OPTIPLAN: A Matlab Toolbox for Model Predictive Control with Obstacle Avoidance

Janeček, Filip; Klaučo, Martin; Kalúz, Martin; Kvasnica, Michal

doi:10.1016/j.ifacol.2017.08.057

Cited by 15 publications

(15 citation statements)

References 8 publications

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“…Since the sum of positive terms is not zero iff at least a term is not zero, we have that ∑ i | •, (i) − (i)| · | •, (i) − + (i)| > 0 is a necessary and sufficient condition for x + ∉ ( •, , ). Repeating for all •, j ∈ Σ • leads to (24), thus concluding the proof.…”

Section: Mixed Integer Representations For the Overapproximated Shadomentioning

confidence: 67%

“…Recalling Remark 8, we note that (23a) to (24) are linear only if is known. If is itself an unknown parameter, we propose the following corollary.…”

Section: Mixed Integer Representations For the Overapproximated Shadomentioning

confidence: 99%

“…Proof. The proof is a direct application of Lemma 3 to the relations of Proposition 4, ie, out of the enumeration of inequalities from (26) and (27) the only ones that are nonredundant are those for which • = and these are exactly (23a) to (24).…”

Section: Mixed Integer Representations For the Overapproximated Shadomentioning

confidence: 99%

“…Our corner cutting avoidance procedure is part of an online scheme where collision avoidance is dealt with "as it comes." Alternatives popular in the community consider a priori path planning followed by subsequent tracking (eg, via command governors 22,23 or dynamic constraint activation 24 ). These approaches have the advantage of guaranteed feasibility (under certain assumptions) but may also make conservative restrictions on the agents' allowed positions.…”

Section: Study Case: An Mpc Problem With Corner Cutting Avoidancementioning

confidence: 99%

“…As for (33a) to (33c), we introduce the sign tuples of the obstacles and of the feasible tuple characterizing the current position in (24). In each of the resulting inequalities, at least a term has to be strictly positive.…”

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confidence: 99%

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Exact and overapproximated guarantees for corner cutting avoidance in a multiobstacle environment

Stoican

Prodan

Grøtli

2018

Intl J Robust & Nonlinear

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The corner cutting avoidance problem is an important but often overlooked part of motion planning strategies. Obstacle and collision avoidance constraints are usually imposed at the sampling time without regards to the intrasample behavior of the agent. Hence, it is possible for an agent to "cut the corner" of an obstacle while apparently respecting the constraints. This paper improves upon state of the art by providing exact and overapproximated descriptions of the undershadow (and of its complement, the visible) region generated by an agent against obstacles. We employ a hyperplane arrangement construction to handle multiple obstacles simultaneously and provide piecewise descriptions of the regions of interest and parametrizations of the corner cutting conditions (useful, eg, in finite horizon optimization problems). Mixed-integer representations are used to describe the regions of interest, leading in the overapproximated case to binary-only constraints. Illustrative proofs of concept, comparisons with the state of the art, and simulations over a standard multiobstacle avoidance problem showcase the benefits of the proposed approach. KEYWORDS corner cutting problem, hyperplane arrangement, mixed-integer programming (MIP), model predictive control (MPC), multiobstacle avoidanceRecent advances in computational resources and the proliferation of (semi)autonomous vehicles has lent new interest to the topic of obstacle and collision avoidance in motion planning strategies. One of the major issues is that avoidance constraints lead to a nonconvex feasible domain. It is worth underlining that such formulations are intrinsic to the problem and cannot be avoided. [1][2][3] This paper concentrates on the "corner cutting" issue, ie, avoidance constraints are checked at each sampling time, but the control input is ultimately applied (eg, via a zero-order hold block) to continuous dynamics. Hence, the intrasample behavior of the agent (the autonomous vehicle to be steered) cannot be overlooked. While alluring, obstacle enlargement techniques 4 or sampling time reduction are not always appropriate. The former increases the conservatism of the formulation (potentially leading to infeasibility), and the latter reduces the time available for computing the input.The computational limitations are particularly troublesome since modeling the associated optimization problem is often done via the mixed-integer (MI) programming framework, 5,6 which scales badly with problem size and complexity (ie, number of obstacles). 4528

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Section: Mixed Integer Representations For the Overapproximated Shadomentioning

confidence: 67%

“…Recalling Remark 8, we note that (23a) to (24) are linear only if is known. If is itself an unknown parameter, we propose the following corollary.…”

Section: Mixed Integer Representations For the Overapproximated Shadomentioning

confidence: 99%

Section: Mixed Integer Representations For the Overapproximated Shadomentioning

confidence: 99%