The fundamental problem of robot motion planning in a dynamic environment (RMPDE) is to find an optimal collision-free path from the start to the goal in a dynamic environment. Our literature survey of over 100 papers from the last four decades reveals that there are more than 30 models of RMPDE, and there is no benchmarking criterion to select one that is the best in a given situation. In this context, generating a regression-based model with 10 attributes is the first and foremost contribution of our research. Given a highly human-interactive environment like a cafeteria or a bus stand, the gross hidden Markov model has special importance for modeling a robot path. A variant of the growing hidden Markov model for a serving robot in a cafeteria is the second contribution of this paper. We simulated the behavior of GHMM in a cafeteria with static and dynamic obstacles (static obstacles were both convex and concave) and with three different arrangements of the tables and obstacles. Robots have been employed in mushroom harvesting. A novel proposition discussed in this paper is probabilistic road map planning for a robot that finds an optimum path for reaching the ripened mushrooms in a randomly planted mushroom farm and a dexterous hand to pluck the selected mushrooms by employing inverse kinematics. Further, two biologically inspired meta-heuristic algorithms, ant colony optimization, and firefly has been studied for their application to latex collection. The simulation results with this environment show that the firefly algorithm outperforms ant colony optimization in the general case. Finally, we have proposed a few pointers for future research in this domain.ย The compilation and comparison of various approaches to robot motion planning in highly dynamic environments, and the simulation of a few models for some typical scenarios, have been the contributions of this paper.