Motion planning aims to compute the high-quality and collision-free robotic trajectory. To solve the planning problems defined in varying dimensional sizes, motion planners, especially sampling-based, are typically computation intensive because of the costly kernel operations, and computation inefficient due to the inherent sequential processing scheme, hindering their efficient deployment. To address these challenges and enable real-time highly efficient motion planning, this paper proposes MOPED, an algorithm and hardware co-design for sampling-based motion planning engine with flexible dimension support. At the algorithm level, MOPED proposes a two-stage processing scheme to reduce the frequency and unit cost of collision check. It also fully leverages the spatial information and unique property of planning process to enable low-cost approximated neighbor search. At the hardware level, MOPED proposes a correctness-ensured speculative processing scheme to overcome the serialization problem. It also develop a multi-level caching strategy to reduce data movement and resolve resource conflict. We demonstrate the effectiveness of MOPED via implementing a design example with CMOS 28nm technology via synthesizing. Compared with the baseline motion planning processors, MOPED brings significant improvement on throughput, energy efficiency and area efficiency.