  We propose a nonlinear model predictive control (NMPC) framework based on a
direct optimal control method that ensures continuous-time constraint
satisfaction and accurate evaluation of the running cost, without compromising
computational efficiency. We leverage the recently proposed successive
convexification framework for trajectory optimization, where: (1) the path
constraints and running cost are equivalently reformulated by augmenting the
system dynamics, (2) multiple shooting is used for exact discretization, and
(3) a convergence-guaranteed sequential convex programming (SCP) algorithm, the
prox-linear method, is used to solve the discretized receding-horizon optimal
control problems. The resulting NMPC framework is computationally efficient,
owing to its support for warm-starting and premature termination of SCP, and
its reliance on first-order information only. We demonstrate the effectiveness
of the proposed NMPC framework by means of a numerical example with
reference-tracking and obstacle avoidance. The implementation is available at
https://github.com/UW-ACL/nmpc-ctcs
