There have been many studies regarding development of autonomous excavation system which is helpful in construction sites where repetitive jobs are necessary. Unfortunately, bucket trajectory planning was excluded from the previous studies. Since, the best use of excavator is to dig efficiently; purpose of this research was set to determine an optimized bucket trajectory in order to get best digging performance. Among infinite ways of digging any given path, criterion for either optimal or efficient bucket moves is required to be established. One method is to adopt work know-how from experienced excavator operator; However the work pattern varies from every worker to worker and it is hard to be analyzed. Thus, other than the work pattern taken from experienced operator, we developed an efficiency model to solve this problem. This paper presents a method to derive a bucket trajectory from optimization theory with empirical CLUB soil model. Path is greatly influenced by physical constraints such as geometry, excavator dimension and excavator workspace. By minimizing a energy function under these constraints, an optimal bucket trajectory could be obtained.