Privacy-preserving online multi-task assignment is a crucial aspect of spatial crowdsensing on untrusted platforms, where multiple real-time tasks are allocated to appropriate workers in a privacy-preserving manner. While existing schemes ensure the privacy of tasks and users, they seldom focus on minimizing the total moving distances for crowdsensing workers when assigning multiple tasks in real time, which adversely impacts the efficiency of online multi-task assignments. To address this issue, we propose POTA, the first privacy-preserving online multi-task assignment scheme with path planning that minimizes the total moving distances for crowdsensing workers without additional noise. POTA cryptographically implements the extended minimum-cost flow model, which models the encrypted data of workers and tasks in a graph and later produces optimized routing. With such a secure path-planning component, POTA reduces the total moving distances by$25.19\%-52.78\%$in the tested dataset compared with the state-of-the-art schemes with obfuscated path planning. Security analysis proves that POTA guarantees the confidentiality of sensitive data, a stronger security property than introducing obfuscation to sensitive data. Experimental evaluations on real-world datasets demonstrate the feasibility of POTA in terms of running time and its ability to achieve minimized total moving distances.