Control Systems for Application in Robotics

Control Systems for Application in Robotics Dara Kusic Department of Computer Science University of Pittsburgh, Pittsburgh, PA 15260 Honors Robotics February 8, 2010

OUTLINE • Control problems in robotics • Centralized, single robot control • Open-loop & closed-loop (feedback) control • Model predictive control • Decentralized, multiple robot control • Advanced control topcis • Machine learning and adaptive control

Control problems in robotics • Localization -- how does a mobile robot know where it is? • Navigation – how does a mobile robot reach its destination? • Actuation – how does the robot manuver its end effector to make contact with a target? • Coordination – how to robot swarms cooperate to solve a common task?

Common control objectives • Tracking -- e.g. maintain a specified distance from a moving target • Disturbance rejection – e.g. maintain dead-reckoning mode under windy conditions • Optimization – e.g. deliver the daily mail to cubicles in the shortest path possible

OUTLINE Control problems in robotics Centralized, single robot control Open-loop & closed-loop (feedback) control Model predictive control Decentralized, multiple robot control Advanced control topcis Machine learning and adaptive control

Single robot open-loop control • Control input is computed only from current state and a model of the system • The use of odometry is an example of open loop control, where the robot position is estimated via data from velocity actuators, integrated over time • Advantage: Simple to use – requires no data from sensors to be integrated in the control scheme • Disadvantage: Error-prone due to inaccuracies in system model and environmental disturbances • Open-loop control does not have the capacity for error-correction noise disturbance output signal setpoint controller system

Closed-loop or feedback control • Control input is computed from current state and measurements of an observable output of the system • Automobile cruise control is a typical example of feedback control, where acceleration or deceleration is updated using the error from the desired velocity from the actual velocity • Advantage: More accurate than open-loop control particularly in uncertain operating conditions; no model requried • Disadvantage: More costly due to the use of measurement instrumentation and sensors; noisy data noise disturbance error setpoint output signal controller system observed value

Feedback control in discrete systems • Robotic systems will typically operate in the discrete domain • Design choices of sampling time must be carefully considered • At what frequency to sample system output? • At which frequency to deliver control input? • Which frequency should be smaller?

On-off feedback ontrol • For example, a thermostat, when the heater is either on or off • Depending on the frequency of control, overhead of on-off, etc, this could cause overshoots and undershoots (ripples) • Oscillation is a common behavior in control systems • Hysteresis may be unacceptable in the system: e.g. To maintain a temperature of 20 °C, one might set a thermostat to turn on the furnace when the temperature drops below 18 °C, and turn it off when the temperature exceeds 22 °C. If the temperature is 21 °C, then it is not possible to predict whether the furnace is on or off without knowing the history of the temperature.

Example of control phenomena Ripple overshoot • Increase the quantity until you get to the setpoint • Temperature, angle, speed, etc • If too much, reduce the quantity, until the setpoint • Design tradeoff between the number and magnitude of the osillations, and the rise time. setpoint

Control properties • Stability – for any bounded input, the output of the system is also bounded • Accuracy – the proximity of the measured output of the system to its desired operating point in its steady-state • Overshoot – how far the control input causes the system to overreach its operating point • Rise time – the time to respond to a disturbance or change in setpoint • Settlng time – the time to converge to the desired operating point

PID feedback control • Proportional-Integral-Derivative control • Proportional value reacts to the current error between the desired setpoint and the measured quantity • Integral value reacts to the cumulative error • Derivative value reacts to the recent change in the error • May implement only P control, I control, D control, or any combination therein • Each type of control, acting independently, will exhibit different behaviors and limitations

PID feedback ontrol • The discrete form of PID control can be represented by the following:

Characterization of P controllers • Proportional controllers will have short rise and settling times, but also a steady-state error • As P increases, the rise time and error will decrease, but the overshoot will increase. To large a value of P will result in instability. Process variable Control variable

Characterization of I controllers • Integral controllers will zero steady-state error, but have longer settlings times. • As P increases, the rise time and error will decrease, but the overshoot will increase. To large a value of P will result in instability.

Characterization of D controllers • Derivative can reduce oscillations but add to the settling time. • Typically, D controllers are used for gradual control in long-running processes such as thermal or chemical.

Characterization of PI controllers • Adding an integral term to a proportional controller will reduce the rise-time and steady-state error, but may introduce additional overshoot and oscillations

Characterization of PID controllers • Adding a derivative term can damp the oscillations, and will generally have little effect on the rise time and settling time.

Summary of effects as term increases

PID tuning • In a real system, PID tuning can be something of an art • Overhoot thresholds • Oscillation tolerance • Rise time constraints • There are, however, some ‘rules of thumb’ for initial values (as applied to the ideal parallel form presented herein) • Start with the integral and derivative terms set to zero, then add integral until error is zero, and deriative until oscillations decrease

Cascading control • Cascading control is when one controller, an outer, or primary controller, controls an inner, or secondary controller. The cascade can continue recursively to the nth inner controller. • Cascading control is implemented when a process with slow dynamics, such as temperature in a large tank, is influenced by a process with fast dynamics, such as the flow rate of hot water into the tank. The primary controller will determine the setpoint for the secondary controller. For example, if the primary controller wishes to raise the tank temperature to 100 Celcius, it will determine a setpoint for the flow rate of steam into the tank. The secondary controller will regulate the valve position to maintain that setpoint. • In robotics, a primary controller might wish to maintain a constant velocity by determining a setpoint acceleration for a secondary controller. The secondary controller will track that acceleration by modulating the pulse rate to the motors.

Model predictive or receding horizon control • Advantages • Systematic use of predictions to improve control performance • Inherent compensation for dead times • Multi-objective and non-linear optimization • Disadvantages • Requires an accurate system model, predictive filter • Computationally expensive state-space control

k+1 k+3 k+4 k+2 • Use a system model to estimate future system states, over a prediction horizon Model predictive or receding horizon control u0 … u0 un • Obtain the sequence of control inputs that maximize (or minimize) an objective function … x(k) un u0 … un • Apply the first control input in the sequence; discard the rest • Repeat the process at time k+1

Statistical filtering • Measurement data may be noisy with statistical variations • Should the robot react to every perceived disturbance? • Statistical filters can smooth noisy data • Exponentially weighted moving averages • Adjusted averages for weighted standard deviation • Outlier rejection (low-pass filtering)

Fully decentralized, multi-robot control • Multiple robots may need to cooperate to achieve a common goal, e.g. Take possession of a soccer ball and attempt to score • What would happen if all the robots simultaneously sought after the goal? • Cell phone transmission protocols such as CSMA can provide inspiration for disbursing actions (e.g. via exponentially weighted action timers) • Distributed and decentralized control algorithms are typically used for coordination tasks • Implicit communication via global data objects • Explicit communication via unicast, multicast, or broadcast in order of increasing bandwidth. Forwarding of messages can occur by default, or by some more conservative algorithm such as gossip

Hierarchical control Global Control • Each robot swarm has one leader, either human or robotic, making global decisions • Each robot in the swarm has a localized controller for autonomous actions Controllable Parameters: e.g. Active swarm memebrs Swarm Leader Messaging Bus Robot swarm Local controller Local controller Local controller Local controller Local controller Robot Robot Robot Robot Robot 1 2 3 4 C Off Decommissioned Messaging Bus Robots Drones Log System Drone Drone

Machine learning • Conrtrols with high computational demand or unidentified systems can benefit from machine learning algorithms • Neural networks • Require discretiziation as output is continuous • Regression trees • Compared to NN, large storage requirement, but faster execution • Bayesian networks • Reinforcement learning • The basic approach is to simulate the system under a range of conditions, and collect the data for training the approximation structure • Approximating structures can be applied to as a system model, or as the controller itself

Online model refinement Adaptation algorithm System • A neural network can be re-trained online to improve the accuracy of the approximation model -1 z -1 -1 z z Predictive Neural network System System filter -1 z -1 -1 z z • The re-training process is computationally expensive can be offloaded S + - System System Optimizer System

Taxonomy of fault handling System Reliability Redundant systems Non-redundant systems Fault-tolerant systems Fault detection Fault avoidance Dyamic redundancy Masking redundancy Online detection/masking Reconfig. Retry Repair

Fault-masking control • Any component of the control system (sensor, actuator, control logic) can be implemented redundantly to provide assurance of correct operation Module 1 Input Output Module 2 Voter Module 3 Spare 1

Additional resources • Feedback control: • HELLERSTEIN, J. L., DIAO, Y., PAREKH, S., AND TILBURY, D. M. Feedback Control of Computing Systems. Wiley-IEEE Press, 2004. • Neural networks: • HAYKIN, S. Neural Networks: A Comprehensive Foundation. Prentice-Hall, 1999. • Fault-tolerant systems: • STOREY, N. Safety-critical Computing Systems. Addison-Wesley, 1996.

Control Systems for Application in Robotics