arXiv subjects

Philippe Müllhaupt

Publications and source records attributed to Philippe Müllhaupt.

2 recordsLinked to original sources

arXiv2026

Efficient flatness-based computation of trajectories for vehicles with many trailers

We address the practical computation of feedforward steering inputs for a car with n trailers via differential flatness. The standard route (iterated symbolic differentiation of the flat output) scales prohibitively with n: even with computer-algebra software the expression sizes grow super-exponentially and become intractable beyond n approx. 5. We propose an algorithm that combines four ingredients (angular intermediate variables, factorisation of the recursion in submaps, rescaled higher-order product/quotient rules, and a composition rule based on truncated formal power series instead of Faa di Bruno's formula). We benchmark the proposed method against (i) direct symbolic differentiation in SymPy and (ii) Faa di Bruno's formula evaluated via Bell polynomials. Both reference methods hit a clear computational wall: SymPy reaches a 20 s timeout at derivative order r = 14, while the Bell-polynomial recursion exceeds a 60 s timeout beyond r = 24. The proposed approach has O(r3) arithmetic complexity in the derivative order and remains under one millisecond up to r = 40, with numerical agreement to machine precision in the regime where the reference methods succeed. As an end-to-end illustration, a 20-trailer parking manoeuvre is computed and animated.

math.OC↗

arXiv2023

A quotient framework for single-input pole placement and associated algorithms

Single-input eigenvalue assignment problem (SEVAS) for dense (non-sparse) weakly controllable pairs A,B using Ackermann's formula is revisited. Factorizations are presented that are interpreted using quotient (factor) vector spaces. Depending on the representations chosen for the equivalence class (given as specific projections by real orthogonal matrices), the numerical behavior of pole placement scheme can be enhanced. One version operates by placing one pole at a time (with complex conjugate poles grouped together to avoid complex arithmetic). Another version operates with the coefficients of the characteristic polynomial directly. The latter version uses orthogoanl real matrices. In both cases, there are no constraint on the number of identical poles. A version of the algorithm uses only ring arithmetic. The algorithms are compared with numerically stable algorithms that appeared in the literature, such as the Miminis-Paige algorithm or the Varga pole shifting method. In case of real distinct eigenvalues to be placed, a geometrical interpretation as the interesection of affine hyperplanes provides the value of the gain vector, which seems a novel interpretation.

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