We are proposing a general framework that incorporates multiple task definitions in the prioritized inverse kinematics problem. First, a mathematical description of multiple task definitions is constructed that provides an efficient way to show unprioritized or prioritized accumulations of tasks. Then, smooth transitions between all task definitions are studied, so a method, called task transition control, is developed that interpolates joint trajectories using barycentric coordinates and linear dynamical systems to overcome difficulties of interpolating task trajectories in the conventional methods. Consequently, smooth, arbitrary, and consecutive task transitions are achieved in a simple, direct, and general manner and also boundedness of joint trajectories is assured regardless of singularity. Lastly, the idea is tested by two kinematic simulations: obstacle avoidance with the KUKA LWR and task scheduling of a humanoid robot.

In this paper, we propose a unified approach to teach and iteratively refine both end-effector and null-space movements. Hence, the robot can be taught to make use of all its degrees-of-freedom (DoF) to adapt its behavior to new dynamic scenarios. In order to achieve this goal we propose an incremental learning approach in a framework of kinesthetic teaching based on a multi-priority kinematic controller, the so-called Task Transition Control (TTC). The learning algorithm is responsible for skill acquisition and their incremental update. On the real-time level, end-effector and null-space motion primitives, as well as the physical guidance are considered as prioritized tasks. The transitions among these tasks and their insertion and removal are managed by the TTC according to the specified transition parameters. This allows to introduce a customized task which guarantees a proper and smooth response to the applied external forces during the kinesthetic teaching. Experimental results on a 7 DoF KUKA lightweight manipulator show the effectiveness of the proposed approach.

This paper proposes new methods for the prioritized inverse kinematics (PIK) by using the QR decomposition (QRD) and the Cholesky decomposition (CLD) on the purpose of separation between orthogonalization and inversion processes that are essential parts of the PIK. The distinctive approach eliminates the interference between two processes which usually induces inaccuracy and sometimes instability on the prioritized inverse solutions. Two degenerate properties of using the QRD are explained and the remedies are provided as the modified damped least-squares pseudoinverse and the numerical reconditioning. The effectiveness are examined by the kinematic simulations with the n-link manipulators in the two-dimensional case and the KUKA LWR in the three-dimensional case.

This paper discusses an unified method of the tracking and balancing controls for leg-wheel hybrid structures in an effort to improve the mobility over hard, flat surfaces. Preliminarily, we analyzed the contact constraint to formulate a dynamically decoupled model in the task space. Then, inequality constraints were determined to restrict the dynamic behavior of the system within the given bounds for the dynamic stability and the actuator saturation. The inequality constraints were applied to the reference control input that was designed for the mechanism to traverse the desired trajectories without the constraints. To find the constrained control input, a quadratic objective function was proposed to minimize the modification error of the control inputs. We tested the effectiveness of the proposed algorithm by comparing simulation results with our previous research.

This paper discusses a balance control method with kinodynamic constraints for leg-wheel hybrid structures in an effort to improve the mobility of locomotion over hard, flat surfaces. Preliminarily, we defined a prioritized Jacobian and a prioritized inverse of Jacobian to formulate the dynamically decoupled model in the task space for the constrained multi-contact multi-rigid-body system with a floating base. Our strategy has two tracks to accommodate the uncertainty and the complexity of the system dynamics. 1) The time-delay estimation and control are combined with the nonlinear programming. 2) Whole kinodynamic constraints are derived as functions of the control input. The proposed balance control algorithm allows the system to traverse desired trajectories satisfying the kinodynamic constraints and improves the mobility of locomotion. The effectiveness of the algorithm is tested with the dynamic simulations.

This paper proposes a balance control algorithm which uses Zero Moment Point (ZMP) in order to improve the mobility of leg-wheel hybrid structures on hard, flat surfaces. The algorithm generates balancing leg motions which continuously adjust the contact points to allow the geometric center of the contact area to follow ZMP. During our simulation of a balance control system which uses Individual Joint PD Control (IJPD), we encountered two main problems-high frequency oscillation and unbalanced control input. To solve these issues, we derived a method for dynamic decoupling and control allocation (DDCA). We tested the effectiveness of the proposed algorithm by simulating the maximum distance that a robot can stably move during a fixed time period. There are three important advantages to our proposed balance control algorithm. First, the balancing motions have no effect on the primary tasks of its arms and upper body. Second, the interaction forces between the contact points are minimized, thereby reducing an unbalance of the control inputs. Third, the task dynamics are decoupled and controlled independently.

This paper proposes a balance-control algorithm which uses the Zero-Moment Point (ZMP) in order to maximize the dynamic stability of leg-wheel hybrid structures on hard, flat surfaces. The algorithm constrains the control input to satisfy the condition in which the ZMP stays at the geometric center of the contact area. This restriction of the control input changes the original fully actuated system into an under-actuated system and generates a problem with the internal dynamics. To solve this issue, we found output variables which reduce and stabilize the internal dynamics by means of an Input/Output Linearization (IOL) process. We tested the effectiveness of the proposed algorithm by comparing three cases in a simulation - no balance control, ZMP feedback balance control, and ZMP feedforward balance control.