The global aging issue is becoming severe increasingly， and the field of elderly care services is facing a challenge of manpower shortage， urgently requiring the introduction of robot technology with intelligent decision-making capabilities. To solve the autonomous path planning problem of assistive robots under a multi-task mechanism in nursing home scenarios， an improved Soft Actor-Critic （SAC） reinforcement learning decision-making algorithm was proposed. Firstly， an obstacle contour reconstruction method based on virtual circles was introduced， which reduced the complexity of environmental modeling and enhanced radar detection efficiency. Then， to tackle the difficulty of reinforcement learning algorithms in optimizing strategies from scratch when solving complex tasks in a continuous state space， Whale Optimization Algorithm （WOA） was integrated with SAC algorithm to obtain WOA-SAC algorithm. At the same time， by constructing an auxiliary supervision mechanism to provide directional guidance for the learning process， the decision-making capability was improved while the convergence was accelerated significantly. Finally， task planning was conducted on the basis of daily needs of the elderly， and model training was completed in environments composed of fixed tasks with static and dynamic obstacles as well as emergent random tasks. Simulation results demonstrate that compared to the traditional SAC algorithm， WOA-SAC algorithm reduces the average path length by 10.42%， increases the success rate by 6.66%， and decreases the average step size by 29.63%. It can be seen the significant enhancement of WOA-SAC algorithm in the learning efficiency and decision-making capability of SAC algorithm， addressing the autonomous path planning problems in multi-task mechanisms effectively.