Wireless-power mobile edge computing, SWIPT-MEC, priority-aware WPT scheduling and swarm resource allocation already solve important parts of the energy-management problem. The novelty of WPT-JCCO is not any one of those elements; it is a single swarm-supervisory feasible set that couples decisions which the three adjacent method classes normally separate. Each epoch-level action jointly selects the robot to charge and one of three physically distinct WPT modalities: far-field radio-frequency, resonant near-field and directional lightwave transfer, together with the SWIPT split, local/edge task placement, CPU frequency, bandwidth and transmit power. Relative to SWIPT-MEC, the formulation adds discrete recipient–modality selection with pose, alignment, blockage and dwell-dependent feasibility. Relative to conventional WPT scheduling, charging is not a separate priority or routing stage but is solved jointly with computation and radio allocation. Relative to swarm resource-allocation methods, energy replenishment is endogenous and an individual minimum-battery constraint protects the weakest robot. A fourth coupling makes the centrally generated resource vector admissible only when the complete sense–compute–actuate age fits the one-second supervisory epoch; otherwise a previously feasible or local-safe action is applied. Nonlinear harvesting, partial offloading, priority scoring and augmented-Lagrangian primal–dual updates are treated as established techniques. This paper derives the continuous block updates, keeps the WPT variables binary through candidate screening, and declares convergence only when stationarity, feasibility, merit-change and binary-hold tests are jointly satisfied. Normalised primal steps are safeguarded by backtracking, dual and penalty updates are bounded, and a local tracking bound plus divergence monitor delimit real-time operation without claiming global mixed-integer optimality or closed-loop motion stability. Numerical evaluation over a 20-robot swarm and 30 Monte Carlo runs shows that WPT-JCCO reduces net energy depletion by 23.8% relative to communication–computation optimisation with static WPT and by 49.7% relative to local-only execution, while increasing task success from 93.5% to 97.3%. A released common-trace comparison shows normalised-cost reductions of 11.1%, 11.3% and 5.8% relative to two-stage WPT+CCO, fixed-SWIPT dynamic offloading and an offline Q-learning scheduler. Convergence and one-factor-at-a-time sensitivity studies further examine swarm size, task load, WPT budget, bandwidth, edge capacity, mobility and channel margin. The headline values remain scoped to the nominal independent-task case; mode-specific RF, near-field and lightwave operating envelopes, robust pose/CSI, WPT-safety and task-DAG extensions are formulated but not presented as hardware-validated results.