The force distribution problem in multilegged vehicles is a constrained optimization problem. The solution to the problem is the setpoints of the leg contact forces for a particular system task. In this paper, the efficient compact QP method which takes into account both the linear and quadratic objective functions is adopted to resolve this constrained optimization problem. Various objective functions such as minimum force, load balance, safety margin on friction constraints can be considered by the compact QP method. This method can also be applied to smooth discontinuities in commanded forces by manipulating the homogeneous solution and including smoothing periods when the leg phase alternates between support and transfer. This smoothing scheme does not require force sensors. Multiple goals which consider several alternative objective functions can also be achieved by the compact QP method.

The window-shaped obstacle avoidance problem is studied in this paper. Several research papers regarding obstacle avoidance including the method proposed by Zghal et al., which we believe is the most suitable for three-dimensional (3-D) window-shaped obstacle avoidance are studied. Consequently, several shortcomings of the Zghal's method are discovered. The Zghal's method will produce chattering solution sequences in joint rates due to its deficiency in determining the shortest distance between the manipulator links and the window edges. This paper proposes a new scheme to determine the shortest distance. This new scheme will remedy the chattering problem. Moreover, the nearest link (NL) method is developed for further improvement. Because the NL method only considers the nearest link in the performance criterion, the on-line weighting assignment problem of the Zghal's method is removed, also, less redundancy is required to accomplish the goal for obstacle avoidance. Therefore, the NL method will allow more redundancy to be useful for the other goals under multiple-goal application environments.

The window-shaped obstacle avoidance problem is studied in this paper. Several research papers regarding obstacle avoidance including the method proposed by Zghal et al. (1992), which we believe is the most suitable for 3D window-shaped obstacle avoidance were studied. Consequently, several short-comings of the Zghal's method were discovered. The Zghal's method will produce a chattering problem due to its deficiency in determining the shortest distance between the manipulator links and the window edges. This paper proposes a new scheme to determine the shortest distance. This new scheme will remedy the chattering problem. Moreover, the most dangerous link (MDL) method is developed to further improve the effectiveness and efficiency. Because the MDL method only considers the most dangerous link in the performance criterion, the online weighting assignment problem of the Zghal's method is removed, also, less redundancy is required to accomplish the goal for obstacle avoidance. Therefore, the MDL method will allow more redundancy to be useful for the other goals under multiple-goal application environments.

The parallel scheme is an effective algorithm to solve the multiple-goal problem of redundant manipulators, but it has limitations. We present an improved parallel scheme to help solve the limitations of the original parallel scheme. The original scheme has problems with the redundancy-release capability. We propose using the exponential function to adaptively adjust the weighting under the improved parallel scheme. The original parallel scheme uses a reciprocal function. Our solution shows both an improved redundancy-release capability and weighting-adjustment capability. Our improved parallel scheme has these advantages plus the original merits of the original parallel scheme.

Upon solving the inverse kinematics problem of robot manipulators, the inherent singularity problem should always be considered. When a manipulator is approaching a singular configuration, a certain degree of freedom will be lost such that there are no feasible solutions of the manipulator to move into this singular direction. In this paper, the singularities of a 6-DOF PUMA manipulator are analyzed in detail and all the corresponding singular directions in task space are clearly identified. In order to resolve this singularity problem, an approach denoted Singularity Isolation Plus Compact QP (SICQP) method is proposed. The SICQP method decomposes the work space into achievable and unachievable (i.e., singular) directions. Then, the exactness in the singular directions are released such that extra redundancy is provided to the achievable directions. Finally, the Compact QP method is applied to maintain the exactness in the achievable directions, and to minimize the tracking errors in the singular directions under the condition that feasible joint solutions must be obtained. In the end, some simulation results for PUMA manipulator are given to demonstrate the effectiveness of the SICQP method.

It becomes obvious that a single optimization criterion is not sufficient to deal with complicated task environments when redundant manipulators execute real-world tasks. Therefore, multiple-goal considerations should be considered. In this research, a systematic algorithm, namely the parallel scheme is proposed to solve the multiple-goal problem. It can adaptively adjust all the weighting factors of the corresponding goals according to their individual needs under dynamically varying environments. As such, smooth solution sequences are obtained. The 7-DOF CESAR redundant manipulator is used as an example mechanism to test the proposed algorithms for multiple-goal considerations.

Due to hardware limitations, physical constraints such as joint rate bounds, joint angle limits, and joint torque constraints always exist. In this paper, these constraints are considered in the general formulation of the redundant inverse kinematic problem. To take these physical constraints into account, the computationally efficient compact quadratic programming (QP) method is formed to resolve the constrained kinematic redundancy problem. In addition, the compact-inverse QP method is also formulated to remedy the inescapable singularity problem with inequality constraints. Two examples are given to demonstrate the generality and superiority of these two methods: to eliminate the drift phenomenon caused by self motion and to remedy saturation-type nonlinearity problems.>

Due to hardware limitations, physical constraints, such as joint rate bounds and joint angle limits, always exist. In the present work, these constraints are included in the general formulation of the redundant inverse kinematic problem. To take into account these physical constraints, the computationally efficient compact QP (quadratic programming) method is derived to resolve the kinematic redundancy problem. In addition, the compact-inverse QP method is developed to remedy the singularity problem. The compact QP (compact and inverse QP) method makes use of the compact formulation to obtain the general solutions and to eliminate the equality constraints. As such, the variables are decomposed into basic and free variables, and the basic variables are expressed by the free variables. Thus, the problem size is reduced and it only requires an optimization algorithm, such as QP, for the free variables subject to pure inequality constraints. This approach will expedite the optimization process and make real-time implementation possible.>

The inverse kinematic problem of redundant manipulators is solved by the compact formulation technique. The compact formulation is derived by applying Gaussian elimination, then the general solutions are still formulated as a particular solution together with homogeneous solutions. The homogeneous solutions are merely functions of free variables. Inverse kinematic solutions derived by the pseudoinverse formulation can always be converted into a compact form. Also, it is proven that the implementation by the compact formulation is computationally more efficient. The inherent singularity problems of inverse kinematics are also considered. In order to obtain continuous and feasible joint-rate solutions even at or in the neighborhood of singular points and to improve the exactness in the achievable directions, the compact-inverse method is introduced. The compact-inverse method applies the compact formulation to constrain the manipulator to move into the achievable directions. It is believed that the compact formulation approach can resolve the inverse kinematic redundancy problem more efficiently and exactly than the traditional pseudoinverse formulation.>

A novel approach to robot guidance in an unfamiliar environment is presented. In previous guiding methods, a preinstalled map or predefined path is required for a robot navigating in its working space. The present method uses an indication post (IP) to provide the information on the destination, the direction, and the distance from the source point to the destination point, assuming that the mobile robot has no information concerning its workplace. To realize the concept, many IPs depicting simple information were designed. The content of IPs can be described by using a finite-state grammar. Image-processing, statistical, and syntactic pattern recognition approaches are integrated to solve the problems of IP finding, robot location determination, IP identification, and understanding. Experiments simulating practical environments were performed. The results verify that the IP candidates can be automatically found and the depicted information can be extracted and understood correctly, so that the mobile robot is able to plan a global optimal path from an arbitrary start point to an arbitrary end point.>