Principles of typical motion planning algorithms are investigated and analyzed in this paper. These algorithms include traditional planning algorithms, classical machine learning algorithms, optimal value reinforcement learning, and policy gradient reinforcement learning. Traditional planning algorithms investigated include graph search algorithms, sampling-based algorithms, interpolating curve algorithms, and reaction-based algorithms. Classical machine learning algorithms include multiclass support vector machine, long short-term memory, Monte-Carlo tree search and convolutional neural network. Optimal value reinforcement learning algorithms include Q learning, deep Q-learning network, double deep Q-learning network, dueling deep Q-learning network. Policy gradient algorithms include policy gradient method, actor-critic algorithm, asynchronous advantage actor-critic, advantage actor-critic, deterministic policy gradient, deep deterministic policy gradient, trust region policy optimization and proximal policy optimization. New general criteria are also introduced to evaluate the performance and application of motion planning algorithms by analytical comparisons. The convergence speed and stability of optimal value and policy gradient algorithms are specially analyzed. Future directions are presented analytically according to principles and analytical comparisons of motion planning algorithms. This paper provides researchers with a clear and comprehensive understanding about advantages, disadvantages, relationships, and future of motion planning algorithms in robots, and paves ways for better motion planning algorithms in academia, engineering, and manufacturing.