This paper introduces approximate time-domain solutions to the otherwise non-integrable double-stance dynamics of the 'bipedal' spring-loaded inverted pendulum (B-SLIP) in the presence of non-negligible damping. We first introduce an auxiliary system whose behavior under certain conditions is approximately equivalent to the B-SLIP in double-stance. Then, we derive approximate solutions to the dynamics of the new system following two different methods: (i) updated-momentum approach that can deal with both the lossy and lossless B-SLIP models, and (ii) perturbation-based approach following which we only derive a solution to the lossless case. The prediction performance of each method is characterized via a comprehensive numerical analysis. The derived representations are computationally very efficient compared to numerical integrations, and, hence, are suitable for online planning, increasing the autonomy of walking robots. Two application examples of walking gait control are presented. The proposed solutions can serve as instrumental tools in various fields such as control in legged robotics and human motion understanding in biomechanics.@en

Sequential composition is a supervisory control architecture for addressing control problems in complex dynamical systems. Although sequential composition works properly for a single system, it is not designed for cooperative systems. This paper extends the standard sequential composition by introducing a novel approach to compose multiple sequential composition controllers towards cooperative control. Given two or more systems, cooperation is achieved by composing each of the systems' control automaton, together with estimation for the domains of attraction of the resulting composed controllers. This typically results in new events for the original sequential composition controllers. Applying these events, the cooperative control system can fulfill the tasks which are not possible to satisfy with the original controllers individually. The simulation results of an inverted pendulum system collaborating with two second-order DC motors are presented for cooperative swing-up maneuvers.

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This paper considers optimal output synchronization of heterogeneous linear multi-agent systems. Standard approaches to output synchronization of heterogeneous systems require either the solution of the output regulator equations or the incorporation of a p-copy of the leader’s dynamics in the controller of each agent. By contrast, in this paper neither one is needed. Moreover, here both the leader’s and the follower’s dynamics are assumed to be unknown. First, a distributed adaptive observer is designed to estimate the leader’s state for each agent. The output synchronization problem is then formulated as an optimal control problem and a novel model-free off-policy reinforcement learning algorithm is developed to solve the optimal output synchronization problem online in real time. It is shown that this optimal distributed approach implicitly solves the output regulation equations without actually doing so.
Simulation results are provided to verify the effectiveness of the proposed approach.@en

This paper presents a coordination controller for the Dual-SLIP model, a novel template for quadrupedal steady and transitional running. The model consists of a pair of "physically-unconnected" Spring-Loaded Inverted Pendulums (SLIPs), each representing a part of the body of a quadruped (see Figure 1). For this model, we propose a spatiotemporal coordination controller that describes the evolution of coordination parameters by simple difference equations. A "time-aware" deadbeat low-level controller is also proposed to realizing the generated control specifications in each SLIP individually. Evaluation of the proposed coordination controller for the Dual-SLIP model in simulation shows that even with remarkably off-phase initial conditions and ground height variation disturbances, quadrupedal bounding, pronking and different transitions between them can be realized.

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This paper addresses the control of steady state and transition behaviors for the bipedal spring-loaded inverted pendulum (SLIP) model. We present an event-driven control approach that enables the realization of active running, walking, and walk-run transitions in a unified framework. The synthesis of the controlled behaviors is illustrated by the notion of hybrid automaton in which different gaits are generated as the sequential composition of SLIP's primary phases of motion. We also propose a novel analytical approximate solution to the otherwise nonintegrable double-stance dynamics of the SLIP model. The analytical simplicity of the solution is utilized in the design and analysis of dynamic walking gaits suitable for online implementation. The accuracy of the approximate solution and its influence on the stability properties of the controlled system are carefully analyzed. Finally, we present two simulation examples. The first demonstrates the practicality of the proposed control strategy in creating human-like gaits and gait transitions. In the second example, we use the controlled SLIP as a planner for the control of a multibody bipedal robot model, and embed SLIP-like behaviors into a physics-based robot simulation model. The results corroborate both the practical utility and effectiveness of the proposed approach.@en

Most stabilizing controllers designed for nonlinear systems are valid only within a specific region of the state space, called the domain of attraction (DoA). Computation of the DoA is usually costly and time-consuming. This paper proposes a computationally effective sampling approach to estimate the DoAs of nonlinear systems in real time. This method is validated to approximate the DoAs of stable equilibria in several nonlinear systems. In addition, it is implemented for the passivity-based learning controller designed for a second-order dynamical system. Simulation and experimental results show that, in all cases studied, the proposed sampling technique quickly estimates the DoAs, corroborating its suitability for real-time applications.

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This paper proposes a new approach to robotic manipulation planning based on the contact between a set of objects, robots and surfaces. We consider making or breaking contact as the most abstract, yet representative element of a manipulation task. Using this paradigm, a robotic manipulation planner has been developed. Given an environment with robots and objects, a manipulation graph is generated by a set of rules and the available geometrical information. Next, the object manipulation planning is formulated as a graph search problem. Paths on this graph divide a complex manipulation task into sub-tasks, followed by low-level path planning and controller assignment for each sub-task. By sequentially executing these controllers in a hybrid fashion, one achieves the overall manipulation task.

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