Receding-Horizon Nonlinear Optimal Control With Safety Constraints Using Constrained Approximate Dynamic Programming
This work addresses control challenges for nonlinear systems with constraints, such as robotics, but is incremental as it builds on existing approximate dynamic programming and control barrier function techniques.
The paper tackled the problem of receding-horizon optimal control for nonlinear continuous-time systems with state constraints, resulting in a method that yields analytic closed-form optimal control functions suitable for real-time implementation, as demonstrated in simulations of a nonholonomic ground robot with performance comparisons to three other approaches.
We present a receding-horizon optimal control for nonlinear continuous-time systems subject to state constraints. The cost is a quadratic finite-horizon integral. The key enabling technique is a new constrained approximate dynamic programming (C-ADP) approach for finite-horizon nonlinear optimal control with constraints that are affine in the control. The C-ADP approach is intuitive because it uses a quadratic approximation of the cost-to-go function at each backward step. This method yields a sequence of analytic closed-form optimal control functions, which have identical structure and where parameters are obtained from 2 Riccati-like difference equations. This C-ADP method is well suited for real-time implementation. Thus, we use the C-ADP approach in combination with control barrier functions to obtain a continuous-time receding-horizon optimal control that is farsighted in the sense that it optimizes the integral cost subject to state constraints along the entire prediction horizon. Lastly, receding-horizon C-ADP control is demonstrated in simulation of a nonholonomic ground robot subject to velocity and no-collision constraints. We compare performance with 3 other approaches.