Mixed‐integer quadratic programming for automatic walking footstep placement, duration, and rotation

Abstract

Summary This paper presents a mixed‐integer model predictive controller for walking. In the proposed scheme, mixed‐integer quadratic programs (MIQP) are solved online to simultaneously decide center of mass jerks, footsteps positions, durations, and rotations while respecting actuation, geometry, and contact constraints. Most walking controllers require preplanned footstep rotations to avoid dealing with the nonlinearity introduced by foot rotation decision. The main contribution of this work is an optimization formulation where feet rotations are automatically planned to attain a reference speed rotation. Finally, simulation results are shown to present and discuss the capabilities of the proposed formulation.

Shortest Paths in Graphs of Convex Sets

“…When all the flows ϕ ij are strictly positive, the objective (8a) is equal to (7) by definition, and this bilinear program is exactly the problem we derived above. On the other hand, when a flow ϕ ij is zero, problem (8) does not raise any issue: the (i, j)th addend in (8a) is well defined and correctly evaluates to zero, even when ij (x i , x j ) = ∞. To see this, notice that ϕ ij = 0 implies y ij = z ij = 0 by (8b) and (8c), and Definition 1 reads…”

“…Proposition 1. The addition of the integrality constraints ϕ ij ∈ {0, 1} for all (i, j) ∈ E does not affect the optimal value of problem (8).…”

“…Another application is robot motion planning, in which case each vertex in our graph is paired with a convex region of space that does not intersect with obstacles (see Section VIII). Problems such as footstep planning for humanoid robots on uneven terrain or collision-free motion planning of autonomous vehicles under dynamic constraints are frequently tackled via mixed-integer programming [2], [3], [4], [5], [6], [7], [8]. However, our problem formulation is substantially different as we do not parameterize the discrete state of the system with binary variables, but instead we use binaries to select transitions between regions of the state space.…”

Study on Multi-Model Soft Sensor Modeling Method and Its Model Optimization for the Fermentation Process of Pichia pastoris

“…Therefore, the solution problem of MISO nonlinear system in each fermentation process can be transformed into a mixed integer quadratic programming (MIQP) problem [40]:…”

Control for hybrid systems: Applications and methods for adaptation and optimality

“…New stability conditions and control designs based on numerical methods, including linear matrix inequalities and gradient based optimization methods, are introduced to address time delays, parametric uncertainties, and the nonlinearities involved in the switching dynamics with stability and performance guarantees. The second group of articles, 5‐14 constituting the major category of this issue, applies adaptive control, optimization methods, and hybrid system theories to various practical fields, ranging from UAVs, AGVs, robotics, and water systems to batch processes. The last group 15,16 considers distributed cyber physical systems, which deals with parametric uncertainties, communication constraints, and signal estimations by resorting to adaptive control and fast Kalman filtering.…”