This contribution presents a novel approach for nonlinear time-optimal model predictive control (MPC) based on Timed-Elastic-Bands (TEB). The TEB merges the states, control inputs and time intervals into a joint trajectory representation which enables planning of time-optimal trajectories in the context of model predictive control. Model predictive control integrates the planning of the optimal trajectory with state feedback in the control loop. The TEB approach formulates the fixed horizon optimal control problem for point-to-point transitions as a nonlinear program. The comparative analysis of the TEB approach with state-of-the-art approaches demonstrates its computational efficiency. The TEB approach generates a trajectory that approximates the analytical time-optimal trajectory in few iterations. This efficiency enables the refinement of the planned state and control sequence within the underlying closed-loop control during runtime.

Timed-Elastic-Bands for time-optimal point-to-point nonlinear model predictive control

This paper deals with novel time-optimal point-to-point model predictive control concepts for nonlinear systems. Recent approaches in the literature apply a time transformation, however, which do n...

Stabilising quasi-time-optimal nonlinear model predictive control with variable discretisation

This contribution presents a novel approach for time-optimal model predictive control. The underlying optimal control problem rests upon an adaptive, local temporal discretization of the shooting grid and automatically determines optimal switching points in the control sequence. Furthermore, the grid size is adapted online in order to solve the control problem with a minimum number of control interventions. The approach offers significant advantages for bang-bang control tasks which exhibit few transitions between a discrete set of piece-wise constant control actions. Experiments and a comparative analysis on different nonlinear control tasks demonstrate the superiority of adaptive shooting grids w.r.t. state-of-the-art approaches in model predictive control.

Sparse shooting at adaptive temporal resolution for time-optimal model predictive control

Model predictive control is a means to transit a nonlinear dynamic system from its current towards a target state subject to state and control constraints. A model-predictive controller based on Timed-Elastic-Bands (TEB-MPC) is particular suitable for time-optimal control. This contribution investigates the convergence behavior of the sparse TEB-MPC approach on two non-trivial benchmark systems under limited computational resources. It evaluates the trade-off between accuracy of the approximate optimal solution and computational efficiency. An alternative formulation of the original TEB-MPC with local transition intervals results in a higher dimensional but albeit banded problem structure. Furthermore, both formulations are compared for two different solvers, an unconstrained least-squares optimization and a primary nonlinear program. For low sampling times the former exhibits a faster rate of convergence, however the later is already superior for medium sample times. In practice, the selection of TEB-MPC realizations depends on the order and complexity of the dynamic systems contrasted with the computational resources and demands on real-time control.

Convergence analysis of time-optimal model predictive control under limited computational resources

This paper presents a novel approach for timeoptimal model predictive control. In contrast to a global uniform time scaling, the underlying optimal control problem rests upon a dynamic, local temporal discretization of the shooting grid. The approach seeks for a grid partition with minimum overall transition time. Furthermore, a multi-stage optimization iteratively adapts the number of grid points during runtime to achieve a minimum number of control interventions. A comparative analysis with previous approaches for three nonlinear control problems demonstrates the superiority of the proposed scheme. The feasibility is experimentally demonstrated for position control of a servo drive operated at 200 Hz.

Time-Optimal nonlinear model predictive control with minimal control interventions

IN the multi-billion dollar motion control industry, systems are often required to traverse along a geometric path, where the speed at which the path is traversed is not pre-determined. Such path-following tasks involve competing control objectives of maximising accuracy while minimising traversal time. Existing trajectory planning routines optimise the path speed with respect to some of these objectives. However, trajectory planning is conducted in an open loop fashion, relying on trajectory tracking controllers to achieve the desired motion. Meanwhile, closed-loop path-following control schemes do not explicitly consider the control objectives. This thesis investigates the development of closed-loop path-following control schemes based on minimisation of a cost function within a receding horizon structure. The cost function is selected to reflect the desired objectives such as minimising traversal time, and is minimised subject to the system constraints. The receding horizon formulation allows for feedback to be taken into account at each sample, in contrast to open loop trajectory planning. A receding horizon path-following control scheme is first developed with the intention of achieving time-optimal path-following. The controller is designed to advance along the path as far as possible within a finite horizon while staying exactly on the path and honouring the constraints. The conditions under which the receding horizon approach replicates the time-optimal path-following solution are identified for second order differentially flat systems. In particular, it is shown that minimum-time path-following is achieved when the horizon is sufficiently long.

A model predictive approach to optimal path-following and contouring control

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A model predictive approach to optimal path-following and contouring control