This paper presents a trajectory planning method for wheeled robots with fixed steering axes while the steering angle of each wheel is constrained. In the past, All-Wheel-Steering(AWS) robots, incorporating modes such as rotation-free translation maneuvers, in-situ rotational maneuvers, and proportional steering, exhibited inefficient performance due to time-consuming mode switches. This inefficiency arises from wheel rotation constraints and inter-wheel cooperation requirements. The direct application of a holonomic moving strategy can lead to significant slip angles or even structural failure. Additionally, the limited steering range of AWS wheeled robots exacerbates nonlinearity issues, thereby complicating control processes. To address these challenges, we developed a novel planning method termed Constrained AWS(C-AWS), which integrates second-order discrete search with predictive control techniques. Experimental results demonstrate that our method adeptly generates feasible and smooth trajectories for C-AWS while adhering to steering angle constraints.