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Trajectory Planning: For smooth and efficient motion, a robot’s path is not just a sequence of points but a
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                        continuous trajectory (a smooth curve in space over time). Dynamics helps in planning these trajectories to avoid
                        excessive forces, vibrations, and jerky movements, ensuring precise and energy-efficient motion.
                        Force Control: In  tasks  requiring interaction  with the environment  (e.g.,  polishing,  assembly  with tight  fits),
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                        dynamics is used to precisely control the forces exerted by the robot on its surroundings, preventing damage.
                    Example: When a robotic arm swings quickly to place an object, dynamics calculations predict the inertia forces
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                    that will act on its joints. This helps the control system anticipate these forces and command the motors to apply the
                    correct counter-torques to ensure smooth, controlled movement without overshooting or vibrating.

                 Control Strategies for Manipulator Arms
                 Beyond  the basic control loops (like PID control), manipulators employ advanced strategies to achieve  their
                 complex tasks.

                 Joint Space Control vs. Task Space Control
                    Joint Space Control: The controller directly regulates the position or velocity of each individual joint. This is simpler
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                    to implement.
                    Task Space Control (Cartesian Control): The controller directly manipulates the position and orientation of the end-
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                    effector in Cartesian (x, y, z) space. This is more intuitive for programming tasks (e.g., “move gripper to x=1, y=2, z=3”)
                    but requires constant inverse kinematics calculations by the controller to translate task space commands into joint
                    commands.
                    Practical Use: Most industrial robots are programmed in task space, but their underlying controllers use complex
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                    algorithms to convert these into joint movements.

                 Trajectory Planning and Control

                    Concept: Instead of just moving from point A to point B abruptly, robots follow a carefully planned trajectory, which
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                    specifies the position, velocity, and acceleration of the end-effector (and often the intermediate joints) over time. This
                    ensures smooth, efficient, and jerk-free motion.
                    Control  Strategy: Control  algorithms  constantly  monitor  the  robot’s  actual  position  and velocity  and adjust
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                    motor commands to make the robot follow the planned trajectory as closely as possible, even in the presence of
                    disturbances.
                    Practical Use: Essential for tasks like continuous welding (where the torch must move smoothly along a seam),
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                    painting (for uniform coating), and assembly (for delicate insertion without damaging parts).
                 Force Control and Compliance

                    Concept: Beyond just controlling position, some advanced manipulators can control the force they apply to an object
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                    or surface. Compliance is the ability of the robot to yield or give way when it encounters an external force.
                    Control Strategy: This often involves using force-torque sensors at the wrist or end-effector. The control system
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                    continuously  measures  the interaction  forces and adjusts  the robot’s  movement  or applied  force to  maintain  a
                    desired contact force or to “feel” its way into a tight fit.
                    Practical Use:
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                        Assembly: Inserting a peg into a hole with a tight fit, where the robot needs to apply a certain force but not too
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                        much to avoid jamming or breaking.
                        Polishing/Grinding: Maintaining a constant contact force with the workpiece to ensure uniform material removal.
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                        Human-Robot  Collaboration (Cobots): If  a cobot  accidentally  touches  a human, force control  allows it  to
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                        immediately detect the contact and limit the force, ensuring safety.


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                                                                                                Applications of Robotic Systems
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