Adaptive time horizon optimization in model predictive control

Droge, Greg; Egerstedt, Magnus

doi:10.1109/acc.2011.5990855

Cited by 17 publications

(11 citation statements)

References 13 publications

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“…In light of this discussion, we will try to find the horizon that minimizes the deviations in the predicted and actual human input signals based on past data. For more details on this method for choosing control horizons, see [26]. However, as the particulars of this design method are not fundamental to the developments in this paper, we simply refer the reader to [26].…”

Section: B Adaptive Prediction Horizonsmentioning

confidence: 99%

Less Is More: Mixed-Initiative Model-Predictive Control With Human Inputs

2013

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This paper presents a new method for injecting human inputs in mixed initiative interactions between humans and robots. The method is based on a model predictive control (MPC) formulation, which inevitably involves predicting the system (robot dynamics as well as human inputs) into the future. These predictions are complicated by the fact that the human is interacting with the robot, causing the prediction method itself to have an effect on future human inputs. We investigate and develop different prediction schemes, including fixed and variable horizon MPCs and human input estimators of different orders. Through a search-and-rescue-inspired human operator study, we arrive at the conclusion that the simplest prediction methods outperform the more complex ones, i.e., in this particular case, less is indeed more.Index Terms-human-robot interaction, model-predictive control, mixed initiative initeractions.

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Section: B Adaptive Prediction Horizonsmentioning

confidence: 99%

Less Is More: Mixed-Initiative Model-Predictive Control With Human Inputs

2013

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“….) subject to the dynamics (1), the constraints (2,3,4) and the initial condition x(0) = x 0 . Assuming the minimum exists for each x 0 ∈ X, we define the optimal cost function…”

Section: Review Of Model Predictive Controlmentioning

confidence: 99%

Adaptive Horizon Model Predictive Control and Al’brekht’s Method

Krener

2020

Encyclopedia of Systems and Control

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A standard way of finding a feedback law that stabilizes a control system to an operating point is to recast the problem as an infinite horizon optimal control problem. If the optimal cost and the optmal feedback can be found on a large domain around the operating point then a Lyapunov argument can be used to verify the asymptotic stability of the closed loop dynamics. The problem with this approach is that is usually very difficult to find the optimal cost and the optmal feedback on a large domain for nonlinear problems with or without constraints. Hence the increasing interest in Model Predictive Control (MPC). In standard MPC a finite horizon optimal control problem is solved in real time but just at the current state, the first control action is implimented, the system evolves one time step and the process is repeated. A terminal cost and terminal feedback found by Al'brekht's methoddefined in a neighborhood of the operating point is used to shorten the horizon and thereby make the nonlinear programs easier to solve because they have less decision variables.Adaptive Horizon Model Predictive Control (AHMPC) is a scheme for varying the horizon length of Model Predictive Control (MPC) as needed. Its goal is to achieve stabilization with horizons as small as possible so that MPC methods can be used on faster and/or more complicated dynamic processes.

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“…which prevents the time horizon from becoming too small (i.e., the cost penalizes small time horizons). Substituting these values into (13), the particular PMPC problem to be solved is arg min…”

Section: A Experiments Setupmentioning

confidence: 99%

“…However, this formulation does not permit the cost metric to influence the time interval, which has practical performance implications. Using the formulated precision and maneuverability costs, this work formulates an appropriate PMPC cost metric and extends the work in [12], [13] to integrate a sampling horizon cost directly into the PMPC program. This paper is organized as follows: Sec.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, MPC approaches solve an optimal control problem over a time interval, utilize a portion of the controller, and re-solve the problem over the next time interval, effectively producing a state-and time-based controller. The authors of [12], [13] produce such a Parametric Model Predictive Control (PMPC) formulation. However, this formulation does not permit the cost metric to influence the time interval, which has practical performance implications.…”

Section: Introductionmentioning

confidence: 99%

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A Parametric MPC Approach to Balancing the Cost of Abstraction for Differential-Drive Mobile Robots

Paul

Egerstedt

2018

2018 IEEE International Conference on Robotics and Automation (ICRA)

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When designing control strategies for differentialdrive mobile robots, one standard tool is the consideration of a point at a fixed distance along a line orthogonal to the wheel axis instead of the full pose of the vehicle. This abstraction supports replacing the non-holonomic, three-state unicycle model with a much simpler two-state single-integrator model (i.e., a velocitycontrolled point). Yet this transformation comes at a performance cost, through the robot's precision and maneuverability. This work contains derivations for expressions of these precision and maneuverability costs in terms of the transformation's parameters. Furthermore, these costs show that only selecting the parameter once over the course of an application may cause an undue loss of precision. Model Predictive Control (MPC) represents one such method to ameliorate this condition. However, MPC typically realizes a control signal, rather than a parameter, so this work also proposes a Parametric Model Predictive Control (PMPC) method for parameter and sampling horizon optimization. Experimental results are presented that demonstrate the effects of the parameterization on the deployment of algorithms developed for the single-integrator model on actual differential-drive mobile robots.

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Adaptive time horizon optimization in model predictive control

Cited by 17 publications

References 13 publications

Less Is More: Mixed-Initiative Model-Predictive Control With Human Inputs

Less Is More: Mixed-Initiative Model-Predictive Control With Human Inputs

Adaptive Horizon Model Predictive Control and Al’brekht’s Method

A Parametric MPC Approach to Balancing the Cost of Abstraction for Differential-Drive Mobile Robots

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