## 1 Introduction  
As autonomous ground vehicles (AGVs) find increasing utility in both military and commercial applications, driving safety has become a critical issue that impedes their further development [1]. Typically, driving safety is deemed as being collision-free, which may be adequate for earlier applications such as small robots and low-speed vehicles [2; 3]. However, since recent research efforts have targeted large-size and high-speed AGVs, the handling stability-related concerns, such as excessive sideslip and rollover, become increasingly important. Inappropriate handling of these dynamics, particularly under a complex road topography, will lead to loss of control of the AGVs or even fatal accidents. Therefore, it is necessary to develop a control scheme that can systematically utilize the knowledge of vehicle dynamics and the road topography information to avoid collisions while ensuring the handling stability of high-speed AGVs. Recent work has shown that model predictive control (MPC) can be used to rigorously handle the vehicle dynamics and multiple safety constraints [4; 5]. Many MPC-based methods have demonstrated successful applications in the field of path following [6], obstacle avoidance [7], emergency maneuvering [8], lane change maneuvers [9], etc. Although these methods do provide good results in their own respective applications, they usually assume simple road topography, i.e., neglecting the road curvature and bank angle. Moreover, most of these applications do not take handling stability-related concerns into account. Instead, they rely on the built-in production systems, such as dynamic stability control (DSC) or electronic stability control (ESC), which enforce stabilization criteria regardless of an impending collision. Thus, while these applications may maintain the stabilization of AGVs, there is no guarantee that the trajectories modified by these built-in systems would be collision-free. Rather than relying on production systems, alternative approaches have explicitly incorporated stabilization criteria in the MPC formulations for the purpose of vehicle stabilization [10]. Among them, envelope control has been widely applied in the automotive field, and a number of stability envelopes have been developed. Earlier analyses of vehicle handling are presented by defining a stable region with respect to the vehicle sideslip and sideslip rate in the phase plane. The open region between the saddle points of this phase plane is used as a safe envelope for vehicle stability [11; 12]. Focusing on limiting the saturation of the tires to prevent loss of control, a vehicle stabilization envelope is proposed to limit the peak forces of the front and rear wheels [13]. Building upon these work, [PERSON] and [PERSON] presented a stable handling envelope that combines the phase plane design approach and the explicit consideration of rear tire saturation [14]. This envelope bounds the yaw rate of the vehicle while limiting the rear tire forces below their peak to prevent rear tire saturation. Vehicle sideslip and yaw rate serve as the phase plane variables that capture this stability envelope. Moreover, [PERSON] also presented a closed envelope in the sideslip and yaw rate phase plane using isolines [15]. This envelope can incorporate more naturally stable regions of the phase plane in vehicles with strong under-steering characteristics. Recent applications of vehicle stability control enforce constraints only on the maximum allowable rear tire force [16; 17]. By virtue of the stability envelope, a continuously-resolved optimization seeking to minimize trajectory tracking errors while satisfying the stabilization criteria is realized. However, this still suffers from the underlying challenge that such constraints may be overly restrictive or conflict with each other, which may lead to tracking errors that result in collisions.