model predictive control
In plain wordsA control method that repeatedly plans the best moves a few seconds ahead using a model of the machine, carries out only the first move, then plans again with fresh measurements.
A control strategy that, at every time step, uses a dynamics model to predict a system's behavior over a finite future horizon, solves an optimization problem for the sequence of inputs that minimizes a cost (tracking error, effort, energy) subject to constraints on states and inputs, applies only the first input, and then repeats from the newly measured state. This receding-horizon loop turns open-loop trajectory optimizationtrajectory optimization, n.: Calculating the best way for a robot to move over time, choosing exact positions, speeds and forces moment by moment so the motion is smooth, fast or energy-efficient and avoids obstacles. into feedback control and handles multiple inputs and outputs and hard constraints — speed limits, actuator saturation, collision avoidance — explicitly, which a PID controllerPID controller, n.: The most common automatic controller in industry. It corrects a machine using three ingredients: how far off it is now, how long it has been off, and how fast the error is changing. cannot. Its price is computation: the optimization must finish within each control period, which convex quadratic formulations, warm starts and specialized solvers make feasible at hundreds or thousands of hertz. Refineries and chemical plants have relied on MPC since the 1980s, and it now also runs in vehicles, power converters, drones, leggedlegged robot, n.: A robot that walks on legs instead of rolling on wheels, such as a four-legged 'robot dog' or a two-legged humanoid, so it can climb stairs and cross rough ground. and humanoidhumanoid robot, n.: A robot built roughly in human shape, with a head, torso, two arms and usually two legs, so that it can work in spaces and with tools designed for people. locomotionlocomotion, n.: How a robot moves itself from place to place: rolling on wheels, walking on legs, crawling, swimming or flying., and autonomous vehicleautonomous vehicle, n.: A vehicle, usually a car, truck or shuttle, that can drive itself, sensing the road, deciding what to do and steering, braking and accelerating with no human driving. motion planning. In model-based reinforcement learningmodel-based reinforcement learning, n.: Learning in which an AI agent builds, or is given, an inner simulation of how its world responds, and uses it to plan or practice in imagination before acting., planning with a learned world modelworld model, n.: An AI's internal simulation of how its world works, which lets it predict what will happen next — especially in response to its own actions — and so plan, imagine or practice without acting for real. in the same receding-horizon fashion is also called MPC.
The quadruped's MPC replans foot forces every 20 milliseconds over a half-second horizon.
Origin
Developed in the process industries in the 1970s: Jacques Richalet and colleagues' 'model predictive heuristic control' (published 1978) and Charles Cutler and Brian Ramaker's dynamic matrix control at Shell (1979–1980). The umbrella name 'model predictive control' was in general use by the late 1980s, alongside theory on the stability of receding-horizon control.
Usage note
'MPC' also abbreviates secure multi-party computationsecure multi-party computation, n.: Cryptographic methods that let several parties compute a result from their combined private data — say, an average salary — without any of them revealing its own data to the others. in cryptography; context disambiguates.
Related
- optimal controloptimal control, n.: Finding the best way to steer a system over time, such as the most fuel-efficient path for a rocket or the smoothest motion for a robot arm, by minimizing a cost while obeying the laws of motion.
- trajectory optimizationtrajectory optimization, n.: Calculating the best way for a robot to move over time, choosing exact positions, speeds and forces moment by moment so the motion is smooth, fast or energy-efficient and avoids obstacles.
- control theorycontrol theory, n.: The mathematics of making machines behave as intended by constantly measuring what they are doing and correcting them, as a thermostat, cruise control or self-balancing robot does.
- PID controllerPID controller, n.: The most common automatic controller in industry. It corrects a machine using three ingredients: how far off it is now, how long it has been off, and how fast the error is changing.
- model-based reinforcement learningmodel-based reinforcement learning, n.: Learning in which an AI agent builds, or is given, an inner simulation of how its world responds, and uses it to plan or practice in imagination before acting.
- world modelworld model, n.: An AI's internal simulation of how its world works, which lets it predict what will happen next — especially in response to its own actions — and so plan, imagine or practice without acting for real.
- locomotionlocomotion, n.: How a robot moves itself from place to place: rolling on wheels, walking on legs, crawling, swimming or flying.
- PID controllerPID controller, n.: The most common automatic controller in industry. It corrects a machine using three ingredients: how far off it is now, how long it has been off, and how fast the error is changing.
Sources
- Richalet, J., Rault, A., Testud, J. L. & Papon, J. (1978). Model predictive heuristic control: Applications to industrial processes. Automatica 14(5), 413–428.
- Rawlings, J. B., Mayne, D. Q. & Diehl, M. (2017). Model Predictive Control: Theory, Computation, and Design, 2nd ed. Nob Hill Publishing.
Mentioned in
humanoid robothumanoid robot, n.: A robot built roughly in human shape, with a head, torso, two arms and usually two legs, so that it can work in spaces and with tools designed for people., world modelworld model, n.: An AI's internal simulation of how its world works, which lets it predict what will happen next — especially in response to its own actions — and so plan, imagine or practice without acting for real., control theorycontrol theory, n.: The mathematics of making machines behave as intended by constantly measuring what they are doing and correcting them, as a thermostat, cruise control or self-balancing robot does., legged robotlegged robot, n.: A robot that walks on legs instead of rolling on wheels, such as a four-legged 'robot dog' or a two-legged humanoid, so it can climb stairs and cross rough ground., locomotionlocomotion, n.: How a robot moves itself from place to place: rolling on wheels, walking on legs, crawling, swimming or flying., model-based reinforcement learningmodel-based reinforcement learning, n.: Learning in which an AI agent builds, or is given, an inner simulation of how its world responds, and uses it to plan or practice in imagination before acting., PID controllerPID controller, n.: The most common automatic controller in industry. It corrects a machine using three ingredients: how far off it is now, how long it has been off, and how fast the error is changing., MuJoCoMuJoCo, prop. n.: A free physics simulator, now maintained by Google DeepMind, that AI researchers use to train and test simulated robots and bodies, especially with trial-and-error learning., optimal controloptimal control, n.: Finding the best way to steer a system over time, such as the most fuel-efficient path for a rocket or the smoothest motion for a robot arm, by minimizing a cost while obeying the laws of motion., trajectory optimizationtrajectory optimization, n.: Calculating the best way for a robot to move over time, choosing exact positions, speeds and forces moment by moment so the motion is smooth, fast or energy-efficient and avoids obstacles., zero moment pointzero moment point, n.: The spot on the ground beneath a walking robot where the floor's push balances out; keeping it inside the area under the robot's feet stops the robot from tipping over.