20/10/2009 IVR Herrmann IVR: Introduction to Control OVERVIEW Control systems Transformations Simple control algorithms

20/10/2009 IVR Herrmann History of control Boulton and Watt’s governor  J. C. Maxwell (1868) On Governors. Wright Brothers (1899) pilot control rather than “inherent stability” flight = wings + engines + control

20/10/2009 IVR Herrmann Examples of Control Pilot control Cruise control Robot control Electronics Power control Thermostat Fire control Process control Space craft control Homeostasis & biological motor control Control in economy

20/10/2009 IVR Herrmann Control Example Dynamical system (plant) Continuous states Physical inputs and outputs (to the system) Control actuators Controller A room (containing air) Temperature at certain points in the room Heater and measurement device A way of switching the heater on or off Thermostat

20/10/2009 IVR Herrmann Questions & Problems What control strategy? Stability  Does the system really behave as desired? Controlability and observability  Are the critical variables accessible and measurable Delays  Is the measurement up to date, when does the control take effect? Efficiency  Can the same effect be achieved with less effort? Adaptivity  Is the control strategy appropriate for changing conditions?

20/10/2009 IVR Herrmann Controller ‘A device which monitors and affects the operational conditions of a given dynamical system’ The controller receives “outputs” and adjusts “input” variables. It may also receive signals from a (human) operator or from another controller Controllers often affect the “outputs” to stay close to a desired setpoint (homeostasis) “Input” from the controlled system can serve as feedback telling the controller to what extend the control goal was achieved Controller System input output

20/10/2009 IVR Herrmann Dynamical systems Differ from standard computational view of systems: – Perception-Action loop rather than input → processing → output – Analog vs. digital, thus set of states describe a state-space, and behaviour is a trajectory On-going debate whether human cognition is better described as computation or as a dynamical system (e.g. van Gelder, 1998)‏

20/10/2009 IVR Herrmann The control problem How to make a physical system (such as a robot) function in a specified manner? Particularly when: The function would not happen naturally The system is subject to a large class of changes e.g. get the mobile robot to a goal, get the end-effector to a position, move a camera…

20/10/2009 IVR Herrmann “Bang-bang” control Simple control method is to have physical end-stop… Stepper motor is similar in principal: M off

20/10/2009 IVR Herrmann The control problem For given motor commands, what is the outcome? For a desired outcome, what are the motor commands? From observing the outcome, how should we adjust the motor commands to achieve a goal? Motor command Robot in environment Outcome Goal = Forward model = Inverse model = Feedback control Action

20/10/2009 IVR Herrmann Want to move robot hand through set of positions in task space: X(t) X(t) depends on the joint angles in the arm A(t) A(t) depends on the coupling forces C(t) delivered by transmission from motor torques T(t) T(t) produced by the input voltages V(t) A less-than-perfect robotic arm

20/10/2009 IVR Herrmann The control problem Depends on: Kinematics and geometry: Mathematical description of the relationship between motions of motors and end effector as transformation of coordinates Dynamics: Actual motion also depends on forces, such as inertia, friction, etc… V(t) T(t) C(t) A(t) X(t) command voltage torque force angle position camera

20/10/2009 IVR Herrmann The control problem Forward kinematics is not trivial but usually possible Forward dynamics is hard and at best will be approximate But what we actually need is backwards kinematics and dynamics Difficult! V(t) T(t) C(t) A(t) X(t)

20/10/2009 IVR Herrmann Inverse model (V given X) Solution might not exist Non-linearity of the forward transform Ill-posed problems in redundant systems Robustness, stability, efficiency,... Partial solution and their composition V(t) T(t) C(t) A(t) X(t)

20/10/2009 IVR Herrmann Beyond Inverse Models Feed-back control Dynamical systems Adaptive control Learning control 1788 by James Watt following a suggestion from Matthew Boulton

20/10/2009 IVR Herrmann Problem: Non-linearity In general, we have good formal methods for linear systems Reminder: Linear function: In general, most robot systems are non-linear x F(x)

20/10/2009 IVR Herrmann Kinematic (motion) models Differentiating the geometric model provides a motion model (hence sometimes these terms are used interchangeably) y = F(x) This may sometimes be a method for obtaining linearity (i.e. by looking at position change in the limit of very small changes) if x=x(y)

20/10/2009 IVR Herrmann Dynamic models Kinematic models neglect forces: motor torques, inertia, friction, gravity… To control a system, we need to understand the continuous process Start with simple linear example: Battery voltage V B Vehicle speed s ? VBVB IR e

20/10/2009 IVR Herrmann A fairly simple control algorithm Compensator High-frequency oscillator Compensator in order to determine the effector characteristics Effector High pass filter Control of the compensator characteristics Addition N. Wiener: Cybernetics, 1948

20/10/2009 IVR Herrmann K = Σ c i x i e.g. x pred = x old System: dx/dt = f(x) System + Controller What if system description is not analytically given? Stabilizing controller for box pushing or wall-following more complex behaviors for more complex predictors A Simple Controller

20/10/2009 IVR Herrmann How to find better parameters c i in K = Σ c i x i ? Perform “test actions” at both sides of the trajectory works best in 1D (e.g. for steering) A Simple Controller c expl = c + a sin(w t) Δc = short-term average

20/10/2009 IVR Herrmann Summary Control systems Calculating control is hard Controlling by probing Standard control schemes (next time)