In this paper, we suggest an optimal force distribution scheme by weak point force minimization and we also present an efficient method to solve the problem. The concept of a weak point is a generalized one which is applicable to any points of interest, as well as joints or contact points between end-effectors and an object. The problem is formulated by a quadratic objective function of the forces exerted at weak points subject to the linear equality and inequality constraints, and its optimal solution is obtained by an efficient method. As regards the solution of the problem, the original problem is reformulated to a reduced order dual problem after the equality constraints are eliminated by force decomposition.

The force distribution problem in multilegged vehicle 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.