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In this paper, we present a convex-optimization-based method to solve speed planning problems over a fixed path for autonomous driving in both static and dynamic environments. Our contributions are twofold. First, we introduce a general, flexible and complete speed planning optimization which includes time efficiency, smoothness objectives and dynamics, friction circle, boundary condition constraints which addresses limitations of existing methods and is able to provide smooth, safety-guaranteed, dynamically-feasible, and time-efficient speed profiles. Second, we demonstrate that our problem preserves convexity with the expanded set of constraints, and hence, global optimality of solutions is guaranteed. We show how our formulation can be used in speed planning for various autonomous driving scenarios by providing several typical case studies in both static and dynamic environments. The results depict …