Motion Planning and Control

5.   Robot motion planning and control

•  Path planning and trajectory generation

•  Control algorithms for robot motion

•  Feedback control systems

Robot Motion Planning and Control:

Robot motion planning and control are important aspects of robotics and automation that enable robots to move and perform various tasks. Robot motion planning involves generating a path or trajectory for the robot to follow, while robot motion control involves executing the planned motion and adjusting the robot's position and velocity in real-time.

Path planning and trajectory generation:

Path planning involves generating a collision-free path for the robot to follow, while trajectory generation involves determining the robot's position and velocity over time to follow the path. Some common path planning and trajectory generation algorithms include A* search, Dijkstra's algorithm, and Rapidly-exploring Random Trees (RRT).Python Example for A* Search:

python code

import numpy as np

import heapq

# Define map and start/goal positions

map = np.array([[0, 0, 0, 0],

                [0, 1, 1, 0],

                [0, 1, 1, 0],

                [0, 0, 0, 0]])

start = (0, 0)

goal = (3, 3)

# Define A* search algorithm

def astar(start, goal, map):

    heap = []

    visited = set()

    heapq.heappush(heap, (0, start, []))

    while heap:

        cost, node, path = heapq.heappop(heap)

        if node == goal:

            return path + [node]

        if node in visited:

            continue

        visited.add(node)

        for dx, dy in [(0, 1), (0, -1), (1, 0), (-1, 0)]:

            x, y = node[0] + dx, node[1] + dy

            if x < 0 or x >= map.shape[0] or y < 0 or y >= map.shape[1]:

                continue

            if map[x][y] == 1:

                continue

            cost = len(path) + 1 + np.sqrt((x - goal[0])**2 + (y - goal[1])**2)

            heapq.heappush(heap, (cost, (x, y), path + [node]))

    return None

# Generate path using A* search algorithm

path = astar(start, goal, map)

print(path)

Control algorithms for robot motion:

Robot motion control involves generating control signals to adjust the robot's position and velocity in real-time. Some common control algorithms include proportional-integral-derivative (PID) control, adaptive control, and model predictive control.

Example for PID Control:

python code

import time

import numpy as np

# Define PID controller parameters

kp = 1.0

ki = 0.1

kd = 0.01

# Define target position and initial position

target_pos = np.array([1.0, 2.0])

curr_pos = np.array([0.0, 0.0])

# Define initial error and integral term

prev_error = target_pos - curr_pos

integral = np.zeros(2)

# Define loop rate and duration

loop_rate = 10

duration = 10

# Perform PID control loop

start_time = time.time()

while time.time() - start_time < duration:

    error = target_pos - curr_pos

    integral += error

    derivative = error - prev_error

    prev_error = error

    control_signal = kp * error + ki * integral + kd * derivative

    curr_pos += control_signal / loop_rate

    print("Current position:", curr_pos)

    time.sleep(1/loop_rate)

Feedback control systems:

Feedback control systems involve measuring the robot's position 

Also Read:

            Introduction

Robotics and Automation

Sensors-Perception-Programming-Applications

Principles of Robotics and Automation

Hardware & Software in Robotics

sensing and perception

motion planning and control

manipulation and grasping

navigation and mapping

Human-robot interaction

Advanced topics

Applications of robotics

Questions and Answers

Research