This brief is concerned with the robust stability problem for a class of discrete-time uncertain Markovian jumping neural networks with defective statistics of modes transitions. The parameter uncertainties are considered to be norm-bounded, and the stochastic perturbations are described in terms of Brownian motion. Defective statistics means that the transition probabilities of the multimode neural networks are not exactly known, as assumed usually. The scenario is more practical, and such defective transition probabilities comprise three types: known, uncertain, and unknown. By invoking the property of the transition probability matrix and the convexity of uncertain domains, a sufficient stability criterion for the underlying system is derived. Furthermore, a monotonicity is observed concerning the maximum value of a given scalar, which bounds the stochastic perturbation that the system can tolerate as the level of the defectiveness varies. Numerical examples are given to verify the effectiveness of the developed results.
Trajectory optimization with contact-rich behaviors has recently gained attention for generating diverse locomotion behaviors without pre-specified ground contact sequences. However, these approaches rely on precise models of robot dynamics and the terrain and are susceptible to uncertainty. Recent works have attempted to handle uncertainties in the system model, but few have investigated uncertainty in contact dynamics. In this study, we model uncertainty stemming from the terrain and design corresponding risk-sensitive objectives under the framework of contact-implicit trajectory optimization. In particular, we parameterize uncertainties from the terrain contact distance and friction coefficients using probability distributions and propose a corresponding expected residual minimization cost design approach. We evaluate our method in three simple robotic examples, including a legged hopping robot, and we benchmark one of our examples in simulation against a robust worst-case solution. We show that our risksensitive method produces contact-averse trajectories that are robust to terrain perturbations. Moreover, we demonstrate that the resulting trajectories converge to those generated by a traditional, non-robust method as the terrain model becomes more certain. Our study marks an important step towards a fully robust, contact-implicit approach suitable for deploying robots on real-world terrain.
This study presents a theoretical method for planning and controlling agile bipedal locomotion based on robustly tracking a set of non-periodic keyframe states. Based on centroidal momentum dynamics, we formulate a hybrid phase-space planning and control method that includes the following key components: (i) a step transition solver that enables dynamically tracking non-periodic keyframe states over various types of terrain; (ii) a robust hybrid automaton to effectively formulate planning and control algorithms; (iii) a steering direction model to control the robot's heading; (iv) a phase-space metric to measure distance to the planned locomotion manifolds; and (v) a hybrid control method based on the previous distance metric to produce robust dynamic locomotion under external disturbances. Compared with other locomotion methodologies, we have a large focus on non-periodic gait generation and robustness metrics to deal with disturbances. This focus enables the proposed control method to track non-periodic keyframe states robustly over various challenging terrains and under external disturbances, as illustrated through several simulations.
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