In this article, we present an intrinsically stable Model Predictive Control (IS-MPC) framework for humanoid gait generation that incorporates a stability constraint in the formulation. The method ...uses as prediction model a dynamically extended Linear Inverted Pendulum with Zero Moment Point (ZMP) velocities as control inputs, producing in real time a gait (including footsteps with timing) that realizes omnidirectional motion commands coming from an external source. The stability constraint links future ZMP velocities to the current state so as to guarantee that the generated Center of Mass (CoM) trajectory is bounded with respect to the ZMP trajectory. Being the MPC control horizon finite, only part of the future ZMP velocities are decision variables; the remaining part, called tail , must be either conjectured or anticipated using preview information on the reference motion. Several options for the tail are discussed, each corresponding to a specific terminal constraint. A feasibility analysis of the generic MPC iteration is developed and used to obtain sufficient conditions for recursive feasibility. Finally, we prove that recursive feasibility guarantees stability of the CoM/ZMP dynamics. Simulation and experimental results on NAO and HRP-4 are presented to highlight the performance of IS-MPC.
This study is focused on analyzing the L1-stochastic internal stability and the design of an L1-gain controller for two-dimensional (2D) continuous positive Markov jumping systems (PMJSs) with ...constraints on the inputs and states. An algorithm is developed to explicitly determine the state feedback control law with the optional L1-gain performance. First, by constructing a co-positive stochastic Lyapunov function for the positive system and establishing the equation for the Markov states' mathematical expectation, several sufficient and necessary conditions for L1-stochastic internal stability are derived. This analysis indicates that 2D PMJSs with directional delays are influenced by sizes of the system matrices and magnitude of delays, and transition matrix. Second, a method for calculating the L1-gain is formulated utilizing linear programming (LP), thus, an L1-gain controller is designed to guarantee that the closed-loop system is positive and L1-stochastically internally stable, while achieving optimal L1-gain performance. Two numerical and practical examples are considered, and the influence of delays and transition probability matrices on the L1-gain is specified to validate the preceding theoretical findings.
The platooning of autonomous vehicles can significantly benefit road traffic. Most previous studies on platoon control have only focused on specific communication topologies, especially those with ...real eigenvalues. This paper extends existing studies on distributed platoon control to more generic topologies with complex eigenvalues, including both internal stability analysis and linear controller synthesis. Linear platoon dynamics are derived using an inverse vehicle model compensation, and graph theory is employed to model the communication topology, leading to an integrated high-dimension linear model of the closed-loop platoon dynamics. Using the similarity transformation, a sufficient and necessary condition is derived for the internal stability, which is completely defined in real number field. Then, we propose a Riccati inequality based algorithm to calculate the feasible static control gain. Further, disturbance propagation is formulated as an <inline-formula> <tex-math notation="LaTeX">\text {H}_{\infty } </tex-math></inline-formula> performance, and the upper bound of spacing errors is explicitly derived using Lyapunov analysis. Numerical simulations with a nonlinear vehicle model validate the effectiveness of the proposed methods.
It is known that the set of internally stabilizing controller Cstab is non-convex, but it admits convex characterizations using certain closed-loop maps: a classical result is the Youla ...parameterization, and two recent notions are the system-level parameterization (SLP) and the input–output parameterization (IOP). In this paper, we address the existence of new convex parameterizations and discuss potential tradeoffs of each parameterization in different scenarios. Our main contributions are: (1) We reveal that only four groups of stable closed-loop transfer matrices are equivalent to internal stability: one of them is used in the SLP, another one is used in the IOP, and the other two are new, leading to two new convex parameterizations of Cstab. (2) We investigate the properties of these parameterizations after imposing the finite impulse response (FIR) approximation, revealing that the IOP has the best ability of approximating Cstab given FIR constraints. (3) These four parameterizations require no a priori doubly-coprime factorization of the plant, but impose a set of equality constraints. However, these equality constraints will never be satisfied exactly in floating-point arithmetic computation and/or implementation. We prove that the IOP is numerically robust for open-loop stable plants, in the sense that small mismatches in the equality constraints do not compromise the closed-loop stability; but a direct IOP implementation will fail to stabilize open-loop unstable systems in practice. The SLP is known to enjoy numerical robustness in the state feedback case; here, we show that numerical robustness of the four-block SLP controller requires case-by-case analysis even when the plant is open-loop stable.
AbstractInternal instability occurs when the finer fraction from a well-graded granular soil escapes with the infiltrates, rendering a filter ineffective. Thus far, numerous particle size as well as ...constriction size distribution–based geometrical methods have been proposed to assess potential internal instability. This paper reports the results from hydraulic tests performed on six granular soils (five well-graded sand-gravel mixtures and medium sand) at different uniformity coefficients and compacted at varying relative density. The study facilitated an objective evaluation of some of the well known published methods, leading to a more realistic interpretation of filtration data based on a revised technique, which accurately demarcates the boundary between internally stable and unstable granular soils. A large body of published data and the current laboratory results were used to validate the proposed criterion for the assessment of internal instability, which is also sensitive to the relative density of the filter that has been ignored in most previous methods.
Gap-graded granular mixtures, consisting of two different sizes with a great range gap, are widely used as filling materials in subgrade engineering. The mixtures usually bear vibration loads in the ...construction stage to meet the compaction requirement, yet surprisingly few studies have focused on its compaction behaviors under vibration loads. To enrich relevant research, this study explores the effects of size ratio (SR) and fine content (FC) on the macro- and mesoscopic compaction behaviors of gap-graded mixtures via calibrated DEM models. Firstly, spherical brown corundum grains, a rock-liked granular material, were used to calibrate contact parameters in the DEM model. Furtherly, the model was verified by comparing with the corresponding physical test using brown corundum mixtures. The study found that the DEM model is reliable in simulating compaction behaviors of gap-graded mixtures, and the calibrated contact parameters can be referenced in the simulation of rock-liked granular materials. Based on simulation results of DEM models, the intense particle motion does not necessarily cause a significant change in permanent deformation, while it would cause an unstable resilient deformation. Limited by the strong internal stability in overfilled assemblies, fine particles remain stable among coarse particles and the contact structure is almost unchanged after vibration compaction.
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•The DEM model of vibration compaction is established with well-calibrated contact parameters.•Model verification of gap-graded granular mixtures is implemented through a series of physical experiments.•Deformation behaviors affected by SR and FC are investigated through particle motions.•The changes in partial contact percentages are related to the internal stability.
This paper deals with the adaptive control and identification of 1-D platoon of non-identical vehicles. Three common different topologies, such as predecessor following, bi-directional leader ...following, and two predecessors following are considered as the communication structures of platoon. For each topology, a new neighbor-based adaptive control law is introduced to estimate the parameter uncertainties, such as rolling resistance and air drag force coefficients. By presenting a new theorem, we prove that the estimates of unknown parameters converge to the actual values. Constant time headway policy is used to adjust the inter-vehicle spacing. For each topology, it is shown that the closed-loop dynamics of platoon is asymptotically stable. Afterward, the necessary conditions on control parameters assuring the string stability for each topology are derived by presenting further theorems. Moreover, the proposed methods are generalized for the heterogeneous platoons with time-varying network topology. Simulation results with different scenarios are provided to show the effectiveness of the presented approaches.
Reinforced soil walls situated at waterfront are susceptible to various modes of failure under dynamic conditions. The internal stability of a waterfront reinforced soil wall is a critical aspect of ...its design and construction. In the present study, internal stability analysis of waterfront reinforced soil wall which is subjected to combined action of earthquake and wave loads has been carried out by considering a log-spiral failure surface. A closed form solution is obtained for the stability of wall using limit equilibrium method (LEM). Internal stability analysis has been performed for soil strata comprising of c-φ partially submerged soil taking horizontal and vertical seismic acceleration (αh and αv) into account following pseudo-static approach. Stability analysis was carried out in terms of a non-dimensional parameter KTeq which represents total geosynthetic reinforcement force required to sustain the stability. This study considers the effect of different parameters like cohesion (c), pore water pressure ratio (ru), internal soil friction angle (φ) hydrostatic and hydrodynamic water pressure (Pst and Pdyn) due to wave loading on stability of wall. It is observed that, due to the increment in the horizontal seismic acceleration coefficient (kh), vertical seismic acceleration coefficient (kv,) and hydrodynamic pressure, the requirement of geosynthetic reinforcement also increases and the presence of water significantly affects the strength of the reinforcement and an increase in the ratio of wave height to the depth of water at the seaward side increases the requirement of reinforcement. Also, it is found that the present study has good agreement with the previous studies conducted.
An improved adaptive cruise control law de Abreu, Marcus P.S.; de Oliveira, Fúlvia S.S.; Souza, Fernando O.
Robotics and autonomous systems,
June 2024, 2024-06-00, Letnik:
176
Journal Article
Recenzirano
To increase the efficiency of road transport and reduce exhaust emissions, research has been intensified in assisted control systems, where adaptive cruise control (ACC) and cooperative adaptive ...cruise control (CACC) stand out. While ACC uses data from onboard sensors and radars, CACC also uses data from inter-vehicle wireless communication. In this context, this paper proposes a new control law for ACC systems that provides a competitive performance compared to CACC, despite not requiring wireless communication between vehicles. The new control law formulation employs both the vehicle acceleration and the relative speed, which generalizes similar ones. The design methodology formulated as a convex optimization problem ensures string and internal stability as well closed-loop pole placement if a set of linear matrix inequalities (LMIs) is satisfied. At the end of the paper, simulations demonstrate the effectiveness of the proposed methodology.
•New control law introduced for ACC systems.•ACC matches CACC performance without wireless communication.•Design grounded in LMIs ensuring internal and string stability.•Passenger comfort boosted via transient response shaping and pole allocation.
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