A planning and control framework for humanoid systems : robust, optimal, and real-time performance

Humanoid robots are increasingly demanded to operate in interactive and human-surrounded environments while achieving sophisticated locomotion and manipulation tasks. To accomplish these tasks, roboticists unremittingly seek for advanced methods that generate whole-body coordination behaviors and meanwhile fulfill various planning and control objectives. Undoubtedly, these goals pose fundamental challenges to the robotics and control community. To take an incremental step towards reducing the performance gap between theoretical foundations and real implementations, we present a planning and control framework for the humanoid, especially legged robots, for achieving high performance and generating agile motions. A particular concentration is on the robust, optimal and real-time performance. This framework constitutes three hierarchical layers, which are presented from the following perspectives. First, we present a robust optimal phase-space planning framework for dynamic legged locomotion over rough terrain. This framework is a hybrid motion planner incorporating a series of pivotal components. Via centroidal momentum dynamics, we define a new class of locomotion phase-space manifolds, as a Riemannian distance metric, and propose a robust optimal controller to recover from external disturbances at runtime. The agility and robustness capabilities of our proposed framework are illustrated in (i) simulations of dynamic maneuvers over diverse challenging terrains and under external disturbances; (ii) experimental implementations on our point-feet bipedal robot. Second, we take a step toward formally synthesizing high-level reactive planners for whole-body locomotion in constrained environments. We formulate a two-player temporal logic game between the contact planner and its possibly-adversarial environment. The resulting discrete planner satisfies the given task specifications expressed as a fragment of temporal logic. The provable correctness of the low-level execution of the synthesized discrete planner is guaranteed through the so-called simulation relations. We conjecture that this theoretical advance has the potential to act as an entry point for the humanoid community to employ formal methods for the planner verification and synthesis. Third, we propose a distributed control architecture for the latency-prone humanoid robotic systems. A central experimental phenomenon is observed that the stability of high impedance distributed controllers is highly sensitive to damping feedback delay but much less to stiffness feedback delay. We pursue a detailed analysis of the distributed controllers where damping feedback effort is executed in proximity to the control plant, and stiffness feedback effort is implemented in a latency-prone centralized control process. Critically-damped gain selection criteria are designed for not only rigid but also series elastic actuators (SEAs). In particular, we devise a novel impedance performance metric, defined as “Z-region”, simultaneously quantifying the achievable SEA impedance magnitude and frequency ranges. Finally, this distributed control strategy is generalized to the time-delayed Whole-Body Operational Space Control with SEA dynamics. To ensure passivity, we separate the overall closed-loop system into two subsystems interconnected in a feedback configuration. By designing Lyapunov-Krasovskii functionals, we propose a delay-dependent passivity criterion of the closed-loop system in the form of linear matrix inequalities (LMIs), and solve for the allowable maximum time delays via the passivity criterion. The proposed distributed control strategy is validated through extensive experimental implementations on UT rigid and series elastic actuators, an omnidirectional mobile base Trikey and a SEA-equipped bipedal robot Hume.