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For the cascaded planning and control modules implemented for robot navigation, the frequency gap between the planner and controller has received limited attention. In this study, we introduce a novel B-spline parameterized optimization-based planner (BSPOP) designed to address the frequency gap challenge with limited onboard computational power in robots. The proposed planner generates continuous-time control inputs for low-level controllers running at arbitrary frequencies to track. Furthermore, when considering the convex control action sets, BSPOP uses the convex hull property to automatically constrain the continuous-time control inputs within the convex set. Consequently, compared with the discrete-time optimization-based planners, BSPOP reduces the number of decision variables and inequality constraints, which improves computational efficiency as a byproduct. Simulation results demonstrate that our approach can achieve a comparable planning performance to the high-frequency baseline optimization-based planners while demanding less computational power. Both simulation and experiment results show that the proposed method performs better in planning compared with baseline planners in the same frequency. 

This work presents an optimal sampling-based method to solve the real-time motion planning problem in static and dynamic environments, exploiting the Rapid-exploring Random Trees (RRT) algorithm and the Model Predictive Path Integral (MPPI) algorithm. The RRT algorithm provides a nominal mean value of the random control distribution in the MPPI algorithm, resulting in satisfactory control performance in static and dynamic environments without a need for fine parameter tuning. We also discuss the importance of choosing the right mean of the MPPI algorithm, which balances exploration and optimality gap, given a fixed sample size. In particular, a sufficiently large mean is required to explore the state space enough, and a sufficiently small mean is required to guarantee that the samples reconstruct the optimal control. The proposed methodology automates the procedure of choosing the right mean by incorporating the RRT algorithm. The simulations demonstrate that the proposed algorithm can solve the motion planning problem for static or dynamic environments. 

We propose a reinforcement learning framework where an agent uses an internal nominal model for stochastic model predictive control (MPC) while compensating for a disturbance. Our work builds on the existing risk-aware optimal control with stochastic differential equations (SDEs) that aims to deal with such disturbance. However, the risk sensitivity and the noise strength of the nominal SDE in the riskaware optimal control are often heuristically chosen. In the proposed framework, the risk-taking policy determines the behavior of the MPC to be risk-seeking (exploration) or riskaverse (exploitation). Specifcally, we employ the risk-aware path integral control that can be implemented as a Monte-Carlo (MC) sampling with fast parallel simulations using a GPU. The MC sampling implementations of the MPC have been successful in robotic applications due to their real-time computation capability. The proposed framework that adapts the noise model and the risk sensitivity outperforms the standard model predictive path integ