Control of today's sophisticated robot arms, regardless of their size or power, often requires simultaneous management along multiple axes for their motion control. Modern electronics–the motors, power-switching devices (Metal-Oxide Semiconductor Field-Effect Transistors [MOSFETs] or Insulated-Gate Bipolar Transistors [IGBTs]), device drivers, control systems (now digital, formerly all analog), and feedback sensors–now make achieving precise motion control easier than it was just a few years ago (Figure 1). At the same time, however, the demands on system performance have increased dramatically, so the overall project is as difficult as ever.

Figure 1: A basic motion-control system for robotics includes algorithm-execution functions, motor drivers, power devices, and a feedback path; mechanical linkages, motor, and sensor (in most cases); and voltage and current measurement and control at key points. (Source: National Instruments)

Nonetheless, there's one unavoidable fact: Robotics is largely a mechanical function, so the realities of such systems must be part of the control loop. These include gear backlash, mechanical tolerances, vibration, motor performance, rotating mass inertia, momentum, flexing of mechanical structures, variable loads, and more. For these reasons, it is important to decide what type of motor is the best fit—usually the choice is between brushless DC motors and stepper motors in low/moderate power situations.

Another necessary decision is related to sensor-based feedback. Most robotic applications use some type of feedback sensor to accurately gauge the end-effector's position, and thus velocity and acceleration (recall that velocity is the time integral of position, and acceleration is the time integral of velocity). This feedback transducer can be a Hall-effect sensor, a synchro/resolver, or an optical encoder. While it is easiest to put the encoder on the motor, placing it there may not provide required data about the end-effector's actual situation, with sufficient accuracy for the application, due to mechanical issues noted above. Therefore, the sensor may need to be mounted closer to the load endpoint.

Some motion-control applications operate without a sensor, which reduces cost and mechanical complexity. Rather than using a sensor for feedback, Sensorless Field-Oriented Control (FOC, also called vector control) uses precise, synchronized readings of the current and voltage at each phase of the motor windings; FOCs then perform complicated frame-of-reference transformations and matrix calculations in real time to determine the motor's position. Eliminating the sensor reduces hardware cost, but it necessitates significant computational capability and more complex programming. Many robotic designs still prefer to use sensors because FOC does not provide the same level of confidence, credibility, and robustness that using direct-sensor readout offers.

Understanding Basic Robotic Configurations

While the general public may associate the term "robot" with a mobile, life-like servant or assistant, most robotic systems in the industrial domain are stationary and use a variety of mechanical arms and configurations to perform tasks. Among the most common arrangements are:

• The Cartesian robot, which has three linear axes of motion, one each in the x, y, and z-planes (Figure 2). This setup is used in pick and place machines, application of sealant, and basic assembly.

  
  
  

  Figure 2: The Cartesian robot is the easiest to comprehend and control because it has the simplest equations and works in the x, y, and z planes. (Source: RobotPark)

• In a cylindrical robot, all motion is confined to a cylinder-shaped zone. It combines linear motion in the y plane, linear motion in the z plane, and rotational motion around the z-axis (Figure 3). This robotic arrangement is used for assembly, tool handling, and spot welding.

  
  
  

  Figure 3: The cylindrical robot has motion along two linear axes and around one rotational axis. (Source: RobotPark)

• The spherical or polar robot combines two rotary joints and one linear joint, and the arm is connected to the base with a twisting joint (Figure 4). Motion is defined by a polar coordinates system and confined to a spherical zone. They are found in welding, casting, and tool-handling applications.

  
  
  

  Figure 4: The spherical or polar robot combines motion around two rotary axes and along one linear axis, and it requires numerous calculation-intensive transformations between coordinate frames of reference. (Source: RobotPark)

The approaches cited here offer three degrees of freedom, using a combination of linear and rotary motion; however, some applications need only one or two degrees. More advanced robotic arms or articulated robots combine additional linear and rotary motion, for almost human-like dexterity and flexibility (Figure 5). Some leading edge arms provide six, eight, or even more degrees of freedom.

Figure 5: The articulated robot arm combines multiple rotation and linear motion modes for many degrees of freedom, but it also requires careful coordination among the actuators and arms. (Source: RobotPark)

Other designs use special combinations of linear and rotary motion for application-specific situations, such as the parallelogram implementation; an implementation used for precise and rapid motion over short distances, for example, pick and place of tiny components. As the number of degrees of freedom increases, achieving rapid, smooth, accurate, and synchronized control along each of these degrees grows exponentially more challenging.

Considering Trajectory Profiles

The motion-control objective in robotics seems simple enough: Have the end-effector optimally reach its target position as quickly and accurately as possible with the supported load. Of course, there are tradeoffs involved, as in all engineering decisions, depending on the priorities associated with the optimum result in the given application.

For example, is it acceptable to accelerate and decelerate more quickly to more rapidly reach a higher velocity if the result is overshot and if there is even possible oscillation at the end point? Is it worth trading accuracy for speed, and to what extent? How are the choices of acceleration, velocity, and position related to the desired transition from position A to position B? What are the priorities and parameters that define "optimum" in a particular application?

Specialists in motion control for robotics and other motion applications have developed standard trajectory profiles that provide various ways to implement the desired tradeoff solution for a given application. All choices involve significant real-time calculation based on the present situation and feedback signal, but some impose a more substantial, high-resolution computation burden. These profiles include:

• The simple trapezoid, where the motor accelerates at a fixed rate from zero to a target velocity, stays at that velocity, and then ramps down at a fixed rate to zero velocity at the desired position (Figure 6). Higher rates might speed up the entire positioning cycle, but they might also induce sudden changes in acceleration motion, called the jerk, which, in turn, adds to inaccuracy and overshoot.

  
  
  

  Figure 6: The simplest motion-trajectory profile is the trapezoid, which has constant acceleration to the target velocity, constant path velocity, and constant deceleration between start and endpoints. (Source: Performance Motion Devices)

• The S-curve, a frequently-used enhancement to the trapezoid, where the acceleration rate ramps up from zero, then decreases as the target velocity is achieved (Figure 7). Then, as the target position is reached, the deceleration rate is ramped up and then reduced as the endpoint is near. The S-curve actually has seven distinct phases, in contrast to the three phases of the trapezoid.

  
  
  

  Figure 7: The S-curve path is more complicated than the basic trapezoid, but it eases the jerk (change in acceleration) at each transition point of the path. (Source: Performance Motion Devices)

• In contoured motion, the user establishes a set of desired positions, and the motion controller directs a smooth, jerk-free transition profile through all of these points (Figure 8). This allows the ultimate in flexibility and control, which is necessary for advanced motion situations. The required calculations of control directions to achieve smooth curve-fitting are complex and must be accomplished without loss of resolution due to rounding or truncation errors, despite the many calculations.

  
  
  

  Figure 8: The contoured-motion path allows the user to define a series of position marker points between starting and ending points, and the controller must guide the end-effector through these in a smooth curve. (Source: National Instruments)

There are other profiles in use, some of which are associated with specific application groups or industries. Regardless of the desired profile, it's one thing to want it and another to make it happen. The well-known, highly effective Proportional-Integral-Derivative (PID) closed-loop control algorithm is the most common approach used to drive the motor and end-effector to do what is wanted with high enough accuracy and precision (Reference 1).

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