| 109 | return |
| 110 | |
| 111 | self._constant_time = 0 |
| 112 | self._acceleration = self._maximum_acceleration |
| 113 | maximum_acceleration_velocity = ( |
| 114 | distance_to_target * 2 * numpy.abs(self._acceleration) |
| 115 | + self._output[1] * self._output[1]) |
| 116 | if maximum_acceleration_velocity > 0: |
| 117 | maximum_acceleration_velocity = numpy.sqrt(maximum_acceleration_velocity) |
| 118 | else: |
| 119 | maximum_acceleration_velocity = -numpy.sqrt(-maximum_acceleration_velocity) |
| 120 | |
| 121 | # Since we know what we'd have to do if we kept after it to decelerate, we |
| 122 | # know the sign of the acceleration. |
| 123 | if maximum_acceleration_velocity > goal_velocity: |
| 124 | self._deceleration = -self._maximum_acceleration |
| 125 | else: |
| 126 | self._deceleration = self._maximum_acceleration |
| 127 | |
| 128 | # We now know the top velocity we can get to. |
| 129 | top_velocity = numpy.sqrt((distance_to_target + |
| 130 | (self._output[1] * self._output[1]) / |
| 131 | (2.0 * self._acceleration) + |
| 132 | (goal_velocity * goal_velocity) / |
| 133 | (2.0 * self._deceleration)) / |
| 134 | (-1.0 / (2.0 * self._deceleration) + |
| 135 | 1.0 / (2.0 * self._acceleration))) |
| 136 | |
| 137 | # If it can go too fast, we now know how long we get to accelerate for and |
| 138 | # how long to go at constant velocity. |
| 139 | if top_velocity > self._maximum_velocity: |
| 140 | self._acceleration_time = ((self._maximum_velocity - self._output[1]) / |
| 141 | self._maximum_acceleration) |
| 142 | self._constant_time = (distance_to_target + |
| 143 | (goal_velocity * goal_velocity - |
| 144 | self._maximum_velocity * self._maximum_velocity) / |
| 145 | (2.0 * self._maximum_acceleration)) / self._maximum_velocity |
| 146 | else: |
| 147 | self._acceleration_time = ( |
| 148 | (top_velocity - self._output[1]) / self._acceleration) |
| 149 | |
| 150 | if self._output[1] > self._maximum_velocity: |
| 151 | self._constant_time = 0 |
| 152 | self._acceleration_time = 0 |
| 153 | |
| 154 | self._deceleration_time = ( |
| 155 | (goal_velocity - top_velocity) / self._deceleration) |
| 156 | |