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The existence of multiple irregular obstacles in the environment introduces nonconvex constraints into the optimization for motion planning, which makes the optimal control problem hard to handle. One efficient approach to address this issue is Successive Convex Approximation (SCA), where the nonconvex problem is convexified and solved successively. However, this approach still faces two main challenges: I) infeasibility, caused by linearisation about infeasible reference points; ii) high computational complexity incurred by multiple constraints, when solving the optimal control problem with a long planning horizon and multiple obstacles. To overcome these challanges, this paper proposes an energy efficient safetyaware control method for motion planning with low computing complexity and address these challenges. Specifically, a control barrier function-based linear quadratic regulator is formulated for the motion planning to guarantee safety and energy efficiency. Then, to avoid infeasibility, Backward Receding SCA (BRSCA) approach with a dynamic constraints-selection rule is proposed. Dynamic programming with primal-dual iteration is designed to decrease computational complexity. It is found that BRSCA is applicable to time-varying control limits. Numerical simulations and hardware experiments vevify the efficiency of BRSCA. Simulations demonstrates that BRSCA has a higher probability of finding feasible solutions, reduces the computation time by about 17.4% and the energy cost by about four times compared to other methods in the literature.