What are manipulator robots? Understanding their Design, Types, and Applications

author avatar

Last updated on 10 Oct, 2023

What are manipulator robots? Understanding their Design, Types, and Applications

With unmatched precision and adaptability, manipulator robots have become indispensable in numerous industries reliant on automation. This article outlines their design, components, classifications, applications, and the emerging trends influencing their role in the world of robotics.

Introduction

Known for their precision and reliability, manipulator robots are indispensable assets in a myriad of industrial applications where both accuracy and repeatability are non-negotiable requirements. These sophisticated machines are designed to efficiently operate in environments that are not only challenging but often hazardous for human workers, thereby providing robust and reliable solutions particularly in the realms of manufacturing, assembly, material handling, and welding.

This article embarks on a detailed analysis of manipulator robots, methodically dissecting their intricate design elements, diverse applications, and the prospective trends likely to influence their development in the foreseeable future. It also categorizes these robots into distinct types, with each category possessing unique structural and operational characteristics that are finely tuned and adapted for specific applications and operational environments.

Understanding  the capabilities, limitations, and the specific applications the robots are best suited for is crucial for anyone looking to explore the significant roles these robots play, as well as their potential for growth and increased adoption across diverse industrial sectors in the years to come.

Further reading: What is Robotics? A Comprehensive Guide to its Engineering Principles and Applications

Components of Manipulator Robots

To better understand the functionality of manipulator robots, it is essential to examine their main components. These include the base, links, joints, actuators, sensors, and end-effectors. Each component plays a crucial role in the robot's overall performance and capabilities.

Base

The base of a manipulator robot serves as the foundation upon which the rest of the robot is built. It provides stability and support for the robot's structure, ensuring that it remains firmly anchored during operation. The design of the base is critical, as it must be able to withstand the forces and loads generated by the robot's movements and payload.

Fig. 1: Base of a manipulator robot in an industrial robotic system

When designing the base, several factors must be considered, such as the robot's size, weight, and intended application. For example, a large manipulator robot used in heavy-duty applications may require a more robust base to support the increased loads and forces. Additionally, the base must be designed to accommodate any necessary connections or interfaces, such as power supplies, control systems, or safety equipment.

In some cases, the base may be designed to allow for mobility, enabling the robot to move within its environment. This can be achieved through the use of wheels, tracks, or other locomotion systems. Mobile bases can be particularly useful in applications where the robot must navigate between multiple workstations or perform tasks in different locations within a facility.

Links

Links are the rigid components that connect the joints of a manipulator robot, forming its structure and defining its shape. They play a crucial role in determining the robot's range of motion, workspace, and overall capabilities. The design of the links directly impacts the robot's performance, as they must be able to support the forces and loads generated during operation.

When designing links, several factors must be considered, such as the material, length, and weight. The material used for the links should be strong and lightweight, as it directly affects the robot's payload capacity, speed, and energy efficiency. Common materials used for links include aluminum, steel, and carbon fiber composites, each offering different trade-offs between strength, weight, and cost.Fig. 2: Designing links and joins is a critical part of building a manipulator robot

The length of the links is another important consideration, as it determines the robot's reach and workspace. Longer links can provide a larger workspace, but they may also introduce additional challenges, such as increased weight and reduced rigidity. Conversely, shorter links can offer increased rigidity and reduced weight, but at the expense of a smaller workspace.

The weight of the links is a critical factor, as it directly impacts the robot's payload capacity, speed, and energy efficiency. Heavier links may require more powerful motors and actuators to move, resulting in increased energy consumption and reduced overall efficiency. Designers must carefully balance the weight of the links with the robot's intended application and performance requirements to ensure optimal performance.

Joints

Joints are the connecting elements between the links of a manipulator robot, allowing for relative motion between the links. They play a critical role in determining the robot's range of motion, flexibility, and overall capabilities. The design and the number of joints directly impacts the robot's performance, as they must be able to support the forces and loads generated during operation while providing the desired range of motion.

There are several types of joints commonly used in manipulator robots, including revolute, prismatic, and ball-and-socket joints. Each type of joint offers different kinematic movement capabilities and trade-offs, making them suitable for specific applications.

Revolute joints allow for rotational movement around a single axis. They are commonly used in articulated manipulator robots, where multiple revolute joints can be combined to provide a wide range of motion. Revolute joints can be designed with various ranges of motion, from a few degrees to a full 360-degree rotation, depending on the application requirements.

Prismatic joints enable linear movement along a single axis. They are often used in Cartesian and cylindrical manipulator robots, where precise linear positioning is required. Prismatic joints can be designed with various travel lengths and load capacities, depending on the robot's intended application and performance requirements.Fig. 3: Each joint plays a crucial role in delivering precise and dynamic movements in robotic applications. Prismatic Joint enabling linear motion, the Revolute Joint providing pivotal rotation, and the Spherical Ball-Socket Joint allowing multi-directional flexibility.

Ball-and-socket joints provide rotational movement around multiple axes, allowing for a high degree of flexibility and dexterity. These joints are less common in manipulator robots but can be found in some specialized applications, such as robotic hands or humanoid robots, where a wide range of motion is necessary.

Further reading: Robotic Joint: How Robotic Solution is Boosting Efficiency

When designing joints for a manipulator robot, factors such as range of motion, load capacity, and wear resistance must be considered. The choice of joint type and design will directly impact the robot's performance, flexibility, and overall capabilities, making it a critical aspect of the robot's design process.

Actuators

Actuators are the driving force behind the robot's movements, converting electrical signals into physical motion. The type of actuator used can significantly influence the robot's speed, accuracy, and efficiency. Common types include electric motors (such as servo motors and stepper motors), pneumatic actuators, and hydraulic actuators. Electric motors are often used for their high efficiency and precision, while pneumatic and hydraulic actuators might be chosen for applications requiring significant force. The selection of actuators is crucial as it directly impacts the robot's performance and suitability for different tasks and environments.

Sensors and Feedback Systems

Sensors and feedback systems are integral components of manipulator robots, enhancing their ability to interact effectively with their environment. These systems provide real-time data, allowing the robots to adjust their actions dynamically. Vision systems, for instance, enable robots to identify, sort, and handle objects, while force-torque sensors help in applying the correct amount of force during operations, preventing damage to both the robot and the objects it handles. Proximity and distance sensors allow the robot to navigate its environment, avoiding obstacles and ensuring safe operation. These feedback mechanisms are crucial for tasks requiring high precision and reliability, as they allow for continuous monitoring and adjustment of the robot's movements and actions.

End-Effector

The end-effector is the component of a manipulator robot that interacts directly with the environment or objects within its workspace. It is responsible for performing the robot's primary tasks, such as gripping, cutting, or welding. The design of the end-effector is crucial, as it must be compatible with the robot's structure and capable of handling the required payload, precision, and task-specific requirements.

There are several types of end-effectors commonly used in manipulator robots, including grippers, suction cups, and welding torches. Each type of end-effector offers different capabilities and trade-offs, making them suitable for specific applications.

Grippers are used for grasping and holding objects, and they come in various designs, such as parallel, angular, and adaptive grippers. Grippers can be designed with different gripping forces, materials, and sizes to accommodate a wide range of objects and applications. For example, a parallel gripper may be used in a pick-and-place application, while an adaptive gripper could be employed for handling objects with irregular shapes.

Suction cups are used for lifting and handling objects with smooth surfaces, such as glass or metal sheets. They rely on vacuum pressure to create a secure bond between the end-effector and the object, allowing for precise and gentle handling. Suction cups can be designed with various sizes, shapes, and materials to accommodate different object types and surface conditions.

Welding torches are specialized end-effectors used for performing welding tasks, such as arc or spot welding. They are designed to deliver the required heat and electrical current to the welding site, ensuring a strong and durable bond between the materials being joined. Welding torches must be compatible with the robot's control system and capable of handling the high temperatures and electrical currents involved in the welding process.

Further reading: What are End Effectors in Robotics? Types of End Effectors, Applications, Future

Additional Components

Other essential components include the control panel or user interface, which is vital for operator interaction and control over the robot. The power supply and distribution system are crucial for the robot’s operation, ensuring efficient energy use and distribution to all components. Cooling systems are often necessary to dissipate heat generated during operation, maintaining optimal temperatures for consistent performance. Communication systems facilitate the robot's interaction with other devices and networks, while safety features are incorporated to protect both the robot and human operators from potential harm. Maintenance and diagnostic tools are also integrated to assist in the identification and resolution of issues, ensuring longevity and reliable operation of the robot. These components collectively contribute to the robot’s functionality, efficiency, and safety in various applications.

When designing an end-effector for a manipulator robot, factors such as payload capacity, precision, and compatibility with the robot's structure must be considered. The choice of end-effector type and design will directly impact the robot's performance and overall capabilities, making it a critical aspect of the robot's design process.

Control Systems for Manipulator Robots

Robot control systems play a vital role in the operation of manipulator robots, as they govern the robot's movements and ensure that it performs its tasks accurately and efficiently. There are two main types of control systems used in manipulator robots: open-loop and closed-loop control systems. Each type offers different advantages and disadvantages, making them suitable for specific applications and performance requirements.

Open-Loop Control Systems

Open-loop control systems are characterized by their lack of feedback, meaning that the robot's movements are determined solely by the input commands provided by the controller. In an open-loop system, the controller sends a series of commands to the robot's actuators, which then execute the movements without any feedback on the actual position or performance of the robot.

The main advantage of open-loop control systems is their simplicity, as they do not require complex feedback mechanisms or sensors to operate. This can result in lower costs and reduced system complexity, making open-loop systems suitable for applications where high precision and accuracy are not critical.

However, open-loop control systems have some significant disadvantages. Without feedback, the system cannot compensate for errors or disturbances that may occur during operation, such as mechanical wear, changes in load, or external forces. This can result in reduced accuracy and repeatability, as the robot's actual position may deviate from the desired position specified by the input commands.

Open-loop control systems are typically used in applications where the required level of precision and accuracy is relatively low, and the risk of errors or disturbances is minimal. Examples of such applications include simple pick-and-place tasks, conveyor systems, or basic material handling operations.

Closed-Loop Control Systems

Closed-loop control systems, in contrast to open-loop systems, incorporate feedback mechanisms and more complex algorithms to monitor and adjust the robot's movements in real-time. In a closed-loop system, the controller sends commands to the robot's actuators, while sensors continuously measure the robot's actual position and performance. This feedback is then used by the controller to adjust the commands, ensuring that the robot's movements closely match the desired position and trajectory.

The main advantage of closed-loop control systems is their ability to compensate for errors and disturbances that may occur during operation. By continuously monitoring the robot's position and performance, the system can make adjustments to the commands, resulting in improved accuracy and repeatability. This makes closed-loop systems suitable for applications where high precision and accuracy are critical.

However, closed-loop control systems have some disadvantages. They typically require more complex hardware and software, as they rely on feedback mechanisms and sensors to operate. This can result in increased costs and system complexity, making closed-loop systems less suitable for applications where simplicity and cost-effectiveness are priorities.

Closed-loop control systems are commonly used in applications where high precision and accuracy are required, such as assembly, inspection, or machining tasks. For example, a closed-loop system might be employed in a robotic welding application, where the robot must maintain a precise position and trajectory to ensure a strong and consistent weld. In this case, the closed-loop system would continuously monitor the robot's position and make adjustments as needed to maintain the desired welding path.

Types of Manipulator Robots

Robotic manipulator arms typically have between three and six degrees of freedom, afforded by a series of joints (analogous to a shoulder, elbow, or wrist) which connect the various links of the device (analogous to an upper arm, forearm, or palm). The joints of a manipulator are usually either revolute joints or prismatic joints.[1] The type of arm determines its number of degrees of freedom, as well as its workspace (how far it can reach).

  • Revolute joint (rotary joint): rotation about one axis, i.e. twisting movement

  • Prismatic joint (linear joint): translation about one axis, i.e. extension movement

  • Cylindrical joint: rotation and translation about one axis

  • Spherical joint (ball and socket joint): three degrees of rotation

arm configurationsFig. 4: Various robotic manipulator arm configurations

Manipulator robots can be classified based on their structure and movement capabilities. Each type has its advantages and disadvantages, making them suitable for specific applications. In this section, we will explore the different types of manipulator robots, including cartesian, cylindrical, spherical, and articulated robots.

Cartesian Manipulator Robots

Cartesian manipulator robots, also known as gantry robots, have a linear design and consist of three orthogonal axes (X, Y, and Z). These robots move in straight lines along each axis, allowing for precise positioning and movement within a defined workspace. The structure of Cartesian robots typically includes linear actuators or slides, which enable the robot to move along each axis independently.

One of the main advantages of Cartesian manipulator robots is their high accuracy and repeatability. Due to their linear design, these robots can achieve positioning accuracies of up to 0.001 mm. Additionally, Cartesian robots are known for their scalability, as they can be easily customized to accommodate various workspace sizes and payload capacities.

However, Cartesian manipulator robots have some limitations. Their movement is restricted to linear paths, which may not be suitable for applications requiring complex or curved trajectories. Furthermore, the size and weight of Cartesian robots can be substantial, especially for large-scale applications, which may result in increased energy consumption and reduced overall efficiency.

Cartesian manipulator robots are commonly used in industries such as manufacturing and automation. Their precise positioning capabilities make them ideal for tasks such as pick-and-place operations, assembly, and inspection. For example, Cartesian robots are often employed in the electronics industry for the assembly of printed circuit boards (PCBs), where high accuracy and repeatability are crucial for placing small components accurately.

Cylindrical Manipulator Robots

Cylindrical manipulator robots have a cylindrical workspace and consist of a combination of linear and rotational movements. These robots typically feature a vertical linear axis (Z-axis), a radial linear axis (R-axis), and a rotational axis (θ-axis) around the vertical axis. The structure of cylindrical robots often includes a vertical column mounted on a revolute joint at the base, with an arm that can extend radially and rotate around the column.

One of the main advantages of cylindrical manipulator robots is their ability to reach around obstacles within their cylindrical workspace. This makes them suitable for applications where access to the target object may be obstructed. Additionally, cylindrical robots can provide a compact footprint, as their vertical column and radial arm design allow them to occupy less floor space compared to other robot types.

However, cylindrical manipulator robots also have some limitations. Their work envelope is confined to a cylindrical shape, which may not be suitable for applications requiring a larger or differently shaped workspace. Moreover, the accuracy and repeatability of cylindrical robots may be lower than that of Cartesian robots, as the combination of linear and rotational movements can introduce additional sources of error.

Cylindrical manipulator robots are commonly used in industries such as assembly and packaging. Their ability to reach around obstacles makes them well-suited for tasks such as loading and unloading machines, where access to the target object may be limited. For instance, cylindrical robots can be employed in the pharmaceutical industry for the assembly of medical devices or the packaging of medication, where their compact footprint and ability to maneuver around obstacles are valuable assets.

Spherical Manipulator Robots

Spherical manipulator robots, also known as polar robots, have a spherical workspace and consist of a combination of linear and rotational movements. These robot arms, much like the human arm, exhibit a remarkable range of motion and flexibility, allowing them to efficiently navigate and perform tasks within a three-dimensional workspace. These robots typically feature a radial linear axis (ρ-axis), a polar rotational axis (θ-axis), and an azimuthal rotational axis (ϕ-axis). Spherical robots come with two revolute and a prismatic joint. The structure of spherical robots often includes a base-mounted arm that can extend radially and rotate around two perpendicular axes.

One of the main advantages of spherical manipulator robots is their ability to cover a large workspace with a relatively small footprint. Their unique combination of linear and rotational movements allows them to access a wide range of positions within their spherical workspace. Additionally, spherical robots can provide a high degree of dexterity, making them suitable for applications requiring complex and precise movements.

However, spherical manipulator robots also have some limitations. Their accuracy and repeatability may be lower than that of Cartesian robots, as the combination of linear and rotational movements can introduce additional sources of error. Moreover, the complexity of their movements can make programming and control more challenging compared to other robot types.

Spherical manipulator robots are commonly used in industries such as material handling and welding. Their ability to cover a large workspace and perform complex movements makes them well-suited for tasks such as transferring objects between different locations or performing intricate welding operations. For example, spherical robots can be employed in the automotive industry for tasks such as spot welding, where their dexterity and large workspace coverage are valuable assets.

Articulated Manipulator Robots

Articulated manipulator robots, also known as robotic arms, have a complex structure consisting of multiple joints and links that allow for a wide range of motion. These robots typically feature a series of revolute joints connected by rigid links, which enable them to perform movements in multiple degrees of freedom (DOF). The structure of articulated robots often includes a base-mounted arm with multiple segments, each connected by a joint that allows for rotational movement.

One of the main advantages of articulated manipulator robots is their high degree of flexibility and dexterity. Their multiple degrees of freedom enable them to perform complex tasks and reach a wide range of positions within their workspace. Additionally, articulated robots can be designed with various numbers of joints and links, allowing for customization to suit specific application requirements.

However, articulated manipulator robots also have some limitations. Their complex structure can make them more challenging to program and control compared to other robot types. Moreover, the accuracy and repeatability of articulated robots may be lower than that of Cartesian robots, as the multiple joints and links can introduce additional sources of error.

Articulated manipulator robots are commonly used in industries such as automotive and aerospace. Their flexibility and dexterity make them well-suited for tasks requiring complex movements and precise positioning, such as assembly, painting, and inspection. For example, articulated robots can be employed in the automotive industry for tasks such as assembling engines or installing windshields, where their ability to maneuver around obstacles and reach various positions within the workspace is crucial.

Applications of Manipulator Robots

Industrial robots and more specifically, manipulator robots are widely used across various industries, offering numerous benefits such as increased productivity, precision, and safety. Certain types of robots may be more suitable for a particular application than others. For instance, SCARA robots are known for their speed and precision in palletizing and assembly tasks in various industrial applications. Choosing other types of manipulator robots would still get the work done, however, the right robot is necessary for maximum productivity and cost savings.

In this section, we will explore some of the key applications of manipulator robots, including manufacturing, assembly and packaging, material handling, and welding and cutting.

Manufacturing

Manipulator robots play a significant role in modern manufacturing processes, where their precision, speed, and repeatability make them ideal for tasks such as pick-and-place operations, assembly, and inspection. By automating these tasks, robots can help manufacturers increase productivity, reduce labor costs, and improve product quality.

For example, in the electronics industry, manipulator robots are commonly used for the assembly of printed circuit boards (PCBs). These robots can accurately place small components, such as resistors and capacitors, onto the PCBs at high speeds, ensuring consistent quality and reducing the risk of human error. Additionally, robots can be used for inspection tasks, such as checking for defects or verifying component placement, further improving product quality and reducing the need for manual inspection.Fig. 5: Industrial robots are most common in industrial manufacturing applications where the tasks can get highly repetitive

In the automotive industry, manipulator robots are employed for tasks such as welding, painting, and assembly. Robots can perform these tasks with high precision and speed, ensuring consistent quality and reducing the time required for production. Moreover, by automating these tasks, manufacturers can reduce the risk of workplace injuries and improve overall safety.

Overall, the use of manipulator robots in manufacturing processes has revolutionized the way products are made, offering numerous benefits in terms of productivity, quality, and safety.

Assembly and Packaging

Manipulator robots are widely used in assembly and packaging processes, where their precision, speed, and flexibility make them ideal for handling a variety of tasks. By automating these processes, robots can help companies reduce labor costs, improve efficiency, and maintain consistent product quality.

In assembly applications, manipulator robots can be used to pick up and place components, fasten screws, or apply adhesives, among other tasks. Their high precision and repeatability ensure that components are assembled accurately and consistently, reducing the risk of defects and improving overall product quality. For example, in the consumer electronics industry, robots can be used to assemble smartphones, tablets, or other devices, where precise component placement and alignment are critical for proper functionality.

Further reading: What are Robotic Assembly Lines? History, Components, Advantages, Limitations, Applications, and Future

In packaging applications, manipulator robots can be used for tasks such as loading and unloading products, sealing packages, or applying labels. Their speed and accuracy enable them to handle these tasks more efficiently than human workers, reducing the time required for packaging and improving overall productivity. For instance, in the food and beverage industry, robots can be used to package products such as bottles, cans, or boxes, ensuring that they are sealed and labeled correctly before being shipped to customers.

By automating assembly and packaging processes, manipulator robots can help companies increase efficiency, reduce labor costs, and maintain consistent product quality, making them an invaluable tool in these industries.

Material Handling

Manipulator robots are extensively used in material handling applications, where their speed, precision, and ability to work in hazardous or challenging environments make them an ideal solution. By automating material handling tasks, robots can help companies increase efficiency, reduce human workload, and improve overall safety.

In material handling applications, manipulator robots can be used for tasks such as transferring objects between different locations, sorting and organizing items, or loading and unloading materials. Their flexibility and adaptability enable them to handle a wide range of object sizes, shapes, and weights, making them suitable for various industries and applications.

For example, in the warehousing and logistics industry, robots can be used to pick up and place items on shelves, sort packages, or load and unload trucks. Their speed and accuracy can help companies reduce the time required for these tasks, improving overall efficiency and reducing labor costs. Additionally, by automating these tasks, companies can minimize the risk of workplace injuries caused by heavy lifting or repetitive motions.

Further reading: Material Handling Automation: A Comprehensive Guide for Engineers

In the manufacturing industry, manipulator robots can be used to transfer raw materials or finished products between different stages of the production process. Their ability to work in hazardous, or inaccessible places such as high temperatures or areas with limited access, makes them an invaluable tool for ensuring the smooth flow of materials throughout the production line.

By automating material handling tasks, manipulator robots can help companies increase efficiency, reduce human workload, and improve overall safety, making them an essential tool in a wide range of industries and applications.

Some of the manipulator robots also come with advanced Robot Operating Systems (ROS) that provide a flexible framework for developing and deploying applications. This makes the process of deploying robotic automation solutions a seamless process. Open Robotics, Boston Dynamics, ABB, Universal Robots, KUKA, Microsoft, and NVIDIA are some of the organizations involved in the development of ROS. 

Healthcare

Manipulator robots are crucial in the healthcare sector, providing unmatched precision essential for surgeries and minimizing errors. Their steady, controlled movements are necessary for procedures requiring exactness, making them vital assets in operating environments. These robots also significantly contribute to patient rehabilitation, offering controlled, repetitive exercises necessary for effective recovery, especially for stroke or spinal cord injury patients.

In pharmaceutical environments, manipulator robots are invaluable, accelerating drug discovery and handling precise tasks efficiently, thereby reducing contamination risks. For instance, tasks like pipetting and vial capping are executed with increased efficiency and accuracy. With the advent of telemedicine, manipulator robots are facilitating remote robotic surgeries, accurately replicating surgeon movements, and providing specialized care in remote locations.

Understanding the applications and functionalities of manipulator robots in healthcare is imperative for professionals in the field. Their precision, efficiency, and adaptability make them indispensable tools in enhancing patient care and driving innovation in medical practices globally.

Conclusion

Manipulator robots have become an integral part of various industries, offering numerous benefits such as increased productivity, precision, and safety. Their diverse designs, including Cartesian, cylindrical, spherical, and articulated robots, enable them to perform a wide range of tasks in applications such as manufacturing, assembly, material handling, and welding. By understanding the components, control systems, and applications of manipulator robots, we can appreciate their importance and potential for continued growth in the years to come.

Frequently Asked Questions (FAQs)

1. What are the main types of manipulator robots?

The main types of manipulator robots are Cartesian, cylindrical, spherical, and articulated robots. Each type has its advantages and disadvantages, making them suitable for specific applications.

2. What are the key components of a manipulator robot?

The key components of a manipulator robot include the base, links, joints, and end-effector. Each component plays a crucial role in the robot's overall performance and capabilities.

3. What is the difference between open-loop and closed-loop control systems?

Open-loop control systems do not use feedback and rely solely on input commands to control the robot's movements. Closed-loop control systems, on the other hand, incorporate feedback mechanisms to monitor and adjust the robot's movements in real-time, resulting in improved accuracy and repeatability.

4. In which industries are manipulator robots commonly used?

Manipulator robots are commonly used in industries such as manufacturing, assembly and packaging, material handling, and welding and cutting. Their precision, speed, and flexibility make them ideal for a wide range of tasks in these industries.

5. What are some future trends in manipulator robots?

Future trends in manipulator robots include the development of more advanced control systems, the integration of artificial intelligence and machine learning technologies, and the use of new materials and designs to improve performance and efficiency. These trends have the potential to further expand the capabilities and applications of manipulator robots in various industries.

References

[1] Lewis FL, Dawson DM, Abdallah CT. Robot manipulator control: theory and practice. CRC Press; 2003 Dec 12.

[2] Gallardo-Alvarado J, Gallardo-Razo J. Robot manipulators. In: Gallardo-Alvarado J, Gallardo-Razo J, editors. Emerging Methodologies and Applications in Modelling, Identification and Control, Mechanisms. Academic Press; 2022. p. 421-488. Available from: https://doi.org/10.1016/B978-0-32-395348-1.00034-X

[3] Fadali MS, Visioli A. Introduction to digital control. In: Fadali MS, Visioli A, editors. Digital Control Engineering. 3rd ed. Academic Press; 2020. p. 1-8. Available from: https://doi.org/10.1016/B978-0-12-814433-6.00001-6

[4] Siciliano, B., Sciavicco, L., Villani, L., & Oriolo, G. (2008). Robotics: Modelling, Planning and Control.

More by Ravi Rao

Meet Ravi, a backend engineer at the world's largest IT services company. He collaborates with solution architects and clients on a massive digital transformation project. Graduating in electrical engineering from a public university in India, Ravi ranked among the top 0.32% of 18,000+ students. His...