This paper presents a hierarchical framework that allows online point-to-point dynamic-stability-constrained optimal trajectory planning of a mobile manipulator robot working on rough terrain. First, the kinematics model of a mobile manipulator robot and the zero moment point stability measure are presented as theoretical background. Then, a sampling-based quasi-static planning algorithm modified for stability guarantee and traction optimization in continuous dynamic motion is presented along with a mathematical proof. The robot’s quasi-static path is then used as an initial guess to warm start a nonlinear optimal control solver which may otherwise have difficulties finding a solution to the stability-constrained formulation efficiently. The performance and computational efficiency of the framework are demonstrated through an application to a simulated timber harvesting mobile manipulator machine working on varying terrain. The results demonstrate feasibility of online trajectory planning on varying terrain while satisfying the dynamic stability constraint. Qualitative and quantitative comparisons with existing methods are also presented.

This paper develops an endogenous growth model with doubly differentiated R&D being the growth engine. The model incorporates dynamic structural change and heterogeneous knowledge spillovers. As a result, decentralized economy may exhibit non-monotonic growth paths and declining R&D productivity. Conditions on the knowledge spillover operator granting the existence of balanced growth for first-best and market economies are obtained. Different regulation tools helpful in achieving the sustainable path and their limits are studied.

Legged robots may become unstable when subjected to unexpected disturbances such as external pushes and environmental irregularities mostly while moving on natural terrains. To enhance the mobility performance, legged robots should be able to keep or restore their balanced configuration when a sudden disturbance is exerted. The aim of this article is to design a controller for a quadruped robot to restore its balanced configuration despite exerting external pushes. This is achieved based on developing a full-dynamics model of the robot moving over even and uneven terrains. The proposed controller is based on a PD module which calculates the required accelerations for restoring the robot equilibrium. However, these accelerations may make the robot unstable and also cause the slippage of stance feet. Therefore, an optimization algorithm is used to compute the maximum admissible accelerations. The constraints of the optimization problem are the conditions which guarantee the robot stability and the stance feet slippage avoidance. The optimization algorithm is transformed into a linear constrained least-squares problem to be solved in real-time. The main contributions of this article are the development of a push recovery algorithm for quadruped robots and also the introduction of an appropriate condition which guarantees the stability of the robot even on uneven terrains. This stability condition is developed based on a full-dynamics model of the robot. The proposed algorithm is applied on an 18-DOF quadruped robot when the robot is standing over both even and uneven terrains. The obtained results show that the robot can successfully restore its balanced configuration by precise adjustment of the position and orientation of its main body while a massive external disturbance is exerted.

This paper explores the design of humanoid complicated dynamic motion based on human motion capture. Captured human data must be adapted for the humanoid robot because its kinematics and dynamics mechanisms differ from those of the human actor. It is expected that humanoid movements are highly similar to those of the human actor. First, the kinematics constraints, including ground contact conditions, are formulated. Second, the similarity evaluation on the humanoid motion based on both the spatial and temporal factors compared with the human motion is proposed. Third, the method to obtain humanoid motion with high similarity is presented. Finally, the effectiveness of the proposed method is confirmed by simulations and experiments of our developed humanoid robot “sword” motion performance.

Studies are the effects of joint flexibility on the dynamic stability of a one-link force-controlled manipulator. The closed-loop dynamic equation with the explicit force controller and the damping force controller are first derived. Stability analysis is then carried out by computing the system eigenvalues. Results indicate a conditionally stable system. Due to the presence of discontinuous contacts with the environment during the interaction process, the system exhibits a stable limit cycle when the force feedback gain goes beyond the critical value.

Several static and dynamic stability criteria have been defined in the course of walking-robot history. Nevertheless, previous work on the classification of stability criteria for statically stable walking machines (having at least four legs) reveals that there is no stability margin that accurately predicts robot stability when inertial and manipulation effects are significant. In such cases, every momentum-based stability margin fails. The use of an unsuitable stability criterion yields unavoidable errors in the control of walking robots. Moreover, inertial and manipulation effects usually appear in the motion of these robots when they are used for services or industrial applications. A new stability margin that accurately measures robot stability considering dynamic effects arising during motion is proposed in this paper. The new stability margin is proven to be the only exact stability margin when robot dynamics and manipulation forces exist. Numerical comparison has been conducted to support the margin's suitability. Stability-level curves are also presented on the basis of a suitable stability margin to control the trajectory of the center of gravity during the support phase.

Several static and dynamic stability criteria have been defined in the course of walking robot history. Nevertheless, different applications may require different stability criteria and, to the authors' best knowledge, there is no qualitative classification of such stability measurements. Using the wrong stability criterion to control a robot gait may prevent the task from succeeding. Furthermore, if the optimum criterion is found, the robot gait can also be optimized. In this paper, the stability criteria that have been applied to walking robots with at least four legs are examined in terms of their stability margins in different static and dynamic situations. As a result, a qualitative classification of stability criteria for walking machines is proposed so that the proper criterion can be chosen for every desired application.

This paper presents the development of a model which can adequately simulate the dynamic stability of manipulators mounted on moveable platforms. The model takes into account the dynamics of the base that can potentially rock back-and-forth. Particularly, the model predicts the changes in the velocities of the manipulator links and the base due to impact with the ground. The application of the study is directed at industrial machines that carry human-operated hydraulic manipulators. The model is therefore used to simulate for the first time, planar movements of'a Caterpillar 215B excavator-based log-loader. The results clearly show the effect of the manipulator movement on turning the base over. The results also show that by proper manipulation of the arms, one can achieve a stable condition and even reverse the ‘tipover' situation in such machines.